Processing apparatus, processing method, and program

Abstract

To select an explanatory variable contributing to an objective variable with high accuracy.SOLUTION: A processing device 100 calculates an appearance frequency 320 of a candidate of an explanatory variable in a plurality of first explanatory variable candidate groups 310a to 310d for each of the candidates of the explanatory variable, generates a plurality of second explanatory variable candidate groups 340a to 340c on the basis of the appearance frequency 320, generates a plurality of first learning model candidates 350a to 350c for each of the plurality of second explanatory variable candidate groups, calculates first evaluation indices 360a to 360c for evaluating an estimation accuracy of the first learning model candidate for each of the plurality of first learning model candidates, and calculates explanatory variable number-first evaluation index relation information 370 indicating a relation between the number of the candidates of the explanatory variable included in the first learning model candidate and a first evaluation index for evaluating the estimation accuracy of the first learning model candidate as information used for selecting the explanatory variable in the first learning model.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a processing apparatus, a processing method, and a program. [Background technology]

[0002] In various fields, learning models that show the relationship between explanatory variables (independent variables) and the target variable (dependent variable) that explains those explanatory variables are used to calculate the value of the target variable.

[0003] Patent Document 1 discloses the identification of microbial groups involved in changes in the amount of a specific substance as explanatory variables. In the technique described in Patent Document 1, a dataset is created from measurement results of a sample containing a specific substance and microorganisms, consisting of the rate of change in the amount of the specific substance and the content of the microbial group into which the microorganisms are classified. Multiple sets of samples are created from the created dataset by resampling. A first selection step is performed to select microbial groups for each of the multiple sets of samples by performing a penalty-based regression analysis, which can reduce the regression coefficient to 0 (zero), with the content of the microbial group as the explanatory variable and the rate of change in the amount of the specific substance as the dependent variable. A second selection step is performed to further select microbial groups based on the calculated confidence level, calculated from the selection frequency of the microbial groups selected in the first selection step in the samples created by resampling. If the total number of microbial groups is 1000 and a certain microbial group is selected 500 times in the first selection step, the confidence level is 0.5 (=500 / 1000). In the second selection process, microbial groups with a confidence level equal to or higher than a predetermined threshold (e.g., 0.6) are selected. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2020-36579 [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] However, the technology described in Patent Document 1 assumes that explanatory variables selected more frequently contribute more to the dependent variable. However, the selection frequency of explanatory variables and their contribution to the dependent variable are not necessarily directly proportional. Therefore, there is a risk that it may not be possible to select explanatory variables that contribute to the dependent variable with high accuracy.

[0006] This invention has been made in view of the above-mentioned problems, and aims to select explanatory variables that contribute to the objective variable with high accuracy. [Means for solving the problem]

[0007] The present invention relates to a processing apparatus that performs the process of selecting explanatory variables in a first learning model that shows the relationship between one or more explanatory variables and a target variable explained by the explanatory variables, and comprises: a first explanatory variable candidate group acquisition means for acquiring a plurality of first explanatory variable candidate groups, each containing one or more explanatory variable candidates; an occurrence frequency calculation means for calculating the occurrence frequency of each explanatory variable candidate in the plurality of first explanatory variable candidate groups for each of the explanatory variable candidates; a second explanatory variable candidate group creation means for creating a plurality of second explanatory variable candidate groups, each containing one or more explanatory variable candidates based on the occurrence frequency; and the second explanatory variable candidate group includes The system includes: a first learning model candidate creation means that creates a plurality of first learning model candidates showing the relationship between the candidate explanatory variables and the target variable for each of the plurality of second explanatory variable candidate groups; a first evaluation index calculation means that calculates a first evaluation index for evaluating the estimation accuracy of the first learning model candidates for each of the plurality of first learning model candidates; and a first relationship calculation means that calculates explanatory variable number-first evaluation index relationship information showing the relationship between the number of explanatory variable candidates included in the first learning model candidates and the first evaluation index for evaluating the estimation accuracy of the first learning model candidates, wherein the explanatory variable number-first evaluation index relationship information is used for selecting the explanatory variables in the first learning model.

[0008] The present invention is a processing method for selecting explanatory variables in a first learning model that shows the relationship between one or more explanatory variables and a target variable explained by the explanatory variables, comprising: a first explanatory variable candidate group acquisition step of acquiring a plurality of first explanatory variable candidate groups, each containing one or more explanatory variable candidates; an occurrence frequency calculation step of calculating the occurrence frequency of each explanatory variable candidate in the plurality of first explanatory variable candidate groups for each of the explanatory variable candidates; a second explanatory variable candidate group creation step of creating a plurality of second explanatory variable candidate groups, each containing one or more explanatory variable candidates based on the occurrence frequencies; and a second explanatory variable candidate group containing The method includes a first learning model candidate creation step, which is performed for each of the multiple second explanatory variable candidate groups to create a plurality of first learning model candidates that show the relationship between the explanatory variable candidate and the target variable; a first evaluation index calculation step, which is performed for each of the plurality of first learning model candidates to calculate a first evaluation index for evaluating the estimation accuracy of the first learning model candidate; and a first relationship calculation step, which is performed to calculate explanatory variable number-first evaluation index relationship information that shows the relationship between the number of explanatory variable candidate included in the first learning model candidate and the first evaluation index for evaluating the estimation accuracy of the first learning model candidate, wherein the explanatory variable number-first evaluation index relationship information is used for selecting the explanatory variables in the first learning model.

[0009] The program of the present invention causes a computer to function as one of the means of the processing apparatus. [Effects of the Invention]

[0010] According to the present invention, explanatory variables that contribute to the objective variable can be selected with high accuracy. [Brief explanation of the drawing]

[0011] [Figure 1] This figure shows a first example of the functional configuration of the processing unit. [Figure 2] This is a flowchart illustrating the first example of the processing method. [Figure 3]This diagram illustrates one example of how to select explanatory variables. [Figure 4] This figure shows an example of the configuration of a biological processing device. [Figure 5] This figure shows an example of the rate of nitrite production. [Figure 6] This figure shows an example of the removal rate of thiocyanate. [Figure 7] This diagram illustrates one example of a method for creating a Bootstrap sample. [Figure 8] This figure illustrates an example of a method for obtaining a candidate group of first explanatory variables. [Figure 9] This diagram illustrates one example of a method for calculating frequency of occurrence. [Figure 10] This figure shows the first example of the relationship between a group of microorganisms (a candidate explanatory variable) and the frequency of occurrence of that group. [Figure 11] This figure shows the first example of the relationship information between the number of explanatory variables and the first evaluation index. [Figure 12] This figure illustrates an example of a threshold value for the first evaluation index in the relationship information between the number of explanatory variables and the first evaluation index. [Figure 13] This figure shows candidate explanatory variables (microbial communities) included in the explanatory variable group, the number of such candidate explanatory variables, and an example of a first evaluation metric for the candidate first learning model that has such candidate explanatory variables. [Figure 14] This figure shows an example of a dependent variable (categorical variable). [Figure 15] This figure shows a second example of the relationship between a group of microorganisms (a candidate explanatory variable) and the frequency of occurrence of that group. [Figure 16] This figure shows a second example of the relationship between the number of explanatory variables and the first evaluation indicator. [Figure 17] This diagram conceptually illustrates one example of how to create data for noise explanatory variables. [Figure 18A] This figure conceptually illustrates an example of a method for selecting a group of candidate first explanatory variables when using a combined matrix that includes the noise explanatory variable matrix calculated by the first noise explanatory variable generation method. [Figure 18B]This figure conceptually illustrates an example of a method for selecting a group of candidate first explanatory variables when using a combined matrix that includes the noise explanatory variable matrix calculated by the second noise explanatory variable generation method. [Figure 19A] This figure shows a second example of the functional configuration of the processing unit. [Figure 19B] This figure shows an example of a more detailed functional configuration of the first explanatory variable selection unit. [Figure 20] This is a flowchart illustrating a second example of the processing method. [Figure 21] This figure shows the third example of the relationship between the number of explanatory variables and the first evaluation indicator. [Figure 22] This figure illustrates examples of variability evaluation indices and gradient evaluation indices. [Figure 23] This figure shows an example of the relationship between the number of explanatory variables and the second evaluation indicator. [Figure 24] This diagram conceptually illustrates an example of a method for selecting explanatory variables in the first learning model. [Modes for carrying out the invention]

[0012] One embodiment of the present invention will be described below with reference to the drawings. Furthermore, the term "same" in terms of length, position, size, spacing, etc., includes not only cases where the items are exactly the same, but also cases where they differ to the extent that they do not deviate from the spirit of the invention (for example, differences within the tolerance range defined at the time of design).

[0013] (First Embodiment) First, the first embodiment will be described. Figure 1 shows an example of the functional configuration of the processing unit 100 of this embodiment. The processing unit 100 has, for example, one or more hardware processors such as a CPU (Central Processing Unit) and one or more memory such as RAM (Random Access Memory) and ROM (Read Only Memory) as hardware, and performs various calculations by executing one or more programs stored in memory using one or more hardware processors. Furthermore, the processing unit 100 has input devices and output devices as hardware.

[0014] The processing unit 100 of this embodiment performs a process that includes selecting explanatory variables in a first learning model that shows the relationship between one or more explanatory variables and the target variable explained by those explanatory variables. The first learning model may be a linear regression equation, a nonlinear regression equation, another machine learning model (such as a neural network), or AI (artificial intelligence). The first learning model may also be a surrogate model or a model that estimates events other than physical phenomena. Furthermore, the number of explanatory variables that the processing unit 100 (finally) selects may be one or multiple.

[0015] The explanatory and dependent variables are not limited. For example, the explanatory variables may include factors used in the treatment process, and the dependent variable may include factors obtained in the treatment process by performing the treatment using the factors used in the treatment process. The treatment process is, for example, a biological treatment process of water to be treated. In this case, the explanatory variables are, for example, factors relating to the amount of microbial communities present in and used in the treatment process. The dependent variable is, for example, a factor relating to the rate of change in the amount of a specific substance before and after treatment (change in the amount of a specific substance). The water to be treated is treated using microorganisms present in the water, and the amount of a specific substance in the water changes (decreases or increases). That is, the rate of change in the amount of a specific substance before and after treatment is influenced by the microbial communities present in the treatment process. Here, the microbial community refers to a group of microorganisms classified based on a certain trait or genotype, and includes, but is not limited to, genera, species, and subspecies. The genotype may also include simply the base sequence of the microbial genome. The number of microbial communities can be, for example, between 100 and 1 million species, or between 1,000 and 10,000 species.

[0016] Furthermore, the treatment process is not limited to a biological treatment process for the water to be treated. For example, the treatment process may be a product manufacturing process. For example, the treatment process may be a hot-rolled coil manufacturing process. In this case, the explanatory variables are, for example, physical quantities used as manipulated quantities for the rolled material (e.g., reduction amount of the finishing rolling mill, flow rate of cooling water in the cooling spray, power consumption of the heating device, conveying speed of the rolled material). The dependent variable is, for example, the quality of the hot-rolled coil (e.g., tensile strength). That is, the quality of the hot-rolled coil is affected by the physical quantities used as manipulated quantities for the rolled material. The explanatory variables may be state factors that determine the characteristics of the objective variable during processing (uncontrollable factors whose attributes (quantity, etc.) cannot be controlled during the processing process), or they may be controllable factors whose attributes can be controlled during the processing process.

[0017] Furthermore, explanatory variables are not limited to factors used in the processing steps. For example, explanatory variables may be factors relating to the number of various genes in a person. In this case, the dependent variable may be, for example, a factor relating to a test item for a specific human disease. That is, the values ​​of test items for a specific disease are influenced by a person's genes. Furthermore, the explanatory variables and the dependent variable are not limited to those mentioned above, as long as the dependent variable is explained by the explanatory variables (i.e., there is a causal relationship between the explanatory variables and the dependent variable).

[0018] In Figure 1, this embodiment illustrates a case where the processing unit 100 includes a first explanatory variable candidate group acquisition unit 110, an occurrence frequency calculation unit 120, a second explanatory variable candidate group creation unit 130, a first learning model candidate creation unit 140, a first evaluation index calculation unit 150, a first relationship calculation unit 160, a first explanatory variable selection unit 170, and an output unit 180. Figure 2 is a flowchart illustrating an example of a processing method performed using the processing unit 100 of this embodiment. Figure 3 is a diagram illustrating an example of a method for selecting explanatory variables. Below, the processing method of this embodiment will be explained with reference to the flowchart in Figure 2 and Figure 3, along with an example of the functions of the processing unit 100 shown in Figure 1.

[0019] [First explanatory variable candidate group acquisition process (S201), first explanatory variable candidate group acquisition unit 110] The first explanatory variable candidate group acquisition unit 110 acquires multiple first explanatory variable candidate groups, each containing either a candidate for one explanatory variable or a candidate for multiple explanatory variables. The first explanatory variable candidate group contains one or more candidates as explanatory variables in the first learning model. As mentioned above, the first learning model may be a linear regression equation, a nonlinear regression equation, another machine learning model (such as a neural network), or AI (artificial intelligence). However, in this embodiment, for the sake of simplicity, we will illustrate the case where the first learning model is a linear regression equation as shown in equation (1) below.

[0020]

number

[0021] (1) In the formula, y i is the target variable, and x ij is the explanatory variable, and β j is the regression coefficient with respect to the explanatory variable x ij , and p is the number of explanatory variables. When p = 1, the formula (1) is a simple regression formula; when p ≥ 2, the formula (1) is a multiple regression formula. β 0i is the intercept (constant term). i is a variable that identifies the first learning model. When the number of the first learning models (the number of regression formulas) is 1, i is unnecessary. In the following, for simplicity of explanation, the notation of the variable i is omitted as necessary. In this case, the explanatory variable is x j , the target variable is y, and the intercept β 0i is represented by β0 respectively.

[0022] The number of candidates for explanatory variables included in a plurality of first explanatory variable candidate groups may be 1 or more. Also, the same candidate for an explanatory variable may be included in two or more first explanatory variable candidate groups. Here, in this embodiment, an example is illustrated in which the candidates for explanatory variables included in the first explanatory variable candidate group are selected from among a plurality of predetermined candidates for explanatory variables. Assuming that the number of a plurality of predetermined candidates for explanatory variables is p, the candidates for explanatory variables x1, x2, ··· x p included in the first explanatory variable candidate group are selected from among them. Note that, for example, selecting an explanatory variable may be represented by setting the regression coefficient with respect to the explanatory variable to 0, and not selecting an explanatory variable may be represented by setting the regression coefficient with respect to the explanatory variable to a non-zero value.

[0023] Also, in this embodiment, the first explanatory variable candidate group acquisition unit 110 uses the data of the candidates for explanatory variables x1, x2, ··· x p in the first learning model (a linear regression formula in this embodiment), and the candidates for explanatory variables x1, x2, ··· x pAn example is given of acquiring multiple sets of first training data, each set consisting of a set of data containing the correct answer data for the target variable y explained by and , as a dataset. The first explanatory variable candidate group acquisition unit 110 may acquire the multiple sets of first training data (datasets) based on input operations of the first training data to the user interface of the processing unit 100, may acquire the multiple sets of first training data by receiving them from an external device, or may acquire them by reading the multiple sets of first training data stored on a storage medium.

[0024] Figure 3 illustrates the following candidate groups of first explanatory variables: group 310a consisting of explanatory variable x1, group 310b consisting of explanatory variables x1 and x5, group 310c consisting of explanatory variables x2, x3 and x5, and group 310d consisting of explanatory variables x2, x4, x5 and x7.

[0025] Candidate explanatory variables included in the multiple candidate groups of first explanatory variables 310a to 310d may be selected, for example, using the method described in Patent Document 1. In this case, for example, the first explanatory variable candidate group acquisition unit 110 creates multiple samples by resampling the aforementioned dataset consisting of the values ​​of the explanatory variables and the target variable. The resampling method may be, for example, the Bootstrap method or the Jackknife method.

[0026] The first explanatory variable candidate group acquisition unit 110 then performs a penalty-based regression analysis on each created sample, which reduces the regression coefficient to zero, and selects explanatory variables for each sample whose regression coefficient does not become zero, thereby selecting candidate explanatory variables to be included in each first explanatory variable candidate group 310a to 310d. In this case, one first explanatory variable candidate group from the first explanatory variable candidate groups 310a to 310d is obtained from one sample. The penalty-based regression analysis method that reduces the regression coefficient to zero is a method that performs L1 regularization (regularization of the L1 norm), such as Lasso (Least Absolute Shrinkage and Selection Operator), Elastic net, and SCAD (Smoothly Clipped Absolute Deviation). Furthermore, the method for selecting candidate explanatory variables to be included in multiple first explanatory variable candidate groups is not limited to the method described in Patent Document 1. For example, the first explanatory variable candidate group acquisition unit 110 selects candidate explanatory variables x1, x2, ...x p You may randomly select candidate explanatory variables to include in the first group of candidate explanatory variables from among them.

[0027] Furthermore, the first explanatory variable candidate group acquisition unit 110 may acquire information indicating the first explanatory variable candidate group 310a to 310d without performing the calculations described above, based on an input operation of such information to the user interface of the processing unit 100, or by receiving such information from an external device, or by reading such information stored on a storage medium.

[0028] [Frequency calculation process (S202), frequency calculation unit 120] The frequency calculation unit 120 calculates the frequency of occurrence of candidate explanatory variables in a group of candidate first explanatory variables 310a to 310d, using candidate explanatory variables x1, x2, ... x p This is done for each of them. For example, if there are B candidates for multiple first explanatory variables 310a to 310d, and a candidate for a certain explanatory variable x r If (r=1, 2, ...p) is included in the G candidate group of first explanatory variables, then the candidate x of that explanatory variable rThe frequency of occurrence is G / B. Note that the frequency of occurrence may also be expressed as a percentage. More specifically, if in Figure 3 only the four candidate groups of first explanatory variables 310a to 310d are acquired by the first explanatory variable candidate group acquisition unit 110, then for example, the frequency of occurrence of candidate explanatory variable x1 is 0.5 (=2 / 4), and the frequency of occurrence of candidate explanatory variable x5 is 0.75 (=3 / 4).

[0029] As described above, the candidate explanatory variables are x1, x2, ...x as shown in Figure 3. p The frequency of occurrence for each of these is calculated (one by one), with a value of 320.

[0030] [Second explanatory variable candidate group creation process (S203), second explanatory variable candidate group creation unit 130] The second explanatory variable candidate group generation unit 130 generates candidate explanatory variables x1, x2, ...x p Based on the frequency of occurrence 320 for each of the above, multiple groups of candidate second explanatory variables are created, each containing either one candidate explanatory variable or multiple candidate explanatory variables. Candidate explanatory variables with relatively high frequencies of occurrence are more likely to be explanatory variables that explain the target variable y with greater accuracy than candidates for explanatory variables with relatively low frequencies of occurrence. Therefore, in this embodiment, we illustrate a case in which the second explanatory variable candidate group creation unit 130 selects candidate explanatory variables to be included in the second explanatory variable candidate group such that there may be more candidates for explanatory variables with relatively high frequencies of occurrence 320 than candidates for explanatory variables with relatively low frequencies of occurrence 320.

[0031] In the example shown in Figure 3, for example, the candidate explanatory variables to be included in the second candidate explanatory variable group may be selected such that candidate explanatory variable x5 is included in a larger number of second candidate explanatory variable groups than candidate explanatory variable x1. Alternatively, for example, the candidate explanatory variables to be included in the second candidate explanatory variable group may be selected such that candidate explanatory variable x5 is included in a larger number of second candidate explanatory variable groups than candidate explanatory variable x7. Alternatively, for example, the candidate explanatory variables to be included in the second candidate explanatory variable group may be selected such that candidate explanatory variable x1 is included in a larger number of second candidate explanatory variable groups than candidate explanatory variable x7.

[0032] Furthermore, the second explanatory variable candidate group creation unit 130 may select explanatory variable candidates to include in the second explanatory variable candidate group such that there are more explanatory variable candidates with a relatively high frequency of occurrence 320 than explanatory variable candidates with a relatively low frequency of occurrence 320. In other words, the explanatory variable candidates to include in the second explanatory variable candidate group may be selected such that there are not more explanatory variable candidates with a relatively low frequency of occurrence 320 than explanatory variable candidates with a relatively high frequency of occurrence 320. In this way, the more likely an explanatory variable is to explain the target variable y accurately, the more of it can be included in the second explanatory variable candidate group. Therefore, in this embodiment, we will illustrate the case where the second explanatory variable candidate group creation unit 130 selects m explanatory variable candidates in order from the highest frequency of occurrence and creates a second explanatory variable candidate group containing the selected m explanatory variable candidates, for each case where M is an integer of 2 or more and m is changed from 1 to M.

[0033] When performing such processing, the second explanatory variable candidate group creation unit 130 generates candidate explanatory variables x1, x2, ...x p These can also be sorted in descending order of frequency. In this case, as shown in Figure 3, we obtain candidate explanatory variables 330 sorted in descending order of frequency. In the following explanation, the candidate explanatory variables sorted in descending order of frequency will be referred to as the sorted candidate explanatory variables, as needed.

[0034] In the example shown in Figure 3, when m=1, the second explanatory variable candidate group creation unit 130 creates a second explanatory variable candidate group that includes only the explanatory variable candidate x5, which is the first explanatory variable candidate in the sorted explanatory variable candidate group 330. When m=2, the second explanatory variable candidate group creation unit 130 creates a second explanatory variable candidate group that includes the explanatory variable candidates x1 and x5, which are the first and second explanatory variable candidates in the sorted explanatory variable candidate group 330. Similarly, when m=3, the second explanatory variable candidate group creation unit 130 creates a second explanatory variable candidate group that includes the explanatory variable candidates x1, x2, ...x. p The number of (=p) can be the same, and the candidate explanatory variables x1, x2, ... x p It is also acceptable for M to be a number less than the number of (=p). For example, M may be the smallest integer that satisfies M / p ≥ Th1 (where the threshold Th1 is a predetermined positive number less than 1).

[0035] In Figure 3, the second explanatory variable candidate group 340 shows the second explanatory variable candidate groups 340a to 340c created as described above. Figure 3 also shows the names of the explanatory variables included in each of the second explanatory variable candidate groups 340a to 340c, namely "x5", "x1,x5", and "x1,x5,x7", and their numbers, namely "1", "2", and "3".

[0036] It should be noted that the second explanatory variable candidate group creation unit 130 does not necessarily have to create the second explanatory variable candidate group in the manner described above. For example, the candidate explanatory variable with the highest frequency of occurrence 320 (x5 in the example shown in Figure 3) may be included in more second explanatory variable candidate groups than the other explanatory variable candidates, and the number of explanatory variable candidates with the second and third highest frequencies of occurrence 320 (x1, x7 in the example shown in Figure 3) included in the second explanatory variable candidate group may be the same.

[0037] [First learning model candidate creation process (S204), first learning model candidate creation unit 140] The first learning model candidate creation unit 140 creates multiple first learning model candidates for each of the multiple second explanatory variable candidate groups 340a to 340c, each of which shows the relationship between the explanatory variable candidates included in the second explanatory variable candidate group and the target variable. As mentioned above, this embodiment exemplifies the case where the first learning model is a linear regression equation. Therefore, this embodiment exemplifies the case where the candidate first learning model is also a linear regression equation. In this case, the first learning model candidate creation unit 140 may create the first learning model candidate by performing supervised learning using a known method such as the least squares method. In this case, the first learning model candidate creation unit 140 may perform supervised learning using the aforementioned dataset or multiple samples obtained by resampling the dataset. In this embodiment, since the aforementioned dataset (first learning data) or multiple samples obtained by resampling the dataset are obtained by the first explanatory variable candidate group acquisition unit 110, it is preferable to create the first learning model candidate by performing supervised learning. However, for example, the first learning model candidate creation unit 140 may create the first learning model candidate by unsupervised learning.

[0038] In Figure 3, candidate 350a of the first learning model shows the relationship between candidate explanatory variables x5 included in the second explanatory variable candidate group 340a and the target variable y1 (y1 = β5x5 + β 01 ) and candidate 350b of the first learning model (y2=β1x1+β5x5+β) which shows the relationship between candidate explanatory variables x1 and x5 included in the second explanatory variable candidate group 340b and the target variable y2. 02 ) and candidate 350c of the first learning model (y3=β1x1+β5x5+β7x7+β) which shows the relationship between candidate explanatory variables x1, x5, x7 included in the second explanatory variable candidate group 340b and the target variable y3. 03 ) and this shows that y1, y2, y3, β 01 , β 02 , β 03 The subscripts 1, 2, and 3 indicate the first, second, and third candidate first learning models, respectively.

[0039] [First evaluation index calculation process (S205), first evaluation index calculation unit 150] The first evaluation index calculation unit 150 calculates a first evaluation index for each of the multiple candidates for the first learning model 350a to 350c to evaluate the estimation accuracy of the candidate first learning model. The first evaluation index is not limited and may be, for example, the coefficient of determination, the adjusted coefficient of determination, the root mean squared error (RMSE), the Akaike Information Criterion (AIC), or the multiple correlation coefficient. The estimation accuracy is evaluated using, for example, the cross-validation method.

[0040] In Figure 3, although specific numerical values ​​are omitted, the first evaluation metrics for candidate first learning models 350a, 350b, and 350c are 360a, 360b, and 360c, respectively. The coefficient of determination R is used as the first evaluation metric. 2 When using this, a larger value for the first evaluation metric indicates higher estimation accuracy for candidate models 350a to 350c of the first learning model. However, the first evaluation metric is not limited to those values ​​that indicate higher estimation accuracy for candidate models 350a to 350c of the first learning model. For example, the coefficient of determination R can be used as the first evaluation metric. 2 Alternatively, the value obtained by multiplying by (-1) may be used as the first evaluation metric. In this case, the first evaluation metric will show a smaller value (a negative value with a large absolute value) as the estimation accuracy of candidate 350a to 350c of the first learning model increases.

[0041] [First relationship calculation process (S206), First relationship calculation unit 160] The first relationship calculation unit 160 calculates the relationship information between the number of explanatory variables and the first evaluation index. This relationship information shows the relationship between the number of candidate explanatory variables included in one candidate first learning model 350a to 350c and the first evaluation index used to evaluate the estimation accuracy of the candidate first learning model.

[0042] In Figure 3, the number of candidate explanatory variables included in candidate 350a of the first learning model is 1 (see the column for the number of candidate explanatory variables in candidate group 340a of the second explanatory variable). Therefore, the number of candidate explanatory variables included in candidate 350a of the first learning model (=1) and the value of the first evaluation metric 360a of candidate 350a of the first learning model are used to calculate the explanatory variable number-first evaluation metric relationship information. Similarly, the number of candidate explanatory variables included in candidate 350b of the first learning model (=2) and the value of the first evaluation metric 360b of candidate 350b of the first learning model are used to calculate the explanatory variable number-first evaluation metric relationship information. The number of candidate explanatory variables included in candidate 350c of the first learning model (=3) and the value of the first evaluation metric 360c of candidate 350c of the first learning model are used to calculate the explanatory variable number-first evaluation metric relationship information.

[0043] Figure 3 shows an example of the explanatory variable number-first evaluation metric relationship information 370. Point 371, which represents the explanatory variable number-first evaluation metric relationship information 370, is determined by the number of explanatory variable candidates included in candidate 350a of the first learning model (=1) and the value of the first evaluation metric 360a of candidate 350a of the first learning model. Similarly, point 372 is determined by the number of explanatory variable candidates included in candidate 350b of the first learning model (=2) and the value of the first evaluation metric 360b of candidate 350b of the first learning model. Point 373 is determined by the number of explanatory variable candidates included in candidate 350c of the first learning model (=3) and the value of the first evaluation metric 360c of candidate 350c of the first learning model.

[0044] The information relating to the number of explanatory variables and the first evaluation metric may be represented by a function that shows the relationship between the number of candidate explanatory variables included in candidate first learning models 350a to 350c and the first evaluation metric used to evaluate the estimation accuracy of the candidate first learning model. Alternatively, the information relating to the number of explanatory variables and the first evaluation metric may be represented by a table that stores the number of candidate explanatory variables included in candidate first learning models 350a to 350c and the first evaluation metric used to evaluate the estimation accuracy of the candidate first learning model in relation to each other.

[0045] [First explanatory variable selection process (S207), first explanatory variable selection unit 170] The first explanatory variable selection unit 170 selects the explanatory variables x1, x2, ..., x in the first learning model based on the explanatory variable number-first evaluation index relationship information. p Select this option. Note that if p=1, the only explanatory variable in the first learning model will be x1. Also, as mentioned above, the regression coefficient β for the selected explanatory variable. j Set a value other than 0 for the regression coefficient β for the explanatory variable that is not selected. j By setting it to 0, the regression coefficient β will have a value other than 0. j You may also indicate that you have selected explanatory variables for [the given condition].

[0046] In this embodiment, an example is given in which the first explanatory variable selection unit 170 selects as explanatory variables in the first learning model a candidate that is included in the first learning model candidate corresponding to the first evaluation index that satisfies predetermined conditions, in the relationship shown by the number of explanatory variables - first evaluation index relationship information 370. Here, the candidate explanatory variables included in the candidate first learning model corresponding to the first evaluation metric are the candidate explanatory variables included in the candidate first learning model from which the first evaluation metric is calculated. For example, in Figure 3, the first evaluation metric determined at point 373 is the first evaluation metric 360c, the candidate first learning model from which the first evaluation metric 360c is calculated is the candidate first learning model 350c, and the candidate first evaluation metric included in the candidate first learning model 350c are the candidate first evaluation metric x1, x5, and x7. Therefore, the candidate first learning model corresponding to the first evaluation metric determined at point 373 is the candidate first learning model 350c, and the candidate explanatory variables included in the candidate first learning model are x1, x5, and x7.

[0047] Furthermore, the predetermined conditions may also be expressed using, for example, the peak value of the first evaluation index in the relationship shown by the number of explanatory variables - first evaluation index relationship information 370. When using a first evaluation index that shows a larger value the higher the estimation accuracy of the candidate first learning model 350a to 350c, for example, the candidate explanatory variable included in the candidate first learning model that corresponds to the first evaluation index showing a maximum value in the relationship shown by the number of explanatory variables - first evaluation index relationship information 370 may be selected as an explanatory variable in the first learning model. In this case, in Figure 3, the first explanatory variable selection unit 170 selects the candidate explanatory variable included in the candidate first learning model that corresponds to the first evaluation index at points 373 to 375 as an explanatory variable in the first learning model. Thus, the first explanatory variable selection unit 170 may select candidate explanatory variables included in multiple candidate first learning models as explanatory variables in the first learning model. Furthermore, when using a first evaluation metric that shows smaller values ​​as the estimation accuracy of candidate models 350a to 350c of the first learning model increases, local minimums may be used instead of the aforementioned local maximums. In the following explanation, the local maximum when using a first evaluation metric that shows larger values ​​as the estimation accuracy of candidate models 350a to 350c of the first learning model increases, and the local minimum when using a first evaluation metric that shows smaller values ​​as the estimation accuracy of candidate models 350a to 350c of the first learning model increases, will be referred to as local peaks as needed.

[0048] Furthermore, from the perspective of suppressing the selection of explanatory variables from overfitted first learning model candidates, the first explanatory variable selection unit 170 may select as explanatory variables in the first learning model the candidate with the smallest number of explanatory variable candidates among the first learning model candidates corresponding to the first evaluation metric showing a local peak. In Figure 3, among the first learning model candidates corresponding to the first evaluation metric at points 373 to 375, the first learning model candidate with the smallest number of explanatory variable candidates is the first learning model candidate 350c corresponding to the first evaluation metric at point 373. Therefore, the first explanatory variable selection unit 170 selects the explanatory variable candidates x1, x5, and x7 included in the first learning model candidate 350c as explanatory variables. In this way, the first explanatory variable selection unit 170 may select as explanatory variables in the first learning model any explanatory variable candidate included in one first learning model candidate.

[0049] Furthermore, when selecting a candidate for the first learning model in which the absolute value of the first evaluation index is larger, the first explanatory variable selection unit 170 may, for example, select as explanatory variables in the first learning model a candidate for the first learning model in which the absolute value of the first evaluation index corresponding to the first evaluation index showing a local peak is larger than the threshold Th2 (Th2 is a positive number) defined for the relationship shown by the explanatory variable number-first evaluation index relationship information 370, among the candidates for the first learning model in which the first evaluation index showing a local peak is larger.

[0050] The threshold Th2 may be a predetermined fixed value or a variable value. For example, the first explanatory variable selection unit 170 may calculate the threshold Th2 based on the explanatory variable number-first evaluation index relationship information 370. More specifically, for example, the first explanatory variable selection unit 170 may calculate the threshold Th2 based on a value (e.g., standard deviation σ) representing the variability of the first evaluation index in the relationship shown in the explanatory variable number-first evaluation index relationship information 370. In this case, for example, the first explanatory variable selection unit 170 may calculate a threshold Th2 whose absolute value is obtained by subtracting a positive integer multiple of σ (e.g., 1 × σ, 2 × σ) from the value of the first evaluation index at the local peak with the largest absolute value in the relationship shown in the explanatory variable number-first evaluation index relationship information 370.

[0051] When using a first evaluation index that shows a larger value the higher the estimation accuracy of the candidate first learning model 350a to 350c, the first explanatory variable selection unit 170 may calculate a threshold Th2 by subtracting a positive integer multiple of σ (for example, 1 × σ, 2 × σ) from the first evaluation index that shows the largest local maximum in the relationship shown in the explanatory variable number-first evaluation index relationship information 370, and select candidate explanatory variables included in the candidate first learning model that correspond to the first evaluation index that is greater than the threshold Th2 as explanatory variables in the first learning model. On the other hand, if a first evaluation index is used in which the estimation accuracy of candidate first learning models 350a to 350c is higher and the value is smaller, the first explanatory variable selection unit 170 may calculate a threshold Th2 by adding a positive integer multiple of σ (for example, 1 × σ, 2 × σ) to the value of the first evaluation index that shows the smallest local minimum in the relationship shown in the explanatory variable number-first evaluation index relationship information 370, and select candidate explanatory variables included in the candidate first learning model that correspond to the first evaluation index that is smaller than the threshold Th2 as explanatory variables in the first learning model.

[0052] Furthermore, for example, if the relationship between the number of explanatory variables and the first evaluation index (370 pieces of information) is expressed as a function, the number of candidate explanatory variables corresponding to the first evaluation index that shows a local peak may not be an integer in that function. In this case, it is acceptable to select the point that is closest to the first evaluation index that shows a local peak from among the points used when calculating the function (points determined by the first evaluation index and the number of candidate explanatory variables).

[0053] A candidate for the first learning model corresponding to a local peak of the first evaluation metric in the relationship shown by the number of explanatory variables - first evaluation metric relationship information 370 can be said to be a candidate for the first learning model whose estimation accuracy is locally good. By searching for candidate first learning models that satisfy the conditions using such a local peak first evaluation metric, it is possible to search for candidate first learning models that include a candidate first evaluation metric that accurately explains the target variable. However, it is not necessarily true that a larger absolute value of the first evaluation metric leads to higher estimation accuracy for the candidate first learning model corresponding to that first evaluation metric. For example, even if the absolute value of the first evaluation metric is large, if the number of candidate explanatory variables included in the candidate first learning model corresponding to that first evaluation metric is large, it may result in overfitting.

[0054] Based on the above, it is preferable that the first explanatory variable selection unit 170, when selecting candidate explanatory variables in the first learning model from among the candidate first learning models corresponding to the first evaluation index that satisfies predetermined conditions in the relationship shown by the number of explanatory variables - first evaluation index relationship information 370, uses conditions expressed using the peak value of the first evaluation index in said relationship. However, the predetermined conditions are not limited to such conditions. For example, the first explanatory variable selection unit 170 may select as explanatory variables in the first learning model from among the candidate first learning models corresponding to the first evaluation index that has the minimum number of candidate explanatory variables among the first evaluation index whose absolute value is greater than or equal to the threshold Th3 in the relationship shown by the number of explanatory variables - first evaluation index relationship information 370. The threshold Th3 may be the same value as the threshold Th2 mentioned above, or it may be a different value.

[0055] In Figure 3, the first evaluation metric showing a local peak is the first evaluation metric at points 373-375. Among the first evaluation metrics at points 373-375, the candidate for the first learning model corresponding to the first evaluation metric with the smallest number of candidate explanatory variables is candidate 350c, which corresponds to the first evaluation metric at point 373. Also in Figure 3, among the first evaluation metrics at points 373-375, the candidates for the first learning model corresponding to the first evaluation metric with a threshold of Th2 or higher are the candidates for the first learning model corresponding to the first evaluation metric at points 373 and 375. Furthermore, among the first evaluation metrics at points 373 and 375, the candidate for the first learning model corresponding to the first evaluation metric with the smallest number of candidate explanatory variables is candidate 350c, which corresponds to the first evaluation metric at point 373.

[0056] Furthermore, if threshold Th3 is the same as threshold Th2, in Figure 3, among the first evaluation metrics that are greater than or equal to threshold Th2 (=Th3), the candidate for the first learning model corresponding to the first evaluation metric with the smallest number of candidate explanatory variables is candidate 350c, which corresponds to the first evaluation metric at point 373.

[0057] Figure 3 illustrates the case where candidate explanatory variables x1, x5, and x7 are selected as explanatory variables in the first learning model (see the end of the arrow next to explanatory variable number-first evaluation metric relationship information 370). However, as mentioned above, it is also possible to select all explanatory variables included in the candidate for the first learning model corresponding to, for example, the first evaluation metric that shows a local peak (the first evaluation metric at points 373-375). Although not shown in Figure 3, in this case, in the example shown in Figure 3, 11 candidate explanatory variables are selected, including candidate explanatory variables x1, x5, and x7.

[0058] [Output process (S208), output section 180] The output unit 180 outputs information about the explanatory variables selected by the first explanatory variable selection unit 170. The output format of the explanatory variable information is at least one of the following: display on a computer display, transmission to an external device, and storage on a portable storage medium.

[0059] As described above, this embodiment illustrates a case in which the first explanatory variable selection unit 170 selects explanatory variables in the first learning model based on the explanatory variable number-first evaluation index relationship information 370. However, as long as the explanatory variable number-first evaluation index relationship information 370 is used for selecting explanatory variables in the first learning model, the processing unit 100 does not necessarily have to spontaneously select the explanatory variables in the first learning model. A user (human) may select the explanatory variables in the first learning model based on the explanatory variable number-first evaluation index relationship information 370. In this case, the output unit 180 may output the explanatory variable number-first evaluation index relationship information 370 calculated by the first relationship calculation unit 160 instead of the explanatory variable information selected by the first explanatory variable selection unit 170. Furthermore, in this case, the processing unit 100 does not need to include the first explanatory variable selection unit 170.

[0060] [summary] As described above, in this embodiment, the processing unit 100 calculates the frequency of occurrence 320 of candidate explanatory variables in a plurality of candidate groups of first explanatory variables 310a to 310d for each candidate explanatory variable, creates a plurality of candidate groups of second explanatory variables 340a to 340c based on the calculated frequency of occurrence 320, creates a plurality of candidate first learning models 350a to 350c for each of the created second candidate groups of second explanatory variables 340a to 340c, calculates a first evaluation index 360a to 360c for each of the created candidate first learning models 350a to 350c to evaluate the estimation accuracy of the candidate first learning model, and calculates explanatory variable number-first evaluation index relationship information 370, which shows the relationship between the number of candidate explanatory variables included in the candidate first learning models 350a to 350c and the first evaluation index for evaluating the estimation accuracy of the candidate first learning model, as information used for selecting explanatory variables in the first learning model. Therefore, it is possible to select explanatory variables that contribute to the dependent variable with higher accuracy than when selecting explanatory variables by comparing the frequency of occurrence of explanatory variables with a threshold, as described in Patent Document 1.

[0061] [Examples of application] As mentioned above, the dependent and independent variables of the first learning model are not limited, but below we will describe an example of the application of this embodiment when a microbial species that affects the rate of change in the amount of a specific substance before and after treatment in a biological wastewater treatment process is selected as the independent variable. In this case, the independent variable in the first learning model is the microbial species, and the dependent variable of the first learning model is the rate of change in the amount of a specific substance before and after treatment in a biological wastewater treatment process.

[0062] <Acquisition of candidate group for the first explanatory variable> The first group of candidate explanatory variables is, for example, a group of microorganisms selected by the first selection process described in Patent Document 1. Since one example of a method for obtaining this first group of candidate explanatory variables is the method described in Patent Document 1, a detailed explanation will be omitted here, and only an overview will be provided.

[0063] (1) Operation of biological wastewater treatment processes, water quality analysis, calculation of decomposition rates, and collection of microbial samples. Industrial water and natural seawater were mixed in a volume ratio of 2:3 to obtain a solvent, into which the solutes shown in Table 1 were dissolved at the concentrations shown in Table 1 to prepare artificial wastewater (treated water).

[0064] [Table 1]

[0065] The rate of change in the amount of a specific substance was collected, for example, by using an integrated biological processing apparatus 20 having a structure in which a biological processing area 20a and a sedimentation area 20b are separated from each other by a partition wall 23 within a single tank, and are in communication with each other below the partition wall 23, as shown in Figure 4.

[0066] Sponge carriers 21 (fluidized carrier (AQ-1 manufactured by Kanto Inoac)) measuring 10 mm × 10 mm × 10 mm were added to the biological treatment area 20a of the biological treatment apparatus 20 in a volume ratio of 20% (v / v). The aforementioned water to be treated 24 (see Table 1) was then introduced into the biological treatment apparatus 20, and activated sludge was added as a microbial inoculation source. During the microbial acclimatization treatment (first stage treatment) to establish microorganisms on the sponge carriers 21, the water to be treated 24 was introduced so that its hydraulic residence time was 24 hours. In addition, air aeration 22 was performed on the water to be treated 24 in each biological treatment apparatus 20 to form an aerobic fluidized bed and acclimatize the microorganisms. Then, the treated water 25 treated in the biological treatment apparatus 20 was discharged from the biological treatment apparatus 20.

[0067] Immediately after the start of this biological treatment, the removal of thiocyanate ions was observed. However, a gradual decrease in pH was observed, and the removal of thiocyanate ions was unstable. Therefore, from the 69th day after the start of operation, the treatment was continued while adjusting the pH to around 7.5 using a 5 wt% sodium hydroxide aqueous solution. The microbial acclimatization treatment (first stage treatment) was terminated when the removal rate of thiocyanate ions stabilized at 98% or more. At the end of this microbial acclimatization treatment (first stage treatment), the amount of nitrite ions had increased.

[0068] After the completion of this microbial acclimatization treatment (first stage treatment), the thiocyanate ion concentration and nitrite ion concentration were measured in the treated water within the biological treatment area 20a of each biological treatment device 20 to monitor thiocyanate ions and nitrite ions. Monitoring was performed approximately every 7 days.

[0069] Furthermore, while monitoring the pH value by measuring the pH of the treated water in the biological treatment area 20a of each biological treatment device 20, the inflow rate of the treated water 24 was increased from the 90th day after the start of operation so that the hydraulic residence time in the area was 18 hours (second stage treatment). From the 111th day after the start of operation, the inflow rate of the treated water 24 was further increased so that the hydraulic residence time in the area was 12 hours (third stage treatment). Furthermore, from the 118th day after the start of operation, the inflow rate of the treated water 24 was further increased so that the hydraulic residence time in the area was 8 hours (fourth stage treatment), and operation was continued until the 175th day.

[0070] During this period, by shortening the hydraulic residence time within the region to 18 hours in the second stage of treatment, a decreasing trend in nitrite ion generation was observed while maintaining a high removal rate of thiocyanate ions. Furthermore, by shortening the hydraulic residence time within the region to 12 hours in the third stage of treatment, it was possible to almost completely suppress nitrite ion generation while maintaining a high removal rate of thiocyanate ions. Moreover, it was confirmed that even when the hydraulic residence time within the region was shortened to 8 hours in the fourth stage of treatment, it was possible to maintain a high removal rate of thiocyanate ions while suppressing nitrite ion generation.

[0071] In the above biological treatments, the daily rate of nitrite production and the rate of thiocyanate removal per day relative to the number of operating days were calculated according to the following equations (2) and (3).

[0072]

number

[0073] Figure 5 shows an example of the nitrite production rate per day of operation. Figure 6 shows an example of the thiocyanate removal rate per day of operation.

[0074] (2) DNA extraction, sequencing, and determination of microbial communities DNA extraction and next-generation sequencing microbial community analysis from the sponge carrier 21 to which microorganisms were attached within the biological treatment area 20a of the biological treatment device 20 were performed by outsourcing (J-Bio21 Center). At each time point corresponding to the measurement of the rate of change in the amount of a specific substance, a sponge carrier to which microorganisms were attached was collected. After dividing the collected sponge carrier into four sections, DNA was extracted and purified using Extrap Soil DNA Plus ver.2 (J-Bio21). The DNA concentration of the purified DNA solution was measured using the PicoGreen dsDNA Assay Kit (Invitrogen). PCR amplification targeting the V4 and V5 regions of the 16S rRNA gene in eubacteria was performed using the primers shown in Table 2 below.

[0075] [Table 2]

[0076] The PCR products were analyzed using a next-generation sequencer (MiSeq) to determine their base sequences. The obtained nucleotide sequences were analyzed using the QIIME (Quantitative Insights Into MicrobialEcology) pipeline. First, the data quality and chimericity were checked, and only sequence data that met the criteria were filtered. For sequence data that met the criteria, sequences with high similarity (homology of 97% or more) were grouped into clusters. The most frequently occurring sequence within each cluster was designated as the representative OTU (Operational Taxonomic Unit) sequence, and subsequent analyses were performed using this representative sequence. In other words, the presence and quantity of each detected OTU were treated as representing the presence and quantity of a single microbial community. As a result, a total of 3,752 OTUs were detected from the microbial samples. These OTUs varied in their detection, with some being found repeatedly in multiple samples and others in only one sample. Furthermore, the relative proportion of each OTU to the total number of OTUs was calculated from the number of times each OTU was detected.

[0077] For each representative OTU sequence, a homology search was performed against the Greengene 16S rRNA gene database to estimate phylogenetic classification.

[0078] (3) Determination of the quantity of each microbial group The number of genes in bacteria attached to a sponge was quantified using QP-PCR (J-Bio21), a real-time PCR method. After appropriately diluting the DNA solution purified in (2) above, a reaction mixture was prepared using the primers and QProbe shown in Table 3 below, and the number of genes was quantified using Rotor-Gene Q (QIAGEN).

[0079] [Table 3]

[0080] In (2) above, the relative proportion of each OTU to the total OTU was calculated. However, the total amount of microorganisms attached to the sponge differs depending on the sampling date. Therefore, in order to accurately grasp the fluctuations of each OTU during the operation period of the biological wastewater treatment process, the amount of each OTU was determined by multiplying the relative proportion of each OTU by the number of eubacterial genes attached to the quantified sponge.

[0081] (4) Preparation of bootstrap samples, identification of major water treatment microbial communities (Denovo) using the Lasso method, and regression analysis. The major microbial groups involved in nitrite production and thiocyanate removal were estimated through statistical analysis. As shown in (3) above, the major OTUs involved in nitrite production and thiocyanate removal were estimated by statistical analysis using the values ​​of each OTU, which were corrected by multiplying the relative proportion of each OTU by the number of genes of eubacteria attached to the quantified sponge.

[0082] The values ​​for each OTU in the dataset used for estimation were obtained by sampling at time points corresponding to the measurement reference time for the nitrite production and thiocyanate removal rate data (for example, using data on the nitrite production rate or thiocyanate removal rate calculated from the amount of substance on day (N+7) of operation, and data on the values ​​of each OTU obtained on day (N+7) of operation).

[0083] However, while there were 23 data points for nitrite production and thiocyanate removal rates, the total number of OTUs obtained using next-generation sequencing was more than 100 times greater, making it impossible to analyze the correlation using conventional regression analysis.

[0084] Therefore, we performed the analysis using the Lasso method. Here, we created 1000 bootstrap samples and applied the Lasso method to these samples to artificially increase the number of datasets obtained from measurements, and then estimated the microbial community using regression analysis.

[0085] As described above, 1000 bootstrap samples were created, and the Lasso method was applied to these samples. Here, we will explain the outlines of the Bootstrap method and the Lasso method. Figure 7 illustrates an example of a method for generating bootstrap samples from a dataset (first training data) using the bootstrap method. In Figure 7, t represents time (in this case, the number of operating days). In Figure 7, n' datasets are randomly resampled from n datasets (left in the figure) to create multiple sets of bootstrap samples (set B) consisting of n' datasets (right in the figure). The values ​​of n and n' are usually the same, but they may be different. The sampled datasets may be duplicated. For example, in the first set shown in Figure 7, t=1 is sampled twice. In Figure 7, B represents the set number. In the example above, B=1000.

[0086] The Lasso method allows for the reduction of regression coefficients to zero. Therefore, it is possible to simultaneously select the variable (microbial community) and estimate the constant term and regression coefficients.

[0087] In the Lasso method, for example, the parameter β that minimizes the value of the cost function expressed in (4) below is used. j We search for the (regression coefficient). The second term of equation (4) below is the regularization term of the L1 norm. Also, λ1 is the regularization coefficient (hyperparameter), which is set to 0.5 (fixed value) here. For example, the cost function can also be obtained by multiplying each term of equation (4) below by (-1). In this case, the value of the cost function is the parameter β 0i (intercept), β j We maximize the (regression coefficient). Alternatively, instead of the Lasso method, we may use, for example, Elastic Net. In this case, for example, the parameter β that minimizes the value of the cost function expressed by equation (5) below is... j We search for the regression coefficients. The second term in equation (5) below is the regularization term of the L2 norm. Also, λ2 is the regularization coefficient (hyperparameter).

[0088]

number

[0089] Figure 8 illustrates an example of a method for obtaining candidate groups of first explanatory variables by performing Lasso analysis on each of the Bootstrap samples from group B. From the first set of Bootstrap samples in Figure 8, three Denovo (microbial communities) were selected as Denovo1, Denovo3, and Denovo9, corresponding to explanatory variables for which the regression coefficient value was not zero. These three Denovo1, Denovo3, and Denovo9 constitute one of the candidate groups of first explanatory variables. Similarly, from the Bootstrap samples of group B, two Denovo1 and Denovo2 were selected. These two Denovo1 and Denovo2 constitute another of the candidate groups of first explanatory variables. As shown here, when each Bootstrap sample is analyzed using the Lasso method, the types of Denovo selected are not necessarily the same, nor are the number of Denovo selected.

[0090] <Calculation of frequency of occurrence> The frequency of occurrence of each candidate explanatory variable (Denovo (microbial group)) in the multiple candidate groups of first explanatory variables obtained as described above is calculated. The frequency of occurrence is expressed, for example, as a confidence level as described in Patent Document 1. Since one example of a method for calculating the frequency of occurrence is the method described in Patent Document 1, a detailed explanation is omitted here, and only an overview is given. Figure 9 is a diagram illustrating one example of a method for calculating the frequency of occurrence.

[0091] In Figure 9, one candidate group of first explanatory variables is obtained from each of the Bootstrap specimens in group B. The number of times each candidate explanatory variable (Denovo (microbial group)) is selected in the first candidate group of first explanatory variables obtained in this way is calculated. In the example shown in Figure 9, Denovo1 is selected 988 times and Denovo2 is selected 675 times. Here, we illustrate the case where the number of Bootstrap specimens (=B) is 1000, so the frequency of occurrence of Denovo1 is 988 / 1000 = 0.988 and the frequency of occurrence of Denovo2 is 675 / 1000 = 0.675.

[0092] <Creation of candidate groups for the second explanatory variable> Based on the frequency of occurrence of candidate explanatory variables (Denovo (microbial community)), multiple candidate groups of second explanatory variables are created, each containing either one candidate explanatory variable or multiple candidate explanatory variables.

[0093] First, the candidates for each explanatory variable (Denovo(microbial community)) are sorted in descending order from the highest frequency of occurrence. Starting with the candidate explanatory variable (Denovo(microbial community)) with the highest frequency of occurrence, an integer is assigned to each explanatory variable, starting with an initial value of 0 and increasing by 1 each time. Figure 10 shows an example of the relationship between the microbial community (candidate explanatory variable) represented by the integers assigned in this way and the frequency of occurrence of that microbial community. Figure 10 shows the frequency of occurrence only for the 50 candidate explanatory variables with a frequency of occurrence of 0.10 or higher, rather than all candidate explanatory variables (Denovo(microbial community)). However, the frequency of occurrence can also be calculated for all candidate explanatory variables included in the first candidate explanatory variable group.

[0094] Then, we selected m candidate explanatory variables (Denovo (microbial community)) in order of frequency, and created a second group of candidate explanatory variables containing the selected m candidates. This process was performed for each case where M was set to 20 and m was varied from 1 to 20. In this way, 20 second groups of candidate explanatory variables were created. Here, we illustrate the case where the value of M is less than the number of candidate explanatory variables included in the first group of candidate explanatory variables, but the value of M may also be the same as the total number of candidate explanatory variables included in the first group of candidate explanatory variables.

[0095] <Creating candidate models for the first learning model> For each of the M (20 in the example above) candidate groups of second explanatory variables, we create multiple candidate first-stage learning models that show the relationship between the candidate explanatory variable (Denovo (microbial community)) included in that candidate group and the target variable. Here, we created 20 linear regression equations as candidates for the first-stage learning models by performing linear regression. In addition, during the linear regression, we used a portion of the 100 sets of Bootstrap samples described in the section on "<Acquisition of Candidate Groups of First Explanatory Variables>" as the first-stage learning data (training data).

[0096] <Calculation of the first evaluation indicator> For each of the M (20 in the example above) candidate first learning models (linear regression equations), a first evaluation metric was calculated to assess the estimation accuracy of that candidate first learning model. Here, a portion of the 100 Bootstrap samples described in the section <Acquisition of Candidate First Explanatory Variables> was used as the first training data (test data). The coefficient of determination R was used as the first evaluation metric. 2 I used it.

[0097] <Calculation of information relating to the number of explanatory variables and the first evaluation indicator, and selection of explanatory variables> The number of candidate explanatory variables (Denovo (microbial community)) included in one candidate first learning model (linear regression equation), and the coefficient of determination R for the candidate first learning model. 2 The relationship between and is calculated as an example of the relationship information between the number of explanatory variables and the first evaluation index, and the coefficient of determination R, which shows a maximum value in the relationship information between the number of explanatory variables and the first evaluation index, is calculated. 2 Candidate explanatory variables corresponding to this were selected as explanatory variables in the first learning model.

[0098] Figure 11 shows an example of the relationship information 1100 between the number of explanatory variables and the first evaluation index. In Figure 11, six local peaks 1101 to 1106 (maxima) were obtained, with (number of microbial groups, coefficient of determination) = (5, 0.875), (9, 0.885), (11, 0.928), (13, 0.972), (16, 0.978), and (18, 0.977). The coefficient of determination R in these six local peaks 1101 to 1106 is R 2 All of the corresponding explanatory variables (Denovo (microbial community)) may also be used as explanatory variables in the first learning model.

[0099] However, here, in order to further narrow down the explanatory variables in the first learning model, the coefficient of determination R in the explanatory variable-first evaluation index relationship information 1100 shown in Figure 11 is calculated from the value of the first evaluation index (=0.977) at local peak 1105, which has the largest absolute value among the six local peaks 1101-1106. 2The threshold Th2 was calculated by subtracting the standard deviation σ (=0.119) (=0.859) (see Figure 12). Then, among the six local peaks 1101-1106, the coefficient of determination R 2 Select local peak 1101 where the value is greater than or equal to the threshold Th2 and the number of microbial communities is smallest, and determine the coefficient of determination R at local peak 1101. 2 Candidate explanatory variables corresponding to this were selected as explanatory variables in the first learning model.

[0100] Coefficient of determination R at local peak 1101 2 The candidate explanatory variables corresponding to this were Denovo1984, Denovo1543, Denovo2960, Denovo2124, and Denovo2358. Therefore, Denovo1984, Denovo1543, Denovo2960, Denovo2124, and Denovo2358 were selected as microbial species that influence the rate of change in the amount of specific substances before and after treatment in the biological wastewater treatment process.

[0101] (Second Embodiment) Next, a second embodiment will be described. In the first embodiment, an example was given in which the values ​​of predetermined hyperparameters used in a penalty-based regression analysis that can reduce the regression coefficients to zero are fixed. Specifically, an example was given in which the regularization coefficient λ1 of the regularization term of the L1 norm in the second term of equation (4) is fixed to 0.5. In this case, one set of candidates 350a to 350c are calculated as multiple candidates for the first learning model, and one explanatory variable-first evaluation metric relation information 370 is calculated as explanatory variable-first evaluation metric relation information 370 (see Figure 3).

[0102] In contrast, in this embodiment, multiple sets of candidate first learning models are calculated by creating candidate first learning models for each case where multiple values ​​are used as predetermined hyperparameter values ​​for regression analysis with penalties. Then, the aforementioned first evaluation index is calculated for each of the multiple sets of candidate first learning models, and explanatory variable number-first evaluation index relationship information is calculated for each set of candidate first learning models. Then, explanatory variables in the first learning model are selected based on the multiple explanatory variable number-first evaluation index relationship information calculated in this way.

[0103] As described above, this embodiment and the first embodiment differ primarily in their configuration and processing, which involve creating candidate first learning models for each case where multiple values ​​are used as predetermined hyperparameter values ​​for regression analysis with penalties. Therefore, in describing this embodiment, parts identical to those in the first embodiment will be denoted by the same reference numerals as those used in Figures 1 to 12, and detailed explanations will be omitted.

[0104] In this embodiment, we illustrate the case where the first learning model is a linear regression equation calculated by the Lasso method (see equation (4)). In this case, the predetermined hyperparameter is the regularization coefficient λ1. However, the first learning model is not limited to a linear regression equation calculated by the Lasso method, as long as it is a regression equation calculated by a penalty-based regression analysis that can reduce the regression coefficients to zero. For example, the first learning model may be a linear regression equation calculated by an Elastic Net. In this case, the predetermined hyperparameters are the regularization coefficients λ1 and λ2 (see equation (5)).

[0105] [First explanatory variable candidate group acquisition process (S201), first explanatory variable candidate group acquisition unit 110] The first explanatory variable candidate group acquisition unit 110 acquires multiple sets of first explanatory variable candidate groups, each containing either one explanatory variable candidate or multiple explanatory variable candidates. Specifically, the first explanatory variable candidate group acquisition unit 110 calculates multiple first explanatory variable candidate groups by performing a penalty-based regression analysis with a predetermined parameter (λ1 in this embodiment) used in the penalty-based regression analysis being the first value. Similarly, the first explanatory variable candidate group acquisition unit 110 calculates multiple first explanatory variable candidate groups by performing a penalty-based regression analysis with a predetermined parameter being the second value, third value, ..., and u value. As a result, u sets of multiple first explanatory variable candidate groups 310a to 310d are calculated.

[0106] The u values ​​of the predetermined parameter (λ1 in this embodiment) used in the penalty-based regression analysis may be fixed values ​​or variable values. For example, the u values ​​of the predetermined parameter (λ1 in this embodiment) used in the penalty-based regression analysis may be values ​​obtained by dividing the range assumed to be the value of the predetermined parameter (λ1 in this embodiment) into equal parts. The first explanatory variable candidate group acquisition unit 110 may also calculate the values ​​within that range using random numbers or the like.

[0107] [Frequency calculation process (S202), frequency calculation unit 120] The frequency calculation unit 120 calculates the frequency of occurrence of candidate explanatory variables in a plurality of candidate groups of first explanatory variables 310a to 310d, similar to the method described in the first embodiment, for candidate explanatory variables x1, x2, ... x p This is done for each of the following. In this embodiment, the frequency calculation unit 120 calculates the candidate explanatory variables x1, x2, ...x p The frequency of occurrence is calculated for each of the candidate explanatory variables in multiple sets (u sets) of candidate first explanatory variables 310a to 310d. The frequency of occurrence of p × u is calculated.

[0108] [Second explanatory variable candidate group creation process (S203), second explanatory variable candidate group creation unit 130] The second explanatory variable candidate group generation unit 130 generates candidate explanatory variables x1, x2, ... x, similar to the first embodiment. p Based on the frequency of occurrence 320 for each of the above, multiple candidate groups of second explanatory variables are created, each containing either a candidate for one explanatory variable or a candidate for multiple explanatory variables. In this embodiment, the second explanatory variable candidate group creation unit 130 creates multiple sets (u sets) of such sets of multiple candidate groups of second explanatory variables.

[0109] [First learning model candidate creation process (S204), first learning model candidate creation unit 140] The first learning model candidate creation unit 140, as described in the first embodiment, creates a plurality of first learning model candidates 350a to 350c that show the relationship between the candidate explanatory variables included in the second explanatory variable candidate group and the target variable, for each of the plurality of second explanatory variable candidate groups 340a to 340c. In this embodiment, multiple sets (u sets) of such sets of multiple first learning model candidates 350a to 350c are created. As a result, u sets of multiple first learning model candidates 350a to 350c are created. The number of multiple first learning model candidates included in each set may be the same or different.

[0110] [First evaluation index calculation process (S205), first evaluation index calculation unit 150] The first evaluation index calculation unit 150 calculates a first evaluation index for evaluating the estimation accuracy of the candidate first learning model for each of the u sets of candidate first learning models 350a to 350c. In the first embodiment, there is one set of candidate first learning models 350a to 350c, while in this embodiment, there are u sets (two or more sets) of candidate first learning models 350a to 350c. If the number of candidate first learning models included in each set is the same as the number of candidate first learning models 350a to 350c calculated in the first embodiment, then in this embodiment, a first evaluation index equal to u times the number of candidate first learning models 350a to 350c calculated in the first embodiment is calculated.

[0111] [First relationship calculation process (S206), First relationship calculation unit 160] The first relationship calculation unit 160 calculates the explanatory variable number-first evaluation metric relationship information 370 for each of the u pairs of candidate first learning models. As a result, u explanatory variable number-first evaluation metric relationship information 370 are calculated.

[0112] [First explanatory variable selection process (S207), first explanatory variable selection unit 170] The first explanatory variable selection unit 170, based on the number of explanatory variables - first evaluation index relation information 370, selects the explanatory variables x1, x2, ..., x in the first learning model. p Select this option.

[0113] For example, the first explanatory variable selection unit 170 selects explanatory variables in the first learning model as described in the first embodiment, based on each of the u explanatory variable number-first evaluation index relation information 370. For example, when selecting a candidate for the first learning model as an explanatory variable in the first learning model, which corresponds to the first evaluation index with the smallest number of candidate explanatory variables among the first evaluation indexes that are greater than the threshold Th2, one set of explanatory variables in the first learning model is selected based on one explanatory variable number-first evaluation index relation information 370. In this embodiment, when selecting one set of explanatory variables in the first learning model based on one explanatory variable number-first evaluation index relation information 370, u sets of explanatory variables in the first learning model are selected. In the following description, the u sets of explanatory variables in the first learning model selected in this way will be referred to as the u set of explanatory variables group, as necessary. In this embodiment, the explanatory variables included in the u set of explanatory variables group are still candidates for explanatory variables in the first learning model.

[0114] Figure 13 shows the candidate explanatory variables (microbial groups) included in the u-group of explanatory variables selected as described above, the number of candidate explanatory variables (microbial groups) included in each group of explanatory variables, and an example of a first evaluation index for the candidate first learning model that has the candidate explanatory variables (microbial groups) included in each group of explanatory variables.

[0115] In Figure 13, the first evaluation index is the coefficient of determination R 2 and the adjusted coefficient of determination adj_R 2 The following is an example of the case. Figure 13 also shows an example of the case where the regularization coefficient λ1 is changed in increments of 0.1 within the range of 0.1 to 20.4. Note that "0.5, 9.9-15.3" in the λ1 column of Figure 13 indicates that the candidate explanatory variables (microbial groups) selected are the same when the value of the regularization coefficient λ1 is 0.5 and when it is between 9.9 and 15.3 (this notation is the same in the other columns of λ1 in Figure 13).

[0116] The first explanatory variable selection unit 170 may select explanatory variables in the first learning model based, for example, on at least one of the following: the number of candidate explanatory variables (microbial groups) included in group u of explanatory variables, and the number of candidate explanatory variables (microbial groups) that overlap in multiple groups of explanatory variables. The first explanatory variable selection unit 170 may also further select explanatory variables in the first learning model using a first evaluation index.

[0117] For example, the first explanatory variable selection unit 170 may select explanatory variables in the first learning model from among the groups of explanatory variables that have candidate explanatory variables (microbial groups) that are overlapping in groups of explanatory variables with a threshold Th4 or higher, and which have the smallest number of candidate explanatory variables (microbial groups). The threshold Th4 is an integer less than or equal to u. For example, Denovo1543 and Denovo1984 are included in all explanatory variable groups. In this case, the group of explanatory variables with the smallest number of candidate explanatory variables (microbial groups) is the group of explanatory variables calculated with a regularization coefficient λ1 of 0.3 (the group of explanatory variables including Denovo1984, Denovo1543, and Denovo2124).

[0118] Furthermore, the first explanatory variable selection unit 170 selects, for example, the first evaluation index (for example, the coefficient of determination R in Figure 13). 2From the explanatory variable groups in which the absolute value of is greater than the threshold Th5, the explanatory variables in the first learning model may be selected. For example, when there are a plurality of explanatory variable groups having candidates for explanatory variables (microbiota) that are overlappingly included in the explanatory variable group of the number pairs of the threshold Th4 or more, the first explanatory variable selection unit 170 may select, among these plurality of explanatory variables, the candidates for the explanatory variables included in the explanatory variable group having the largest absolute value of the first evaluation index as the explanatory variables in the first learning model.

[0119] Also, the first explanatory variable selection unit 170 may, for example, select the candidates for the explanatory variables included in the explanatory variable group in which the number of candidates for the explanatory variables (microbiota) is the smallest among the explanatory variable groups in which the absolute value of the first evaluation index (for example, the coefficient of determination R in FIG. 13 2 ) is greater than the threshold Th5 as the explanatory variables in the first learning model. Note that, as the selection target, the explanatory variable groups in which the absolute values of a plurality of first evaluation indexes (the coefficient of determination R in FIG. 13 2 and the adjusted coefficient of determination adj_R 2 ) are each greater than the threshold may be selected.

[0120] [Summary] As described above, in the present embodiment, the processing device 100 creates a set of candidates for each of the first learning models when using a plurality of values as the value of a predetermined hyperparameter (for example, the regularization coefficient λ1) used in the regression analysis with penalties, thereby calculating a plurality of sets of candidates for the first learning models. Then, for each of the sets of candidates for the plurality of first learning models, a first evaluation index (for example, the coefficient of determination R 2 ) is calculated, and the explanatory variable number - first evaluation index relationship information is calculated for each of the sets of candidates for the plurality of first learning models. Therefore, for example, more information can be obtained as useful information for selecting explanatory variables that accurately explain the objective variable, such as the possibility that the explanatory variables existing in a large number of sets and overlapping are important explanatory variables is high. Note that, in the present embodiment, various modifications described in the first embodiment may also be adopted.

[0121] (Third Embodiment) Next, the third embodiment will be described. In the first and second embodiments, the case where the target variable y i is a quantitative variable was exemplified. In contrast, in this embodiment, the case where the target variable y i is a categorical variable (qualitative variable) will be exemplified. Thus, in this embodiment, compared with the first and second embodiments, the configuration and processing mainly differ due to the target variable y i being a categorical variable. Therefore, in the description of this embodiment, for the same parts as those in the first and second embodiments, the same reference numerals as those attached to FIGS. 1 to 13 will be used and detailed description will be omitted. Note that a categorical variable is a variable indicating two or more classes and is a variable that takes discrete values. The number of values that a categorical variable can take (the number of discrete values) corresponds to, for example, the number of classes to be classified. Also, the classes indicated by the categorical variable are, for example, the classes to which the quantitative variable explained by the explanatory variable belongs.

[0122] In this embodiment, a case where the regression analysis used for calculating a plurality of first explanatory variable candidate groups 310a to 310d is a penalized logistic regression analysis capable of shrinking the regression coefficient to 0 will be exemplified.

[0123] The logistic regression equation for K classes (K is an integer of 2 or more) is represented by the following equation (6).

[0124]

Equation

[0125] Here, β 10 , β 20 , ···, β (K-1)0 are intercepts (constant terms). β T 1, β T 2, ···, β T K-1 represents the transposed vector of the regression coefficients for the explanatory variable x. Note that β T 1, β [[ID=四十二]] T 2, ···, β T K-1In equation (6), these are β1, β2, ..., β K-1 These correspond to the symbols 1, 2, ..., and K-1 with a T above them.

[0126] Intercept β0(=[β 10 ,β 20 ,···,β (K-1)0 ]) and regression coefficients β(=[β1,β2,···,β K-10 The cost function is calculated by solving the problem of maximizing or minimizing the value of a cost function that includes a regularization term of the L1 norm. For example, if K=2 (2 classes) and the dependent variable and independent variable of the i-th dataset are y i , x i Assuming that the regularization coefficient of the L1 norm regularization term is λ1, N is the number of datasets, and p is the number of explanatory variables, the problem is to solve for maximizing the value of the cost function. The intercept β0 and regression coefficient β are determined by calculating equation (7) below using convergence algorithms such as the coordinate gradient method or the alternating direction multiplier method. Alternatively, the cost function may be obtained by multiplying each term in equation (7) below by (-1). In this case, the value of the cost function is minimized with respect to the parameters β0 (intercept) and β (regression coefficient). Furthermore, although a two-class logistic regression equation is given as an example here, multi-class logistic regression equations of three or more classes can be calculated by using the softmax function.

[0127]

number

[0128] [First explanatory variable candidate group acquisition process (S201), first explanatory variable candidate group acquisition unit 110] In this embodiment, using a dataset with categorical variables as the target variable (first training data), we search for the parameters β0 (intercept) and β (regression coefficient) that minimize the value of the cost function expressed by equation (7) instead of equation (4).

[0129] Figure 14 shows an example of a dependent variable (categorical variable) when there are two classes. In Figure 14, the dependent variable is set to 1 as an integer indicating that water treatment is possible when the nitrite concentration value, a quantitative variable, is 50 or higher, and to 0 as an integer indicating that water treatment is not possible otherwise. This illustrates a case where the water treatment status is classified into one of two classes for each operating day.

[0130] For example, the first explanatory variable candidate group acquisition unit 110 uses the target variable (see nitrite concentration (binarized)) shown in Figure 14 and the explanatory variable (microbial community) when the quantitative variable (nitrite concentration) corresponding to the target variable is obtained as a dataset, and performs resampling (e.g., creation of a bootstrap sample) and a penalized logistic regression analysis that can reduce the regression coefficient to zero for each sample, as described in the first embodiment, to select explanatory variables whose regression coefficients do not become zero. Then, for each sample, the first explanatory variable candidate group acquisition unit 110 selects the explanatory variables whose regression coefficients do not become zero, selected from one sample, as candidates for explanatory variables to be included in one first explanatory variable candidate group.

[0131] [Frequency calculation process (S202), frequency calculation unit 120] The processing performed by the frequency calculation unit 120 may be, for example, the processing described in the first embodiment. Figure 15 is a diagram showing an example of the relationship between a microbial group (candidate explanatory variable) and the frequency of occurrence of that microbial group. In Figure 15, as in Figure 10, integers are assigned to each explanatory variable in order from the candidate explanatory variable with the highest frequency of occurrence (Denovo (microbial group)), starting with an initial value of 0 and increasing by 1 each time, and the microbial group on the horizontal axis is represented by the assigned integers.

[0132] [Second explanatory variable candidate group creation process (S203), second explanatory variable candidate group creation unit 130] The processing performed by the second explanatory variable candidate group creation unit 130 may be, for example, the processing described in the first embodiment. For example, the second explanatory variable candidate group creation unit 130 selects m explanatory variable candidates in order of frequency of occurrence and creates a second explanatory variable candidate group containing the selected m explanatory variable candidates, for each case where M is an integer of 2 or more and m is changed from 1 to M.

[0133] [First learning model candidate creation process (S204), first learning model candidate creation unit 140] The processing performed by the first learning model candidate creation unit 140 may, for example, be a process in which the linear regression equation, which is an example of the first learning model described in the first embodiment, is replaced with a logistic regression equation.

[0134] [First evaluation index calculation process (S205), first evaluation index calculation unit 150] The first evaluation metric calculation unit 150 calculates a first evaluation metric for each of the multiple candidates for the first learning model to evaluate the estimation accuracy of the candidate first learning model. For example, accuracy or precision may be used as the first evaluation metric. Also, if the number of datasets belonging to each class is unbalanced, for example, the F-score or AUC (Area Under the Curve) may be used as the first evaluation metric. Furthermore, logit loss, Brier score, pseudo-coefficient of determination, etc., derived from the prediction probability in the logistic regression equation may be used as the first evaluation metric. Here, the prediction probability in the logistic regression equation is calculated using N input data x (explanatory variable x of the i-th dataset). i For each of the following, the probability of obtaining class 1 (positive) is calculated using the logistic regression equation. Specifically, the predicted probability in the logistic regression equation is the logit W TA continuous value between 0 and 1 ([0,1]) obtained by applying a sigmoid function to X+b is also acceptable. Here, X is a matrix that stores N input data x, W is a matrix that stores the regression coefficients for the N input data x, and b is a matrix that stores the intercept. Alternatively, known evaluation metrics (such as recall or specificity) used as the first evaluation metric for the first learning model performing classification may be used.

[0135] [First relationship calculation process (S206), First relationship calculation unit 160] The processing performed by the first relationship calculation unit 160 is, for example, the first evaluation index (coefficient of determination R) described in the first embodiment. 2 The process can be performed by replacing (etc.) with the aforementioned first evaluation indicator (accuracy rate, etc.). Figure 16 shows an example of 1600 explanatory variable-first evaluation indicator relationship information.

[0136] [First explanatory variable selection process (S207), first explanatory variable selection unit 170] The processing performed by the first explanatory variable selection unit 170 is, for example, the first evaluation index (coefficient of determination R) described in the first embodiment. 2 The process can be performed by replacing (etc.) with the aforementioned first evaluation index (accuracy rate, etc.). In the example shown in Figure 16, for example, the local peak (maximum value) is the accuracy rate with the largest absolute value when the number of microbial communities is 1. Therefore, the first explanatory variable selection unit 170 may select a candidate explanatory variable (a candidate for one explanatory variable) included in the candidate first learning model corresponding to the first evaluation index that shows the local peak as an explanatory variable in the first learning model. The candidate microbial community for this explanatory variable is Denovo1767.

[0137] Also, as shown in FIG. 16, in the explanatory variable number - first evaluation index relationship information 1600, since the peak is flattened, the first evaluation index indicating the local peak is not determined to be one, and there may be a plurality of candidates 1601 to 1603 as candidates for the point indicating the local peak. In this case, any one of the values of the plurality of first evaluation indexes that are candidates for the local peak may be selected. For example, the median of the plurality of first evaluation indexes that are candidates for the local peak may be selected. Thus, it is not necessary to select the first evaluation index itself indicating the local peak. This is the same in the first embodiment and the second embodiment.

[0138] [Summary] As described above, in this embodiment, the processing device 100 selects an explanatory variable in the first learning model having the category variable as the target variable. Therefore, an explanatory variable that accurately explains the category variable can be selected. Also, in this embodiment, the processing device 100 calculates a first explanatory variable candidate group by performing a penalized logistic regression analysis that can shrink the regression coefficient to 0. Therefore, an explanatory variable that explains the category variable with higher accuracy can be selected.

[0139] When performing a penalized logistic regression analysis that can shrink the regression coefficient to 0, the method of this embodiment may be applied to the second embodiment. In this case, the predetermined hyperparameter used in the penalized regression analysis is, for example, the regularization coefficient λ1 in equation (7). Also, in this embodiment, various modifications described in the first embodiment and the second embodiment may be adopted.

[0140] (Fourth Embodiment) Next, a fourth embodiment will be described. In the first to third embodiments, examples were given of selecting candidate explanatory variables to be included in the first candidate group of explanatory variables 310a to 310d by performing a penalty-based regression analysis that reduces the regression coefficient to 0 on each sample created by the Bootstrap method, etc., and selecting explanatory variables for which the regression coefficient does not become 0 for each sample. However, the data of the explanatory variables used to perform the penalty-based regression analysis may contain noise. If this noise has a large impact on the dependent variable y, there is a risk that explanatory variable candidates that are not suitable for explaining the dependent variable y will be selected as candidates for explanatory variables to be included in the first candidate group of explanatory variables. Therefore, in this embodiment, an example is given of selecting candidate explanatory variables to be included in the first candidate group of explanatory variables by considering the noise that may be contained in the data of the explanatory variables used to perform the penalty-based regression analysis, thereby further suppressing the selection of explanatory variable candidates that are not suitable for explaining the dependent variable y. Thus, the main difference between this embodiment and the first to third embodiments is the processing involved in selecting candidate explanatory variables to be included in the first candidate group of explanatory variables. Therefore, in describing this embodiment, parts identical to those in the first to third embodiments will be denoted by the same reference numerals as those used in Figures 1 to 16, and detailed descriptions will be omitted.

[0141] [First explanatory variable candidate group acquisition process (S201), first explanatory variable candidate group acquisition unit 110] The first explanatory variable candidate group acquisition unit 110 acquires multiple first explanatory variable candidate groups, each containing either a candidate for one explanatory variable or a candidate for multiple explanatory variables. This is the same as in the first embodiment. However, in this embodiment, the specific processing for acquiring multiple first explanatory variable candidate groups differs from the first to third embodiments. In this embodiment as well, for the sake of simplicity, we will illustrate the case where the first learning model is a linear regression equation (see equation (1)).

[0142] In this embodiment, first, the first explanatory variable candidate group acquisition unit 110 creates data for noise explanatory variables, which are variables that simulate noise that may be included in the data of candidate explanatory variables. Then, using the data of candidate explanatory variables, the data of noise explanatory variables, and the data of the target variable, the first explanatory variable candidate group acquisition unit 110 performs a regression analysis with a penalty that can reduce the regression coefficients to zero, as a regression analysis to calculate the regression coefficients of a regression equation that shows the relationship between the candidate explanatory variables, the noise explanatory variables, and the target variable. Then, based on the result of comparing the regression coefficients for the candidate explanatory variables and the regression coefficients for the noise explanatory variables, the first explanatory variable candidate group acquisition unit 110 calculates a plurality of first explanatory variable candidate groups. An example of the functions of the first explanatory variable candidate group acquisition unit 110 in this embodiment will be described in detail below.

[0143] The first explanatory variable candidate acquisition unit 110 may extract noise contained in the data of the candidate explanatory variables from the candidate explanatory variable data and use it as noise explanatory variable data. However, it is not easy to identify what kind of data (for example, data of what frequency) is noise. Alternatively, the noise explanatory variable data may be created using random numbers. However, doing so may reduce the influence of the noise explanatory variable on the target variable (the regression coefficient for the noise explanatory variable, as described later, may become too small).

[0144] Therefore, in this embodiment, we illustrate a case in which the first explanatory variable candidate group acquisition unit 110 creates noise explanatory variable data using the data of candidate explanatory variables. In this case, the first explanatory variable candidate group acquisition unit 110 may create data for noise explanatory variables such that the correlation of the noise explanatory variables with respect to the target variable is lower than the correlation of the candidate explanatory variables with respect to the target variable. In this case, the first explanatory variable candidate group acquisition unit 110 may set the correlation of the noise explanatory variables with respect to the target variable to be uncorrelated. The first explanatory variable candidate group acquisition unit 110 may also set the candidate noise explanatory variables to be independent of the target variable. Furthermore, if the first learning model is a linear regression model, the first explanatory variable candidate group acquisition unit 110 may create data for noise explanatory variables such that the noise explanatory variables have conditional independence from the target variable, conditional on the candidate explanatory variables.

[0145] Furthermore, the first explanatory variable candidate group acquisition unit 110 may create data for noise explanatory variables such that the statistical distribution (frequency distribution) of the noise explanatory variables is the same as or based on the statistical distribution of the candidate explanatory variables.

[0146] Furthermore, the first explanatory variable candidate group acquisition unit 110 may create data for noise explanatory variables such that both of the following conditions are met: the correlation of the noisy explanatory variables with respect to the dependent variable is lower than the correlation of the candidate explanatory variables with respect to the dependent variable, and the statistical distribution of the noise explanatory variables is the same as or based on the statistical distribution of the candidate explanatory variables.

[0147] The following describes in detail an example of the processing of the first explanatory variable candidate group acquisition unit 110 when creating data for noise explanatory variables so that the correlation of the noise explanatory variables with respect to the dependent variable is low compared to the correlation of the candidate explanatory variables with respect to the dependent variable, and the statistical distribution of the noise explanatory variables is the same as or based on the statistical distribution of the candidate explanatory variables.

[0148] First, in order to select candidate explanatory variables to be included in a group of multiple candidate explanatory variables, the first explanatory variable candidate group acquisition unit 110 creates multiple samples by resampling a dataset (first training data) consisting of candidate explanatory variables and the values ​​of the target variable.

[0149] For example, resampling may be performed as described with reference to Figure 7 (in the following description, such a resampling method will be referred to as the first resampling method as needed). In this case, the n' datasets sampled (resampled) as described in the first embodiment may be duplicates. Note that, as described in the first embodiment, the values ​​of n and n' may be different, but here we will assume n = n'.

[0150] Alternatively, the following method may be used as a resampling technique: Randomly resample n' datasets from n datasets to create multiple sets of n' datasets. In this process, ensure that the n' datasets do not contain any duplicate datasets (the same dataset). Here, n' is less than n, for example, n' = n / 2. In the following explanation, this type of resampling technique will be referred to as the second resampling technique as needed.

[0151] Furthermore, the values ​​of n datasets are randomly shuffled, and n' datasets (=n datasets) are resampled to create multiple sets (set B) consisting of n' datasets (=n datasets). In the following explanation, this resampling method will be referred to as the third resampling method as needed.

[0152] The first explanatory variable candidate group acquisition unit 110 may use any of the first resampling method, the second resampling method, and the third resampling method. In this case, only one of the first resampling method, the second resampling method, and the third resampling method may be used. Alternatively, two or three of the first resampling method, the second resampling method, and the third resampling method may be used. In addition, in the first to third embodiments, the first explanatory variable candidate group acquisition unit 110 may resample the dataset (first training data) using at least one of the second resampling method and the third resampling method, instead of or in addition to the first resampling method. Furthermore, when resampling, the first explanatory variable candidate group acquisition unit 110 may standardize or normalize the values ​​of each dataset (first training data). Standardization is performed, for example, by transforming the values ​​of the dataset so that the mean is 0 and the variance is 1 for each explanatory variable. Normalization is performed, for example, by summing the values ​​of all explanatory variables included in each dataset, and then dividing the value of each element (each explanatory variable) included in that dataset by that sum, so that the sum of the values ​​of the elements (explanatory variables) in each dataset becomes 1. Such standardization or normalization may also be performed in the first to third embodiments.

[0153] The first explanatory variable candidate acquisition unit 110 uses the data of candidate explanatory variables included in one (one set) sample to create data for noise explanatory variables, which are variables that simulate noise that may be included in the data of the candidate explanatory variables. Figure 17 is a diagram that conceptually illustrates an example of how to create data for noise explanatory variables.

[0154] In Figure 17, the candidate explanatory variable matrix X(∈R n' × p) is a matrix that includes, as components, data of candidate explanatory variables included in one (a set of) sample. In FIG. 17, the “1, 2, ··· n'” attached to the left side of the candidate explanatory variable matrix X represents symbols for n' resampled data sets. Also, the “1, 2, ···, p” attached to the upper side of the candidate explanatory variable matrix X are symbols representing candidate explanatory variables. Also, the “x i1 ,x i2 ,···,x ip ” above is a symbol representing candidate explanatory variables and corresponds to x ij in Equation (1) (where i is a variable for identifying the first learning model).

[0155] In FIG. 17, for example, x i1_1 , x i1_2 , ···, x i1_n' are the first, second, ··· n'-th data of the candidate explanatory variable x i1 . Note that the values of the components in the columns corresponding to candidate explanatory variables that have not been resampled become 0 (zero). In FIG. 17, the data showing the values of each component of the candidate explanatory variable matrix X is an example of the data of candidate explanatory variables. The first candidate explanatory variable group acquisition unit 110 calculates a plurality of candidate explanatory variable matrices X as described above. These plurality of candidate explanatory variable matrices X correspond to a plurality (a plurality of sets) of samples.

[0156] Next, the first candidate explanatory variable group acquisition unit 110 calculates a noise explanatory variable matrix X noise (∈R n' × p ) based on the candidate explanatory variable matrix X. The noise explanatory variable matrix X noise is a matrix of the same dimension as the candidate explanatory variable matrix X (a matrix of n' rows and p columns) and is a matrix that includes, as components, data of noise explanatory variables. In FIG. 17, the “n noise , n i1 , ···, n i2 ” attached to the upper side of the noise explanatory variable matrix X ip are symbols representing noise explanatory variables. The noise explanatory variable matrix X noise includes noise explanatory variables n i1 , n i2 , ···, nip Each data set contains n' data points. In Figure 17, for example, n i1_1 , n i1_2 , , , n i1_n' The noise explanatory variable n i1 These are the 1st, 2nd, ..., n'th data points.

[0157] The first explanatory variable candidate group acquisition unit 110, for example, by swapping at least two rows of the explanatory variable candidate matrix X, obtains the noise explanatory variable matrix X noise The following calculation may be performed. In this case, the first explanatory variable candidate group acquisition unit 110 may swap all rows of the explanatory variable candidate matrix X with other rows, or some rows may not be swapped. The first explanatory variable candidate group acquisition unit 110 may also randomly determine the row numbers to be swapped and the number of rows to be swapped, for example, using random numbers. The first explanatory variable candidate group acquisition unit 110 may also ensure that the column numbers of the components of each row are not changed before and after the swap. For example, when the first row and the third row are swapped in this way, the components of the first row and third column before the swap become the components of the third row and third column after the swap, and the components of the third row and third column before the swap become the components of the first row and third column after the swap.

[0158] In this way, it is possible to create data for noise explanatory variables such that the correlation of the noise explanatory variables with respect to the dependent variable is low compared to the correlation of the candidate explanatory variables with respect to the dependent variable, and the statistical distribution of the noise explanatory variables is the same as or based on the statistical distribution of the candidate explanatory variables. In the following explanation, by swapping at least two rows of the candidate explanatory variable matrix X, the noise explanatory variable matrix X noise The method for calculating this will be referred to as the first noise explanatory variable creation method, as needed.

[0159] Furthermore, the first explanatory variable candidate group acquisition unit 110 may calculate the knock-off variables as noise explanatory variables. The matrix X~ that stores the knock-off variables is the matrix represented by equation (8) below. Note that X~ corresponds to the symbol with ~ above X in equation (8).

[0160]

number

[0161] Matrix X is the matrix from which the knockoff variables are calculated, and in this embodiment, it is the explanatory variable candidate matrix X. Also, matrix X~ is the matrix that stores the knockoff variables, and in this embodiment, it is the noise explanatory variable matrix X. noise As shown in equation (8), the values ​​of the components stored in matrices X and X~ follow a normal distribution with mean μ and covariance matrix Σ~ represented by equation (9). Note that Σ~ corresponds to the symbol with a ~ above Σ in equation (8).

[0162] In equation (8), the mean value μ of the components stored in matrix X is the same as the mean value μ of the components stored in matrix X~. Also, in equation (9), matrix Σ represents the covariance matrix of the original explanatory variables, and matrix S is a positive definite symmetric matrix introduced to satisfy the conditions for generating knockoff variables (exchangeability conditions), and is chosen such that 2Σ-S is positive semi-definite. The unified matrix [X,X~] T The covariance matrix has a block structure, and each of its diagonal blocks coincides with the covariance matrix Σ of the original matrix X.

[0163] Since the knockoff variable itself is a well-known technique described, for example, in "RF Barber, EJ Candes, Controlling the False Discovery Rate Via Knockoffs, The Annals of Statistics, 2015, Vol. 43, No. 5, p. 2055-2085," a detailed explanation will be omitted here.

[0164] However, instead of using known techniques, for example, matrix S may be a diagonal matrix. In this case, the values ​​of the components contained in matrix S are 0 ≤ s q ≤2σ qq It may be defined in such a way. σ qq is the value of the diagonal element (the element at row q, column q) of the matrix Σ. By doing so, the positive semi-definite condition (2Σ-S≧0), which generally has to be solved as an off-diagonal matrix, can be easily satisfied, and the calculation of the knock-off variable can be performed efficiently.

[0165] As described above, even when creating data for noise explanatory variables such that the noise explanatory variables have conditional independence from the dependent variable based on the candidate explanatory variables, it is possible to create data for noise explanatory variables such that both the correlation of the noise explanatory variables with respect to the dependent variable is lower than the correlation of the candidate explanatory variables with respect to the dependent variable, and the statistical distribution of the noise explanatory variables is the same as or based on the statistical distribution of the candidate explanatory variables. In the following explanation, the knockoff variable is used to define the noise explanatory variable matrix X noise The method for calculating this will be referred to as the method for creating the second noise explanatory variable, as needed.

[0166] The first explanatory variable candidate group acquisition unit 110 uses either the first noise explanatory variable creation method or the second noise explanatory variable creation method to obtain the noise explanatory variable matrix X corresponding to the explanatory variable candidate matrix X. noise This is calculated for each of the multiple (or multiple sets of) candidate explanatory variable matrices X.

[0167] Next, the first explanatory variable candidate group acquisition unit 110 obtains an explanatory variable candidate matrix X and a noise explanatory variable matrix X corresponding to the explanatory variable candidate matrix X. noise The n' x 2p joined matrix X is formed by combining and . argmented (=[X,X noise ](∈R n' × 2p Calculate the combination matrix X in Figure 17. argmented The "1,2,···,p,p+1,p+2,···,2p" attached to the top represents the combination matrix X argmentedThis symbol indicates the column number. As shown in Figure 17, the combined matrix X argmented The first to p columns of the matrix contain the components of the first to p columns of the candidate explanatory variable matrix X, respectively, and the combined matrix X argmented The p+1 to 2p columns contain the noise explanatory variable matrix X. noise The components of columns 1 to p are stored respectively. The first explanatory variable candidate group acquisition unit 110 generates the above-described combined matrix X argmented This is calculated for each of the multiple (or multiple sets of) candidate explanatory variable matrices X.

[0168] Next, the first explanatory variable candidate group acquisition unit 110 generates the combined matrix X argmented And, in the first training data, the combination matrix X argmented The candidate explanatory variables x that make up the components of the explanatory variable candidate matrix X contained therein i1 ,x i2 ,···,x ip The target variable y is paired with the data. i Using the data, the regression coefficients of the regression equation showing the relationship between candidate explanatory variables, noise explanatory variables, the target variable, and are calculated. In this process, the first explanatory variable candidate group acquisition unit 110 performs a penalty-based regression analysis that can reduce the regression coefficients to zero. As described in the first embodiment, the penalty-based regression analysis that can reduce the regression coefficients to zero is a method that performs L1 regularization (regularization of the L1 norm).

[0169] Figure 18A shows the noise explanatory variable matrix X calculated using the first noise explanatory variable creation method. noise The join matrix X containing argmented This figure conceptually illustrates an example of a method for selecting the first explanatory variable candidate group when using [a specific method]. Figure 18B shows the noise explanatory variable matrix X calculated by the second noise explanatory variable creation method. noise The join matrix X containing argmented This figure conceptually illustrates one example of a method for selecting candidate first explanatory variables when using [a specific method / tool].

[0170] In Figures 18A and 18B, candidate explanatory variables and noise explanatory variables are shown, along with the target variable y. iThe regression equation showing the relationship between and is expressed by equation (10) below. As shown in equation (10), here we illustrate the case where the regression equation is a linear regression equation.

[0171]

number

[0172] In equation (10), the regression coefficient matrix B(∈R 2p × 1 ) is a 2p x 1 matrix that stores the regression coefficients for candidate explanatory variables and noise explanatory variables. The components of the first row, second row, ..., p row of the regression coefficient matrix B (regression coefficient b) i1 , b i2 , , , b ip ) are candidate explanatory variables x i1 , x i2 , , , x ip These are the regression coefficients for . Also, the components of the (p+1), (p+2), ..., and 2p) rows of the regression coefficient matrix B are (regression coefficient b ip+1 , b ip+2 , , , b i2p ) are the noise explanatory variables n, respectively. i1 , n i2 , , , n ip These are the regression coefficients for [the given value].

[0173] Next, the first explanatory variable candidate group acquisition unit 110 selects the candidate explanatory variable x i1 , x i2 , , , x ip Regression coefficient b for i1 , b i2 , , , b ip And the noise explanatory variable n i1 , n i2 , , , n ip Regression coefficient b for ip+1 , b ip+2 , , , b i2p Based on the results of comparing and , we calculate a group of candidate first explanatory variables.

[0174] In Figures 18A and 18B, the first explanatory variable candidate acquisition unit 110 acquires the regression coefficient b for the candidate explanatory variables included in the regression coefficient matrix B. i1 , b i2 , , , b ip p-row, 1-column explanatory variable regression coefficient matrix B that stores the regression coefficients. argmented (∈R p × 1 ) and the regression coefficient b for the noise explanatory variable ip+1 , b ip+2 , , , b i2p A p-row, 1-column noise explanatory variable regression coefficient matrix B that stores the noise explanatory variable. noise (∈R p × 1 ) and create . Note that here, b i The regression coefficient matrix B of the explanatory variables is such that the values ​​appended after (1, 2, ..., p, p+1, p+2, ..., 2p) are stored in rows with smaller row numbers as the regression coefficients become smaller. argmented and noise explanatory variable regression coefficient matrix B noise This is an example of when it is created.

[0175] In this embodiment, the first explanatory variable candidate group acquisition unit 110 acquires the explanatory variable regression coefficient matrix B argmented (∈R p × 1 ) and the noise explanatory variable regression coefficient matrix B noise (∈R p × 1 This example illustrates how to calculate multiple candidate first explanatory variables based on the results of comparing ) and .

[0176] First, referring to Figure 18A, the noise explanatory variable matrix X calculated using the first noise explanatory variable creation method is shown. noise This section describes an example of a method for calculating multiple candidate first explanatory variables when using [a specific method / tool].

[0177] The first explanatory variable candidate group acquisition unit 110 generates the noise explanatory variable regression coefficient matrix B noise The regression coefficient b for the noise explanatory variable stored in ip+1 , b ip+2 , , , b i2pThe absolute value of is calculated, and the maximum value of this absolute value is identified. In the following explanation, the maximum value of the absolute value identified in this way will be referred to as the maximum absolute value of the regression coefficient for the noise explanatory variable, as needed. In Figure 18A, max(|b ip+1 |,|b ip+2 |,···,|b i2p |) represents the regression coefficient b for the noise explanatory variable. ip+1 , b ip+2 , , , b i2p The absolute value of |b ip+1 |,|b ip+2 |, ···,|b i2p This symbol indicates that the maximum value of | is selected. The first explanatory variable candidate group acquisition unit 110 calculates max(|b ip+1 |,|b ip+2 |,···,|b i2p By performing the calculation of |), the maximum absolute value of the regression coefficient for the noise explanatory variable |b| max_noise Calculate.

[0178] Then, the first explanatory variable candidate group acquisition unit 110 generates the explanatory variable regression coefficient matrix B argmented Each component included (regression coefficient b for candidate explanatory variables) i1 , b i2 , , , b ip For each of the above, the absolute value of the component |b ik |b| is the maximum absolute value of the regression coefficient for the noise explanatory variable. max_noise It determines whether or not it exceeds [a certain value]. Then, the first explanatory variable candidate group acquisition unit 110 generates the explanatory variable regression coefficient matrix B argmented Regression coefficient b for candidate explanatory variables included in ik ( = b i1 , b i2 , , , b ip ) Among them, |b| is the maximum absolute value of the regression coefficient for the noise explanatory variable. max_noise The first explanatory variable candidate group is calculated to include candidates for explanatory variables that correspond to regression coefficients exceeding |b ik |>|b| max_noiseIn this case, the candidate explanatory variables stored in the k-th column of the explanatory variable candidate matrix X shown in Figure 17 are to be included as candidate explanatory variables in the first explanatory variable candidate group. Note that the explanatory variable regression coefficient matrix B argmented Regression coefficient b for candidate explanatory variables included in ik ( = b i1 , b i2 , , , b ip ) Among them, |b| is the maximum absolute value of the regression coefficient for the noise explanatory variable. max_noise Candidate explanatory variables corresponding to regression coefficients that do not exceed a certain threshold are not included in the first candidate explanatory variable group. The matrix that stores the candidate explanatory variables included in the first candidate explanatory variable group is the first candidate explanatory variable group matrix X. feature Therefore, the candidate matrix of the first explanatory variable X feature This can be expressed by equation (11) below.

[0179]

number

[0180] Note that the explanatory variable regression coefficient matrix B argmented Regression coefficient b for candidate explanatory variables included in i1 , b i2 , , , b ip The absolute value of |b ik |b| is the maximum absolute value of the regression coefficient for the noise explanatory variable. max_noise Instead of whether it exceeds or exceeds, the explanatory variable regression coefficient matrix B argmented Regression coefficient b for candidate explanatory variables included in i1 , b i2 , , , b ip The absolute value of |b ik |b| is the maximum absolute value of the regression coefficient for the noise explanatory variable. max_noise You may also determine whether or not the condition is greater than or equal to the above.

[0181] Next, referring to Figure 18B, we obtain the noise explanatory variable matrix X calculated using the second noise explanatory variable creation method. noise This section describes an example of a method for calculating multiple candidate first explanatory variables when using [a specific method / tool].

[0182] The first explanatory variable candidate acquisition unit 110 generates the regression coefficient b for the explanatory variable candidate. i1 , b i2 , , , b ip One of the regression coefficients b ik And, the noise explanatory variable regression coefficient matrix B noise Among the regression coefficients for the noise explanatory variable stored in, the regression coefficient b for the candidate explanatory variable is ik The corresponding regression coefficient b ik+p Extract and their absolute values ​​|b ik |, |b ik+p Calculate | (k is an integer between 1 and p). Note that the noise explanatory variable regression coefficient matrix B noise Among the regression coefficients for the noise explanatory variable stored in, the regression coefficient b for the candidate explanatory variable ik The corresponding regression coefficient b ik+p The candidate x for the explanatory variable is ik The noise explanatory variable n was calculated as the corresponding knockoff variable. ik These are the regression coefficients for [the given value].

[0183] The first explanatory variable candidate acquisition unit 110 obtains the absolute value of the regression coefficient for the candidate explanatory variable |b ik |From this, the regression coefficient b ik Regression coefficient b for the corresponding noise explanatory variable ik+p The absolute value of |b ik+p The value obtained by subtracting | (||W i :=||=|b ik |-|b ik+p This determines whether |) exceeds the threshold Thred. The threshold Thred is a threshold determined from the data based on statistics so as to satisfy a pre-set FDR (False Discovery Rate) value q_fdr. Specifically, for a certain positive threshold s, #[i: W i <-s], W i <- s is the number of occurrences, and #[s: W i ≥s] to W i Assuming that the number of occurrences is ≥ s, the threshold Thered is determined such that it satisfies equation (12) below.

[0184]

number

[0185] Then, the first explanatory variable candidate acquisition unit 110 obtains the absolute value of the regression coefficient for the explanatory variable candidate |b ik |From this, the regression coefficient b ik Regression coefficient b for the corresponding noise explanatory variable ik+p The absolute value of |b ik+p The value obtained by subtracting | (=|b) ik |-|b ik+p If |) exceeds the threshold Thred, the regression coefficient b ik If a candidate explanatory variable corresponding to [the specified value] is not included in the first candidate group of explanatory variables, it is determined that the regression coefficient b is included. ik We determine that the candidate explanatory variable corresponding to this is not to be included in the first candidate explanatory variable group.

[0186] The first explanatory variable candidate group acquisition unit 110 determines whether or not to include each candidate explanatory variable in the first explanatory variable candidate group in the manner described above. The matrix that stores the candidate explanatory variables included in the first explanatory variable candidate group is the first explanatory variable candidate group matrix X. feature Therefore, the candidate matrix of the first explanatory variable X feature This can be expressed by equation (13) below.

[0187]

number

[0188] Note that the absolute value of the regression coefficient for the candidate explanatory variable |b ik |From this, the regression coefficient b ik Regression coefficient b for the corresponding noise explanatory variable ik+p The absolute value of |b ik+p The value obtained by subtracting | (=|b) ik |-|b ik+p Instead of determining whether |) exceeds the threshold Thred, use the absolute value of the regression coefficient |b for the candidate explanatory variable. ik |From this, the regression coefficient b ik Regression coefficient b for the corresponding noise explanatory variable ik+pThe absolute value of |b ik+p The value obtained by subtracting | (=|b) ik |-|b ik+p You can also determine whether |) is equal to or greater than the threshold Thred.

[0189] The first explanatory variable candidate group acquisition unit 110 then generates the first explanatory variable candidate group matrix X as described above. feature This process is performed for each of the multiple samples (multiple candidate explanatory variable matrices X). In this embodiment, the frequency calculation unit 120 calculates the multiple first explanatory variable candidate group matrices X that are created for each of the multiple samples (multiple explanatory variable candidate matrices X) as described above. feature The frequency of occurrence of candidate explanatory variables included in the expression is calculated using candidate explanatory variables x1, x2, ...x p This is done for each of them. The processing of the occurrence frequency calculation unit 120 itself is implemented, for example, by the processing described in the first embodiment.

[0190] [summary] In the first embodiment, the regression coefficient b for the candidate explanatory variable i1 , b i2 , , , b ip Among these, candidates for explanatory variables that are not zero are included in the first group of candidate explanatory variables. In contrast, in this embodiment, the regression coefficient b for the candidate explanatory variables i1 , b i2 , , , b ip Even among candidate explanatory variables that are not zero, those whose influence on the dependent variable is small compared to the regression coefficients for the noise explanatory variables are not included in the first group of candidate explanatory variables. Therefore, it is possible to further suppress the selection of candidate explanatory variables that are not suitable for explaining the dependent variable. Furthermore, if the first learning model is a linear regression model, a statistically meaningful threshold (Thred) can be used by creating the noise explanatory variable data (knockoff variable data in this embodiment) such that the noise explanatory variables have conditional independence from the dependent variable based on the candidate explanatory variables. In addition, various modifications described in the first to third embodiments may also be adopted in this embodiment.

[0191] (Fifth embodiment) Next, a fifth embodiment will be described. In the first embodiment, the first explanatory variable selection unit 170 selects explanatory variables in the first learning model. In this embodiment, based on the explanatory variables thus selected, candidate explanatory variables suitable for explaining the target variable y are further selected as explanatory variables in the first learning model. Thus, the main difference between this embodiment and the first to fourth embodiments is the process for selecting explanatory variables in the first learning model. Therefore, in describing this embodiment, parts that are the same as those in the first to fourth embodiments will be denoted by the same reference numerals as those used in Figures 1 to 18, and detailed explanations will be omitted.

[0192] Figure 19A shows an example of the functional configuration of the processing unit 1900 of this embodiment. Since the processing unit 1900 is implemented with the same hardware configuration as the processing unit 100 described in the first embodiment, a detailed explanation of the hardware configuration of the processing unit 1900 is omitted here. Figure 20 is a flowchart illustrating an example of a processing method performed using the processing unit 1900 of this embodiment.

[0193] In Figure 19A, this embodiment illustrates a case where the processing unit 1900 includes a first explanatory variable candidate group acquisition unit 110, an occurrence frequency calculation unit 120, a second explanatory variable candidate group creation unit 130, a first learning model candidate creation unit 140, a first evaluation index calculation unit 150, a first relationship calculation unit 160, a first explanatory variable selection unit 170, a second explanatory variable selection unit 1910, and an output unit 180. Thus, in this embodiment, the processing unit 1900 illustrates a case where a second explanatory variable selection unit 1910 is added to the processing unit 100 described in the first embodiment. The first and second examples of the second explanatory variable selection unit 1910 are described below.

[0194] [Example 1] [Second explanatory variable selection process (S2001), second explanatory variable selection unit 1910] The second explanatory variable selection unit 1910 calculates a correlation index representing the correlation between the explanatory variable and the candidate explanatory variable, based on the data of at least one explanatory variable selected by the first explanatory variable selection unit 170 (as an explanatory variable in the first learning model) and the data of candidate explanatory variables not selected by the first explanatory variable selection unit 170. Based on the value of the correlation index, it selects an explanatory variable for the first learning model from the candidate explanatory variable. Here again, as shown in the first embodiment, the number of predetermined candidate explanatory variables is p. Also, the number of explanatory variables selected by the first explanatory variable selection unit 170 is p1. In this case, the number of candidate explanatory variables not selected by the first explanatory variable selection unit 170, p2, is p-p1.

[0195] For example, the second explanatory variable selection unit 1910 may calculate a correlation coefficient R as a correlation index representing the correlation between the explanatory variable and the candidate explanatory variable, based on the data of the explanatory variable selected by the first explanatory variable selection unit 170 and the data of the candidate explanatory variable that was not selected by the first explanatory variable selection unit 170, and (further) select candidate explanatory variables as explanatory variables in the first learning model if the correlation coefficient R exceeds (or is greater than or equal to) a threshold. This may be done for each of the explanatory variables selected by the first explanatory variable selection unit 170.

[0196] However, the relationship between the explanatory variables selected by the first explanatory variable selection unit 170 and the candidate explanatory variables not selected by the first explanatory variable selection unit 170 may be nonlinear. Also, the data for the explanatory variables selected by the first explanatory variable selection unit 170 and the data for the candidate explanatory variables not selected by the first explanatory variable selection unit 170 may contain many outliers. In these cases, it is preferable to use rank correlation as the correlation between the explanatory variables selected by the first explanatory variable selection unit 170 and the candidate explanatory variables not selected by the first explanatory variable selection unit 170. In this case, the correlation index may be, for example, the rank correlation coefficient. More specifically, the rank correlation coefficient may be, for example, Spearman's rank correlation coefficient or Kendall's rank correlation coefficient. In this case, the second explanatory variable selection unit 1910 further selects candidate explanatory variables whose rank correlation coefficient exceeds (or is greater than or equal to) a threshold as explanatory variables in the first learning model. The second explanatory variable selection unit 1910 may perform such selection of explanatory variables for all of the explanatory variables selected by the first explanatory variable selection unit 170, or for some of the explanatory variables selected by the first explanatory variable selection unit 170. In this example, in the latter case (where the second explanatory variable selection unit 1910 performs selection for some of the explanatory variables selected by the first explanatory variable selection unit 170), for example, the user (human) may select those some explanatory variables based on the number of explanatory variables - first evaluation index relationship information 370.

[0197] Furthermore, even if there is a high correlation between the explanatory variables selected by the first explanatory variable selection unit 170 and the candidate explanatory variables that were not selected, it may not actually be necessary to include those candidates in the first learning model. For example, if the explanatory variable is the abundance (number of reads) of a microbial group, standardization may cause even microbial groups with small abundances during the sampling period to show large relative fluctuations, leading to them being selected as excessively important variables. However, in reality, such microbial groups are often small in abundance and their impact on the processing process can be ignored. Therefore, the second explanatory variable selection unit 1910 may further select explanatory variables in the first learning model based on a correlation index representing the correlation between the explanatory variables selected by the first explanatory variable selection unit 170 and the candidate explanatory variables that were not selected by the first explanatory variable selection unit 170, and the values ​​of the candidate explanatory variables. In this case, the second explanatory variable selection unit 1910 may (further) select candidate explanatory variables in the first learning model, for example, those whose correlation index (e.g., rank correlation coefficient) exceeds (or is greater than or equal to) a threshold, and whose sum of the absolute values ​​of the data values ​​exceeds (or is greater than or equal to) a threshold. Alternatively, instead of the sum of the absolute values ​​of the data values, the maximum value, median, or mean may be used. The second explanatory variable selection unit 1910 may perform such selection of explanatory variables for all of the explanatory variables selected by the first explanatory variable selection unit 170, or for some of the explanatory variables selected by the first explanatory variable selection unit 170.

[0198] [Second example] [Second explanatory variable selection process (S2001), second explanatory variable selection unit 1910] Figure 19B shows an example of a more detailed functional configuration of the second explanatory variable selection unit 1910 (functional configuration in the second example). In Figure 19B (second example), the second explanatory variable selection unit 1910 is illustrated as having a selected explanatory variable group creation unit 1911, a second learning model creation unit 1912, a regression equation calculation unit for model evaluation 1913, a second evaluation index calculation unit 1914, a second relationship calculation unit 1915, and an explanatory variable additional selection unit 1916.

[0199] [[Selected explanatory variable group creation unit 1911]] The selected explanatory variable group creation unit 1911 creates multiple selected explanatory variable groups, each containing one or more explanatory variables from those selected by the first explanatory variable selection unit 170. Here, the number of explanatory variables selected by the first explanatory variable selection unit 170 is denoted as W. Details will be described later in the section [Specific example of the processing of the second explanatory variable selection step (S2001) in the second example], but in this embodiment, we will illustrate the case in which the selected explanatory variable group creation unit 1911 sequentially creates multiple selected explanatory variable groups, each containing 1, 2, ..., W explanatory variables. In this case, no two selected explanatory variable groups contain the same explanatory variables.

[0200] Figure 21 shows an example of the relationship between the number of explanatory variables and the first evaluation index (2100). In Figure 21, the coefficient of determination R 2 The example shows a case where the value of is greater than or equal to the threshold Th2 (=0.92 (see dashed line in Figure 21)). Also, in Figure 21, the first explanatory variable selection unit 170 selects the local peak 2101 where the number of microbial groups is smallest, and the coefficient of determination R at the local peak 2101 is selected. 2 Eight explanatory variables (Denovo201, Denovo2512, Denovo1302, Denovo110, Denovo580, Denovo249, Denovo100, Denovo546) corresponding to the above have been selected. In this case, W=8.

[0201] [[Second Learning Model Creation Section 1912]] The second learning model creation unit 1912 creates multiple second learning models for each of the multiple selected explanatory variable groups, which show the relationship between the explanatory variables included in the selected explanatory variable group created by the selected explanatory variable group creation unit 1911 and the target variable. The second learning model may be a linear regression equation, a nonlinear regression equation, another machine learning model (such as a neural network), or AI (artificial intelligence). Furthermore, the second learning model may be a surrogate model or a model that estimates phenomena other than physical phenomena. Thus, the second learning model is not limited, but in this embodiment, for the sake of simplicity, we will illustrate the case where the second learning model is a linear regression equation as shown in equation (14) below.

[0202]

number

[0203] For the sake of explanation and notation, the notation for i, the variable that identifies the first learning model, will be omitted here. Also, y e is the dependent variable (estimated value). Note that y e The value of e represents an estimated value. An estimated value is the value of the target variable calculated by the second learning model (regression equation). Also, x j x is an explanatory variable. In equation (14), the explanatory variable x that is not included in the selected group of explanatory variables is... j The value becomes 0 (zero).

[0204] a j The explanatory variable x i These are the regression coefficients for . p is the number of explanatory variables. Explanatory variables x that are not included in the selected group of explanatory variables. j If the number is 1, equation (14) is a simple regression equation; if it is 2 or more, equation (14) is a multiple regression equation. b is the intercept.

[0205] [[Model evaluation regression equation calculation unit 1913]] The model evaluation regression equation calculation unit 1913 calculates estimated data for the target variable based on the data of the explanatory variables included in the selected explanatory variable group created by the selected explanatory variable group creation unit 1911 and the second learning model created by the second learning model creation unit 1912. Then, the model evaluation regression equation calculation unit 1913 uses the estimated data for the target variable and the data of the target variable that is paired with the data of the explanatory variable (in the first learning data) to calculate a model evaluation regression equation, which is a linear regression equation showing the relationship between the ground truth value, which is the value of the data of the target variable, and the estimated value, which is the value of the estimated data of the target variable calculated by the second learning model.

[0206] In the first training data, the data of the target variable paired with the data of the explanatory variables included in the selected explanatory variable group created by the selected explanatory variable group creation unit 1911 becomes the ground truth data for the target variable in the second training model. The regression equation for model evaluation is, for example, the ground truth value y, which is the value of the ground truth data for the target variable in the second training model. t And the estimated value y, which is the data value of the target variable calculated by the second learning model. e This is a linear regression equation showing the relationship between and . The regression equation for model evaluation is, for example, represented by equation (15) below. In the following explanation, the ground truth value y is the ground truth value of the target variable in the second learning model. t If necessary, the correct value y of the target variable in the second learning model. t , or the correct value y of the dependent variable t This is referred to as [the model name]. Furthermore, in the following explanation, the estimated value y is the value of the target variable calculated by the learning model. e If necessary, the estimated value of the target variable y in the second learning model e It is called that.

[0207]

number

[0208] Here, c is the regression coefficient, and d is the intercept. The intercept d does not have to be 0 (zero), but in this embodiment, when the intercept d is 0 (zero), (i.e., the regression equation for model evaluation is y) e =cy t This example illustrates the case where...

[0209] The regression equation calculation unit 1913 for model evaluation calculates the explanatory variable x included in the first training data. g By providing the data values ​​to the second learning model, the estimated value of the target variable y in the second learning model can be obtained. e The model evaluation regression equation calculation unit 1913 then calculates the estimated value y of the dependent variable. e And, in the first training data, the estimated value of the target variable y e Explanatory variables x1~x used in the calculation p The correct value of the target variable y, paired with the data. t A second set of L-type training data is created, consisting of a set of data including and .

[0210] The regression equation calculation unit 1913 for model evaluation may standardize or normalize the second training data when creating the second training data. The standardization or normalization method itself may be the same as when standardizing or normalizing the first training data. Note that the second training data may be standardized or normalized regardless of whether the first training data has been standardized or normalized. Also, the first training data may be standardized or normalized regardless of whether the second training data has been standardized or normalized. Furthermore, one of the first and second training data may be standardized and the other normalized.

[0211] The regression equation calculation unit 1913 for model evaluation calculates the second training data (estimated value of the target variable y). e and the correct value y tThe regression equation (regression coefficient c) for model evaluation is calculated using the set of (15). Note that the method for calculating the regression coefficient c using the training data is achieved by using known regression analysis methods such as the least squares method, so a detailed explanation is omitted here. Here, the case where the intercept d of equation (15) is 0 (zero) is given as an example, so the regression equation calculation unit 1913 for model evaluation performs regression analysis with the intercept d fixed at 0 (zero). If the intercept d of equation (15) is not 0 (zero), the regression equation calculation unit 1913 for model evaluation also calculates the value of the intercept d.

[0212] [[Second Evaluation Index Calculation Unit 1914]] The second evaluation index calculation unit 1914 calculates a second evaluation index for evaluating the second learning model for each of the multiple second learning models. The second evaluation index includes a variability evaluation index V and a gradient evaluation index grad. The variability evaluation index V is an index that represents the variability of the estimated data of the target variable from the regression equation for model evaluation. The gradient evaluation index grad is an index that represents the gradient (slope) of the regression equation for model evaluation.

[0213] Figure 22 illustrates an example of the variability evaluation index V and the gradient evaluation index grad. Figure 22(a) illustrates the case where the second training data is represented by points (black circles (●)) in a two-dimensional Cartesian coordinate system. The horizontal axis (first axis) of the two-dimensional Cartesian coordinate system represents the ground truth value y of the target variable in the second training model. t This axis represents the y-axis of the 2D Cartesian coordinate system. The vertical axis (second axis) of the 2D Cartesian coordinate system represents the estimated value of the target variable y in the second learning model. e This is the axis that indicates [something].

[0214] The black circles (●) in Figure 22(a) represent the correct values ​​of the target variable y in the second learning model. t And, in the first training data, the correct value y t The corresponding explanatory variable x g By substituting the data values ​​into the second learning model, the estimated value of the target variable y calculated by the second learning model is obtained. e This is the point that is determined from that.

[0215] Here, the estimated value y of the target variable in the second learning model is included in the l-th set of second learning data from the L-set of second learning data. e to y e1_l This will be the notation. Also, the correct value y of the target variable in the second learning model included in the second training data of the l-th set. t to y t_l This is expressed as follows, and the mean of the L correct values ​​of the target variable in the second learning model is y- t This will be the notation. Also, the correct value y of the target variable in the second learning model included in the second training data of the l-th set. t_l The estimated value of the dependent variable y is calculated by substituting this into the regression equation for model evaluation. e to, y e2_l We will use this notation. Then, the variability evaluation index V can be expressed, for example, by equation (16) below. Equation (16) illustrates a case where a larger value of the variability evaluation index V (closer to 1) indicates a smaller degree of variability from the regression equation used for model evaluation of the second training data. y- t In equation (16), y t This corresponds to the symbol with a hyphen above the 't' (this notation is the same for other symbols as well).

[0216]

number

[0217] Here, the expression in parentheses in the denominator of equation (16) is an example of the first variation, and the expression in parentheses in the numerator is an example of the second variation. The first variation is, for example, the estimated value y of the target variable included in the second training data. e1_l And the mean value of the target variable y- t It is expressed using the difference between and . The second variation is, for example, the estimated value y of the target variable included in the second training data. e1_l And, in the second training data, the estimated value of the target variable y e1_l The correct value y of the dependent variable paired with this t_l The estimated value of the dependent variable y is calculated by substituting this into the regression equation for model evaluation (Equation (15)). e2_lThe difference between and the correct value y of the target variable in the second learning model. t_l The estimated value of the dependent variable y is calculated by substituting it into the regression equation for model evaluation. e2_l And the mean value of the target variable y- t It is expressed using the difference between and and one of . More specifically, equation (16) illustrates a case where the variability evaluation index V is expressed using the ratio of the value obtained by summing the square of the first variation over all sets of the second training data (=L) to the value obtained by summing the square of the first variation over all sets of the second training data (=L). However, the variability evaluation index V does not necessarily have to be expressed in this way. For example, instead of the square of the first variation and the square of the second variation, the square root of the square of the first variation and the square root of the square of the second variation may be used, respectively. The gradient evaluation index grad is represented by the gradient of the learning model (regression equation for model evaluation) 2211 (the regression coefficient c in equation (15)).

[0218] Here, the variability evaluation index V and the gradient evaluation index grad are used, and the coefficient of determination R is used. 2 The difference between the two will be explained. Figure 22(b) shows the coefficient of determination R 2 This is a diagram illustrating this. In Figure 22(b), for the sake of simplicity, we illustrate the case where the learning model 2221 is a linear simple regression equation represented by equation (17) below.

[0219]

number

[0220] Figure 22(a) illustrates the case where the second training data is represented by points (black circles (●)) on a two-dimensional Cartesian coordinate system. On the other hand, Figure 22(b) illustrates the case where the first training data is represented by points (black circles (●)) on a two-dimensional Cartesian coordinate system. The horizontal axis (first axis) of the two-dimensional Cartesian coordinate system represents the data values ​​of the explanatory variable x1 in the training models 2211 and 2221. The vertical axis (second axis) of the two-dimensional Cartesian coordinate system represents the estimated value y of the dependent variable in the training model (regression equation for model evaluation) 2211 and the training model (simple regression equation) 2221. e This is the axis that indicates [something].

[0221] The black circles (●) in Figure 22(b) represent the data values ​​of the explanatory variable x1 included in the first training data, and the correct values ​​y of the target variable corresponding to the data of explanatory variable x1 in the first training data. t This is the point that is determined from that.

[0222] Here, the data value of the explanatory variable x1 in the learning model 2211 is included in the first training data of the l-th set of the first training data of the L-set set. 1_t_l This will be the notation. Also, the correct value y of the target variable in the learning model 2211 included in the first training data of the l-th set. t to y t_l We will use this notation. Then, the coefficient of determination R 2 This can be expressed, for example, by equation (18) below.

[0223]

number

[0224] The denominator of equation (18) represents the total variation. The middle numerator of equation (18) represents the residual variation. The last numerator of equation (18) represents the regression variation. As described above, the coefficient of determination R 2 While the first training data is an index representing the variability of the learning model (simple regression equation) 2221, the variability evaluation index V is an index representing the variability of the second training data for the learning model (regression equation for model evaluation) 2211.

[0225] The inventors have found that when the learning model is a linear regression equation, if the gradient evaluation index grad is non-negative (or positive), the variability evaluation index V is equal to the coefficient of determination R 2 Since this is in close agreement, we obtained the finding that the learning model can be evaluated by using the variability evaluation index V. That is, under the condition that the gradient evaluation index grad is non-negative (or positive), the larger the value of the variability evaluation index V, the better the estimated value of the target variable y in the second learning model. eThe reliability is high (the dependent variable is well explained by the explanatory variables).

[0226] On the other hand, if the gradient evaluation index grad is negative (or less than or equal to 0 (zero)), the coefficient of determination R 2 Since it tends to be a negative value, if the gradient evaluation index grad is negative (or less than or equal to 0 (zero)), the coefficient of determination R 2 By using this method, it is not easy to accurately evaluate the variability of the first training data, but by using the variability evaluation index V, the variability of the second training model can be expressed as (coefficient of determination R 2 We found that evaluation can be performed more easily and accurately than when using [another method].

[0227] Thus, the inventors have determined the coefficient of determination R 2 While it is not possible to evaluate the nonlinear regression equation using the method described above, we found that by using the variability evaluation index V and the gradient evaluation index grad, if the variability of the second training data is small relative to the regression equation used for model evaluation (nonlinear regression equation), the variability evaluation index V approaches 1. Therefore, the nonlinear regression equation can be evaluated using the variability evaluation index V.

[0228] Based on the above, this embodiment illustrates a case in which the second evaluation index calculation unit 1914 calculates a variability evaluation index V and a gradient evaluation index grad as second evaluation indices for evaluating the second learning model. The second evaluation index calculation unit 1914 calculates the second evaluation indices (variability evaluation index V and gradient evaluation index grad) for each of the multiple second learning models created by the second learning model creation unit 1912 as described above. While it is preferable to calculate the variability evaluation index V and the gradient evaluation index grad as second evaluation indices for evaluating the second learning model, the second evaluation indices are not limited to the variability evaluation index V and the gradient evaluation index grad. For example, when evaluating a linear regression equation, the coefficient of determination R 2 This can also be used as a second evaluation indicator.

[0229] [[Second Relationship Calculation Unit 1915]] The second relationship calculation unit 1915 calculates the relationship information between the number of explanatory variables and the second evaluation index. This relationship information shows the relationship between the number of explanatory variables included in the second learning model created by the second learning model creation unit 1912 and the second evaluation index (in this embodiment, the variability evaluation index) for the second learning model calculated by the second evaluation index calculation unit 1914. Figure 23 shows an example of the relationship information between the number of explanatory variables and the second evaluation index 2300. The number of microbial communities on the horizontal axis of Figure 23 is the number of microbial communities included as explanatory variables in the second learning model created by the second learning model creation unit 1912 using eight explanatory variables (Denovo201, Denovo2512, Denovo1302, Denovo110, Denovo580, Denovo249, Denovo100, Denovo546) selected based on the explanatory variable number-first evaluation index relation information 2100 shown in Figure 21 (the explanatory variables themselves are factors related to the quantity of microbial communities). Furthermore, although the details will be described later in the section [Specific example of processing of the second explanatory variable selection step (S2001) in the second example], the variability evaluation index V on the vertical axis of Figure 23 is the variability evaluation index V that represents the minimum degree of variability among the variability evaluation index V paired with the gradient evaluation index grad, which represents that the gradient of the regression equation for model evaluation is non-negative (it is the variability evaluation index V with the maximum value in equation (16)). This variability evaluation index V (variability evaluation index V on the vertical axis in Figure 23) is calculated for each case of the number of explanatory variables in the second learning model (each case of w = 1, 2, 3, 4, 5, 6, 7, and 8 in the second learning model in equation (14)). The number of microbial communities on the horizontal axis in Figure 23 is the number of microbial communities included as explanatory variables in the second learning model, which are evaluated by the variability evaluation index V.

[0230] [[Explanatory variable addition / selection section 1916]] The explanatory variable addition selection unit 1916 selects explanatory variables from the explanatory variables selected by the first explanatory variable selection unit 170, based on the explanatory variable number-second evaluation index relationship information calculated by the second relationship calculation unit 1915, to be used for calculating the correlation index described above in the section [First Example].

[0231] In this embodiment, the explanatory variable addition selection unit 1916 selects, as an example, an explanatory variable to be used to calculate the correlation index, from among the second learning models that have (as the number of explanatory variables) the number of explanatory variables that cause an increase or decrease in the variability evaluation index in the explanatory variable number-second evaluation index relationship information, and which was used when calculating the explanatory variable number-second evaluation index relationship information. An increase or decrease in the variability evaluation index refers to a change in the ratio of the change in the variability evaluation index to the change in the number of explanatory variables in the explanatory variable number-second evaluation index relationship information from positive to 0 (zero) or negative, or from negative to 0 (zero) or positive. For example, an increase or decrease in the variability evaluation index is represented by a change in the slope of a straight line determined by the values ​​of two variability evaluation indices that are adjacent to each other in the explanatory variable number-second evaluation index relationship information, from positive to 0 (zero) or negative, or from negative to 0 (zero) or positive. Furthermore, changes in the variability evaluation index may be represented by a graph showing the relationship between the number of explanatory variables and the second evaluation index, obtained by performing curve fitting or similar methods. In this case, changes in the variability evaluation index may be represented by the slope (derivative value) of the graph changing from positive to 0 (zero) or negative, or from negative to 0 (zero) or positive.

[0232] The explanatory variable addition selection unit 1916 may select explanatory variables to be used in calculating the correlation index as follows. First, the explanatory variable addition selection unit 1916 calculates the number of explanatory variables when the variability evaluation index increases or decreases in the explanatory variable number-second evaluation index relationship information. Note that when calculating a graph showing the explanatory variable number-second evaluation index relationship information as described above, the number of explanatory variables when the variability evaluation index increases or decreases in the graph may not be an integer. In this case, for example, the smallest integer greater than the number of explanatory variables when the variability evaluation index increases or decreases in the graph, or the largest integer less than the number of explanatory variables when the variability evaluation index increases or decreases in the graph, may be calculated as the number of explanatory variables when the variability evaluation index increases or decreases.

[0233] Then, the explanatory variable addition selection unit 1916 selects the explanatory variables included in the second learning model used when calculating the explanatory variable number-second evaluation index relationship information from among the second learning models having the number of explanatory variables calculated as described above (as the number of explanatory variables), and uses them as explanatory variables to be used for calculating the correlation index. The second learning model used when calculating the explanatory variable number-second evaluation index relationship information is a second learning model evaluated by the variability evaluation index V, which is paired with the gradient evaluation index grad, which indicates that the gradient of the regression equation for model evaluation is non-negative, and which indicates that the degree of variability is minimized.

[0234] In the example shown in Figure 23, the number of microbial groups (explanatory variables) whose variation evaluation index V increases or decreases is 4 in the explanatory variable number-second evaluation index relationship information 2300 (the case where the variation evaluation index increases or decreases at point 2301). The explanatory variable addition and selection unit 1916 selects the explanatory variables included in the second learning model used when calculating the explanatory variable number-second evaluation index relationship information as explanatory variables to be used in calculating the correlation index.

[0235] As described above, in the region where the absolute value of the variability evaluation index V increases in the explanatory variable number-second evaluation index relationship information 2300, explanatory variables that are correlated (rank correlation in this embodiment) with the explanatory variables included in the second learning model can contribute to the improvement of the first learning model (i.e., explanatory variables that are correlated with the explanatory variables included in the second learning model become explanatory variables that better explain the target variable in the first learning model). On the other hand, in the region where the absolute value of the variability evaluation index V does not increase (i.e., remains flat or decreases) in the explanatory variable number-second evaluation index relationship information 2300, adding explanatory variables that are correlated (rank correlation in this embodiment) with the explanatory variables included in the second learning model may not contribute to the improvement of the first learning model and may result in the adverse effects of multicollinearity. Therefore, in this embodiment, we focus on the change in the increase or decrease of the variability evaluation index in the explanatory variable number-second evaluation index relationship information, and illustrate a case in which the explanatory variable addition selection unit 1916 selects as explanatory variables to be used for calculating the correlation index from among the second learning models that have the number of explanatory variables (as the number of explanatory variables) for which the increase or decrease of the variability evaluation index in the explanatory variable number-second evaluation index relationship information is changed, and which were included in the second learning model used when calculating the explanatory variable number-second evaluation index relationship information.

[0236] Figure 23 illustrates a case in the explanatory variable-second evaluation index relationship information 2300 where the value of the variability evaluation index V increases and then decreases as the number of microbial groups (explanatory variables) increases. However, the relationship between the number of explanatory variables and the increase or decrease of the variability evaluation index V in the explanatory variable-second evaluation index relationship information is not limited to this relationship. For example, if the value obtained by multiplying the right-hand side of equation (16) by (-1) is used as the variability evaluation index, the value of the variability evaluation index V decreases and then increases as the number of microbial groups (explanatory variables) increases.

[0237] Figure 24 conceptually illustrates an example of a method for selecting explanatory variables in the first learning model. In Figure 24, four explanatory variables (Denovo201, Denovo2512, Denovo1302, Denovo110, Denovo580, Denovo249, Denovo100, Denovo546) selected by the first explanatory variable selection unit 170 are chosen by the explanatory variable addition selection unit 1916 based on the explanatory variable number - second evaluation index relationship information 2300, and these four variables are used as explanatory variables for calculating the correlation index. As shown in Figure 24, explanatory variables with a high frequency of occurrence (microbial groups) are not necessarily selected as explanatory variables for calculating the correlation index.

[0238] The explanatory variable addition selection unit 1916 calculates a correlation index representing the correlation between the explanatory variable selected as an explanatory variable to be used for calculating the correlation index as described above, and candidate explanatory variable data not selected by the first explanatory variable selection unit 170, and selects an explanatory variable for the first learning model from the candidate explanatory variable based on the value of the correlation index. This process itself is the same as the process described above in the section on [First Example].

[0239] Figure 24 illustrates a case in which candidate explanatory variables not selected by the first explanatory variable selection unit 170 are further selected as explanatory variables in the first learning model if their rank correlation coefficient with the explanatory variables selected by the additional explanatory variable selection unit 1916 (Denovo201, Denovo2512, Denovo1302, Denovo110) is 0.750 or higher, and they have more than 1000 reads. Specifically, Figure 24 shows that Denovo119 is selected as a candidate explanatory variable with a rank correlation coefficient of 0.750 or higher with Denovo201 and more than 1000 reads, and that Denovo867 is selected as a candidate explanatory variable with a rank correlation coefficient of 0.750 or higher with Denovo2512 and more than 1000 reads.

[0240] Furthermore, the candidate data for explanatory variables that are compared with the data of the explanatory variable selected by the explanatory variable addition selection unit 1916 for use in calculating the correlation index may include data for explanatory variables other than those selected by the first explanatory variable selection unit 170.

[0241] [Specific example of the second explanatory variable selection step (S2001) in the second example] Next, a specific example of the process for selecting explanatory variables to be used in calculating a correlation index (rank correlation coefficient in this embodiment) from the explanatory variables selected by the first explanatory variable selection unit 170 will be described below. In this embodiment, we illustrate the case where a stepwise forward selection method (variable increase method), a type of sequential feature selection method, is used as a method for selecting (narrowing down) the explanatory variables to be used for calculating the correlation index from the explanatory variables selected by the first explanatory variable selection unit 170. However, the method for selecting the explanatory variables to be used for calculating the correlation index from the explanatory variables selected by the first explanatory variable selection unit 170 is not limited to the stepwise forward selection method (variable increase method). For example, a variable decrease method, a variable increase / decrease method, or a variable decrease / increase method may be used. However, in the sequential feature selection method, factors (explanatory variables in this embodiment) that have been selected once are not re-evaluated. Therefore, there is a risk that the factors selected initially will greatly influence the factors selected in the end. In this case, there is a risk that the factors selected in the end will be a local optimum. Therefore, in this embodiment, we illustrate the case where a second evaluation index (variability evaluation index V and gradient evaluation index grad) is used to select the factors (explanatory variables in this embodiment) to suppress the convergence of the factors selected in the end to an undesirable local optimum. In other words, this embodiment illustrates a case where the selection conditions for factors (explanatory variables in this embodiment) in an algorithm such as the variable augmentation method are conditions using a second evaluation index (variability evaluation index V and gradient evaluation index grad). Below, a specific example of the selection process for sequentially selecting explanatory variables to be used in calculating the correlation index is described. As mentioned above in the section on [[Selected Explanatory Variable Group Creation Unit 1911]], here, the number of explanatory variables selected by the first explanatory variable selection unit 170 is denoted as W.

[0242] [[First selection process]] First, the selected explanatory variable group creation unit 1911 selects one of the W explanatory variables to be included in the selected explanatory variable group for each of the W explanatory variables. This creates a group of W selected explanatory variables. In the first selection process, we will illustrate the case where the number of explanatory variables included in each of the W selected explanatory variable groups is 1 (i.e., the number of explanatory variables selected in the first selection process (initial value of the number of explanatory variables) is 1).

[0243] Then, the second learning model creation unit 1912 calculates the second learning model (equation (14)) as a simple linear regression equation using the first learning data, individually for each of the W explanatory variables. In this way, W second learning models (simple linear regression equations) are calculated.

[0244] Here, let x be one of the W explanatory variables. r This is how it is written. The first training data contains explanatory variables x1~x, which include W explanatory variables. p The data and the explanatory variables x1~x p The correct value of the dependent variable y explained by t This includes the explanatory variable x. r When calculating a second learning model that has as an explanatory variable x, the second learning model creation unit 1912 calculates the explanatory variable x included in the first learning data. r The data and the correct value y of the target variable paired with that data in the first training data. t By using this as a set of training data, a second learning model is calculated.

[0245] The second learning model in the first selection process is represented, for example, by equation (19) below. As shown in equation (19) below, in this embodiment, we illustrate the case where the second learning model in the first selection process is a simple linear regression equation (equation (19) is expressed in equation (14) as x j (This is rewritten as a simple linear regression equation, excluding the part where the expression is 0 (zero).)

[0246]

number

[0247] The regression equation calculation unit 1913 for model evaluation calculates the explanatory variable x included in the first training data used when calculating the second learning model. r By substituting the data values ​​into the second learning model (equation (19)), we obtain the estimated value of the target variable y in the second learning model. eThe model evaluation regression equation calculation unit 1913 then calculates the estimated value y of the target variable in the second learning model. e And, in the first training data used when calculating the second learning model, the estimated value of the target variable y e Explanatory variable x used in the calculation r The correct value of the target variable y, paired with the data. t The second set of training data consists of L sets of data including and (L is an integer greater than or equal to 2, and is the number required to create the second learning model). The regression equation calculation unit for model evaluation 1913 creates such L sets of second training data for each of the W second learning models created by the second learning model creation unit 1912. As a result, W sets of second training data are created, each consisting of L sets of second training data.

[0248] The model evaluation regression equation calculation unit 1913 calculates a model evaluation regression equation (the regression coefficient c in equation (15)) using each of the W second training data sets individually. As a result, one model evaluation regression equation is calculated for each of the W second training models (W model evaluation regression equations are calculated). The model evaluation regression equation for a second training model is the model evaluation regression equation calculated using the second training data set created using that second training model. The model evaluation regression equation calculation unit 1913 stores the second training model and the model evaluation regression equation for that second training model in relation to each other.

[0249] The second evaluation index calculation unit 1914 calculates a variability evaluation index V and a gradient evaluation index grad for each of the W second training data sets, using one of the W second training data sets and the regression equation for model evaluation calculated using that second training data set. This is done individually for each of the W second training data sets. As a result, W sets of variability evaluation index V and gradient evaluation index grad are calculated. The variability evaluation index V and gradient evaluation index grad for the second training model are the variability evaluation index V and gradient evaluation index grad calculated using the regression equation for model evaluation for that second training model. The second evaluation index calculation unit 1914 stores the second training model and the variability evaluation index V and gradient evaluation index grad for that second training model in relation to each other.

[0250] Once the W-set pairs of variability evaluation index V and gradient evaluation index grad are calculated as described above, the second relationship calculation unit 1915 selects one variability evaluation index V (the variability evaluation index V with the maximum value in equation (16)) from the W-set pairs of variability evaluation index V and gradient evaluation index grad, which are paired with the variability evaluation index V that indicates that the gradient of the regression equation for model evaluation is non-negative. The second relationship calculation unit 1915 then stores the selected variability evaluation index V and the explanatory variables included in the second learning model that are stored in association with the variability evaluation index, relating them to each other. The variability evaluation index V is used in the explanatory variable number-second evaluation index relationship information as the variability evaluation index when the number of explanatory variables is 1. Furthermore, the explanatory variables stored in association with the variability evaluation index V are the "explanatory variables included in the second learning model used when calculating the relationship information between the number of explanatory variables and the second evaluation index" as described in the section on [[explanatory variable addition selection unit 1916]]. In the following explanation, the explanatory variables stored in association with the variability evaluation index V will be referred to as the explanatory variables selected up to the (w-1)th selection process, as needed. In the second selection process, the explanatory variables selected up to the (w-1)th selection process are the explanatory variables selected in the first selection process.

[0251] [[Selection process for the second and subsequent times]] As described above, in this embodiment, we illustrate the case where a stepwise forward selection method (variable increment method) is used as a method for selecting (narrowing down) explanatory variables to be used for calculating the correlation index from the explanatory variables selected by the first explanatory variable selection unit 170. In this case, the number of explanatory variables in the second learning model is set to w in the second selection process from the second selection process onward (by adding 1 to the number of explanatory variables in the second learning model in the w-1 selection process). In this embodiment, we illustrate the case where one explanatory variable is selected in the first selection process. Therefore, in the second selection process, the number of explanatory variables in the second learning model will be 2.

[0252] First, the selected explanatory variable group creation unit 1911 selects the explanatory variables selected up to the (w-1)th selection process, along with one of the new explanatory variables excluding the selected explanatory variable, to be included in the selected explanatory variable group. This is done by selecting each of the explanatory variables excluding the explanatory variable selected up to the (w-1)th selection process from the W explanatory variables as a new explanatory variable. In the w-th selection process, the number of explanatory variables excluding the explanatory variable selected up to the (w-1)th selection process from the W candidate explanatory variables is W-w+1. A group of W-w+1 selected explanatory variables is created. In the second selection process, W-w+1 is 7.

[0253] Then, the second learning model creation unit 1912 determines that the explanatory variables in the second learning model are the explanatory variables x selected up to the w-1th selection process. r' Then, the selected explanatory variable group creation unit 1911 selects a new candidate explanatory variable x r Assuming this is the case, the second learning model is calculated using the first learning data, and the explanatory variables x selected up to the w-1th selection process out of W explanatory variables are used. r' This process is performed for each of the explanatory variables except for the one specified. This results in the calculation of W-w+1 second learning models (multiple regression equations). In this case, the explanatory variables x selected up to the w-1th selection process are... r'And one of the W-w+1 explanatory variables is included as an explanatory variable in the second learning model.

[0254] Note that the explanatory variable x selected up to the (w-1)th selection process. r' And a new candidate explanatory variable x r When calculating a second learning model having the above, the second learning model creation unit 1912 selects the w-1 explanatory variables x selected up to the w-1 selection process. r' and a new explanatory variable x r The data and the correct value y of the target variable paired with that data in the first training data. t A second learning model is created by using this as a set of training data.

[0255] Furthermore, the second learning model in the second and subsequent w-th selection processes can be represented, for example, by equation (20) below. As shown in equation (20) below, in this embodiment, we illustrate the case where the second learning model in the second and subsequent w-th selection processes is a multiple regression equation.

[0256]

number

[0257] The regression equation calculation unit 1913 for model evaluation calculates candidate explanatory variables x included in the first training data used when creating the second learning model. r' , x r By substituting the data values ​​into the second learning model, the estimated value of the target variable y in the second learning model is obtained. e The model evaluation regression equation calculation unit 1913 then calculates the estimated value y of the target variable in the second learning model. e And, in the first training data used when calculating the second learning model, the estimated value of the target variable y e Explanatory variable x used in the calculation r' , x r The correct value of the target variable y, paired with the data. tL sets of second training data are created as training data consisting of sets of data including and . The regression equation calculation unit for model evaluation 1913 creates such L sets of second training data for each of the W-w+1 second training models created by the second training model creation unit 1912. As a result, W-w+1 sets of second training data are created as second training data sets consisting of L sets of second training data.

[0258] The model evaluation regression equation calculation unit 1913 calculates a model evaluation regression equation (the regression coefficient c in equation (15)) using each of the W-w+1 second training data sets individually. As a result, one model evaluation regression equation is calculated for each of the W-w+1 second learning models (W-w+1 model evaluation regression equations are calculated). The model evaluation regression equation calculation unit 1913 stores the second learning models and the model evaluation regression equations for those second learning models in relation to each other.

[0259] The second evaluation index calculation unit 1914 calculates a variability evaluation index V and a gradient evaluation index grad for each of the W-w+1 second training data sets, using one of the W-w+1 second training data sets and the regression equation for model evaluation calculated using that second training data set. This is done individually for each of the W-w+1 second training data sets. As a result, W-w+1 pairs of variability evaluation index V and gradient evaluation index grad are calculated. The second evaluation index calculation unit 1914 stores the second training model and the variability evaluation index V and gradient evaluation index grad for that second training model in relation to each other.

[0260] Once the W-w+1 pairs of variability evaluation index V and gradient evaluation index grad are calculated as described above, the second relationship calculation unit 1915 selects from the W-w+1 pairs of variability evaluation index V and gradient evaluation index grad a variability evaluation index V that is paired with a gradient evaluation index grad which indicates that the gradient of the regression equation for model evaluation is non-negative, the variability evaluation index V that represents the smallest degree of variability of the second learning data with respect to the regression equation for model evaluation (the variability evaluation index V with the largest value in equation (16)). The second relationship calculation unit 1915 then stores the selected variability evaluation index V and the explanatory variables included in the second learning model that are stored in association with the variability evaluation index, relating them to each other. The variability evaluation index V is used in the explanatory variable number-second evaluation index relationship information as the variability evaluation index when the number of explanatory variables is w. Furthermore, the explanatory variables stored in association with the variability evaluation index V are the "explanatory variables included in the second learning model used when calculating the relationship information between the number of explanatory variables and the second evaluation index" as described in the section [[explanatory variable addition selection unit 1916]].

[0261] [[Conditions for ending the selection process]] The selection process from the wth time onward is repeated W times, with w incremented by 1, until there are no more explanatory variables to be included in the selected explanatory variable group created by the selected explanatory variable group creation unit 1911 (i.e., the final value of w is W). When there are no more explanatory variables to be included in the selected explanatory variable group created by the selected explanatory variable group creation unit 1911, the selection process ends. The second relationship calculation unit 1915 calculates the explanatory variable number - second evaluation index relationship information using the variability evaluation index V and the number of explanatory variables that have been stored in relation to each other in each of the first to W selection processes.

[0262] As mentioned above, the method for selecting (narrowing down) the explanatory variables to be used in calculating the correlation index from the explanatory variables selected by the first explanatory variable selection unit 170 is not limited to the stepwise forward selection method (variable increase method). For example, if the variable reduction method or the variable reduction / increase method is used as the method for selecting (narrowing down) the explanatory variables to be used in calculating the correlation index from the explanatory variables selected by the first explanatory variable selection unit 170, the number of explanatory variables selected in the first selection process (initial value of the number of explanatory variables) will be W. Also, if the variable reduction method is used as the method for selecting explanatory variables to be used in calculating the correlation index from W explanatory variables, in the second and subsequent w-th selection processes, the number of explanatory variables in the second learning model will be W-w+1 (the number of explanatory variables in the second learning model will be the value obtained by subtracting 1 from the number of explanatory variables in the second learning model in the w-1 selection process). Furthermore, when using the variable addition / subtraction method or the variable subtraction / addition method as a method for selecting (narrowing down) the explanatory variables to be used for calculating the correlation index from the explanatory variables selected by the first explanatory variable selection unit 170, the number of explanatory variables in the second learning model in the w-th selection process from the second onward is set to a value obtained by adding or subtracting 1 from the number of explanatory variables in the second learning model in the (w-1)th selection process.

[0263] When reducing the number of explanatory variables in the w-th selection process, for example, the selected explanatory variable group creation unit 1911 selects the explanatory variables to be included in the selected explanatory variable group by removing one explanatory variable from the explanatory variables selected up to the (w-1)th selection process. The one explanatory variable to be removed from the explanatory variables selected up to the (w-1)th selection process is selected one by one from the explanatory variables selected up to the (w-1)th selection process.

[0264] The second learning model creation unit 1912 calculates a second learning model in the w-th selection process that has the explanatory variables included in the selected explanatory variable group created by the selected explanatory variable group creation unit 1911 as explanatory variables. If the number of explanatory variables in the second learning model obtained in the selection processes up to the (w-1)th selection process is z, then c second learning models are obtained in the w-th selection process. Subsequently, the regression equation calculation unit 1913 for model evaluation and the second evaluation index calculation unit 1914, as described in the section <Selection Process from the Second Time Onward>, perform a process in which "W-w+1 second learning models" are replaced with "z second learning models".

[0265] [Output process (S208), output section 180] The output unit 180 outputs information about the explanatory variables selected by the first explanatory variable selection unit 170 and the second explanatory variable selection unit 1910. Thus, in this embodiment, in addition to the explanatory variables selected by the first explanatory variable selection unit 170, the explanatory variables selected by the second explanatory variable selection unit 1910 become explanatory variables in the first learning model. The output form of the explanatory variable information is at least one of the following: display on a computer display, transmission to an external device, and storage on a portable storage medium. [summary] In the first embodiment, the explanatory variables in the first learning model are selected only based on the relationship information between the number of explanatory variables and the first evaluation index. In contrast, in this embodiment, explanatory variables in the first learning model are further selected from the candidate explanatory variables not selected based on the relationship information between the number of explanatory variables and the first evaluation index, based on the value of a correlation index that represents the correlation between the explanatory variables selected based on the relationship information between the number of explanatory variables and the first evaluation index and the candidate explanatory variables not selected based on the relationship information. Therefore, it is possible to further suppress the case in which candidate explanatory variables suitable for explaining the target variable y are not selected as explanatory variables in the first learning model.

[0266] Furthermore, while L1 regularization can suppress the effects of multicollinearity when calculating the first set of candidate explanatory variables, L1 regularization alone may not be sufficient in some cases. In contrast, in this embodiment, a second learning model is created that has explanatory variables selected based on the relationship information between the number of explanatory variables and the first evaluation index. Based on the results of evaluating the created second learning model using the variability evaluation index V and the gradient evaluation index grad, explanatory variables to be used in calculating the correlation index are selected from these explanatory variables. Therefore, when selecting explanatory variables that are correlated with the explanatory variables selected based on the relationship information between the number of explanatory variables and the first evaluation index as explanatory variables in the first learning model, the effects of multicollinearity can be further suppressed. In addition, various modifications described in the first to fourth embodiments may also be adopted in this embodiment.

[0267] (Other embodiments) Furthermore, the embodiments of the present invention described above can be realized by a computer executing a program. A computer-readable recording medium on which the program is stored, and a computer program product such as the program itself, can also be applied as embodiments of the present invention. Examples of recording media include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, non-volatile memory cards, ROMs, etc. Moreover, embodiments of the present invention may be realized by a PLC (Programmable Logic Controller) or by dedicated hardware such as an ASIC (Application Specific Integrated Circuit). Furthermore, the embodiments of the present invention described above are merely examples of how the invention can be implemented, and the technical scope of the invention should not be interpreted as being limited by them. In other words, the present invention can be implemented in various forms without departing from its technical concept or its main features.

[0268] Furthermore, the disclosure of the above embodiments is as follows, for example. [Disclosure 1] A processing device that performs the process of selecting explanatory variables in a learning model that shows the relationship between one or more explanatory variables and the target variable explained by those explanatory variables, A first explanatory variable candidate group acquisition means for acquiring multiple first explanatory variable candidate groups, each containing one or more explanatory variable candidate groups, A frequency calculation means for calculating the frequency of occurrence of each candidate explanatory variable in the plurality of candidate first explanatory variables, A means for creating a group of candidate second explanatory variables, each of which contains one candidate explanatory variable or multiple candidates explanatory variables, based on the frequency of occurrence. A first learning model candidate creation means that creates a plurality of first learning model candidates that show the relationship between the candidate explanatory variables included in the second explanatory variable candidate group and the target variable, for each of the plurality of second explanatory variable candidate groups, A first evaluation index calculation means that calculates a first evaluation index for each of the plurality of candidate first learning models to evaluate the estimation accuracy of the candidate first learning model, The system includes a first relationship calculation means for calculating explanatory variable number-first evaluation index relationship information that shows the relationship between the number of candidate explanatory variables included in the candidate first learning model and a first evaluation index for evaluating the estimation accuracy of the candidate first learning model, The aforementioned explanatory variable number-first evaluation index relationship information is used for the selection of the explanatory variables in the first learning model, in a processing device. [Disclosure 2] The apparatus according to Disclosure 1, wherein the means for creating the second candidate group of explanatory variables selects candidates for explanatory variables to be included in the second candidate group of explanatory variables such that there are more candidates for explanatory variables with relatively high occurrence frequencies than candidates for explanatory variables with relatively low occurrence frequencies. [Disclosure 3] The processing apparatus according to disclosure 2, wherein the means for creating the second explanatory variable candidate group selects m explanatory variable candidates in order of their frequency of occurrence, and creates the second explanatory variable candidate group containing the selected m explanatory variable candidates, for each case where M is an integer of 2 or more, from 1 to M. [Disclosure 4] The processing apparatus according to any one of disclosures 1 to 3, wherein the means for creating the second explanatory variable candidate group is a plurality of second explanatory variable candidate groups, which include only a portion of the explanatory variable candidates included in the first explanatory variable candidate group. [Disclosure 5] The processing apparatus according to any one of disclosures 1 to 4, further comprising a first explanatory variable selection means for selecting the explanatory variables in the first learning model based on the explanatory variable number-first evaluation index relationship information. [Disclosure 6] The processing apparatus according to disclosure 5, wherein the first explanatory variable selection means selects, in the relationship indicated by the explanatory variable number-first evaluation index relationship information, a candidate for the first evaluation index that is included in the candidate for the first learning model that satisfies predetermined conditions, as the explanatory variable in the first learning model. [Disclosure 7] The apparatus according to disclosure 6, wherein the predetermined condition is a condition expressed using the peak of the first evaluation index in the relationship shown by the explanatory variable number-first evaluation index relationship information. [Disclosure 8] The apparatus according to disclosure 6 or 7, wherein the predetermined condition is a condition expressed using the number of explanatory variables in the relationship shown by the explanatory variable number-first evaluation index relationship information. [Disclosure 9] The first explanatory variable candidate group acquisition means calculates the plurality of first explanatory variable candidate groups based on the results of a regression analysis with a penalty that can reduce the regression coefficient to 0, which is performed as a regression analysis to calculate the regression coefficient of a regression equation showing the relationship between the explanatory variables and the dependent variable, using the data of the explanatory variables and the data of the dependent variable. The means for obtaining the first explanatory variable candidate group calculates multiple sets of multiple sets of the multiple first explanatory variable candidate group by using multiple values ​​as predetermined hyperparameter values ​​used in the penalty-based regression analysis, The frequency calculation means calculates the frequency of occurrence of each candidate explanatory variable in the plurality of candidate groups of first explanatory variables for each of the plurality of sets of candidate groups of first explanatory variables, thereby calculating a plurality of sets of frequency calculations. The means for creating the second explanatory variable candidate group creates multiple second explanatory variable candidate groups, each containing one explanatory variable candidate or multiple explanatory variable candidates, based on the frequency of occurrence, for each of the multiple sets of frequency of occurrence, thereby creating multiple sets of multiple second explanatory variable candidate group sets. The first learning model candidate creation means creates the plurality of first learning model candidates for each of the plurality of sets of plurality of second explanatory variable candidate groups, thereby creating a set of the plurality of sets of plurality of first learning model candidate groups. The first evaluation index calculation means calculates the first evaluation index for each of the multiple sets of candidate first learning models. The processing apparatus according to any one of disclosures 1 to 8, wherein the first relationship calculation means calculates the explanatory variable number-first evaluation index relationship information for each of the multiple sets of candidate first learning models. [Disclosure 10] The apparatus according to any one of disclosures 1 to 9, wherein the objective variable is a categorical variable. [Disclosure 11] The apparatus according to disclosure 10, wherein the means for obtaining the first explanatory variable candidate group calculates the plurality of first explanatory variable candidate groups based on the results of a penalty-based logistic regression analysis that can reduce the regression coefficients to zero, as a regression analysis for calculating the regression coefficients of a regression equation showing the relationship between the explanatory variables and the dependent variable. [Disclosure 12] The processing apparatus according to any one of disclosures 1 to 11, wherein the first learning model is created by performing supervised learning. [Disclosure 13] The apparatus according to any one of disclosures 1 to 12, wherein the means for obtaining the first explanatory variable candidate group creates data for noise explanatory variables, which are variables that simulate noise that may be included in the data of the explanatory variable candidate group; uses the explanatory variable candidate data, the noise explanatory variable data and the target variable data to perform a regression analysis with a penalty that can reduce the regression coefficient to 0, as a regression analysis for calculating the regression coefficient of a regression equation showing the relationship between the explanatory variable candidate, the noise explanatory variable and the target variable; and calculates the plurality of first explanatory variable candidate groups based on the result of comparing the regression coefficient for the explanatory variable candidate and the regression coefficient for the noise explanatory variable. [Disclosure 14] The processing apparatus according to disclosure 13, wherein the first explanatory variable candidate group acquisition means creates noise explanatory variable data using the explanatory variable candidate data. [Disclosure 15] The processing apparatus according to disclosure 14, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variables such that the correlation of the noise explanatory variables with respect to the objective variable is lower than the correlation of the candidate explanatory variables with respect to the objective variable. [Disclosure 16] The processing apparatus according to disclosure 14 or 15, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variable such that the statistical distribution of the noise explanatory variable is the same as the statistical distribution of the candidate explanatory variable or a statistical distribution based on the statistical distribution of the candidate explanatory variable. [Disclosure 17] The first learning model described above is a linear regression model, The processing apparatus according to any one of disclosures 14 to 16, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variables such that the noise explanatory variables have conditional independence from the target variable, conditional on the candidate explanatory variables. [Disclosure 18] The apparatus according to any one of disclosures 13 to 17, wherein the means for obtaining the first candidate group of explanatory variables calculates a regression coefficient for each candidate explanatory variable as a regression coefficient for the noise explanatory variable, and calculates the plurality of candidate groups of first explanatory variables based on the result of comparing the regression coefficient for the candidate explanatory variable with the regression coefficient for the noise explanatory variable that corresponds to the candidate explanatory variable. [Disclosure 19] A first explanatory variable selection means for selecting the explanatory variables in the first learning model based on the aforementioned explanatory variable number-first evaluation index relationship information, The apparatus according to any one of disclosures 13 to 18, further comprising: a second explanatory variable selection means that calculates a correlation index representing the correlation between an explanatory variable and a candidate explanatory variable based on data for at least one explanatory variable selected by the first explanatory variable selection means and data for a candidate explanatory variable not selected by the first explanatory variable selection means, and further selects an explanatory variable in the first learning model from the candidate explanatory variable based on the value of the correlation index. [Disclosure 20] The apparatus according to disclosure 19, wherein the correlation is a rank correlation. [Disclosure 21] The apparatus according to disclosure 19 or 20, wherein the second explanatory variable selection means selects the explanatory variable in the first learning model from the candidate explanatory variable based on the correlation index and the data values ​​of the candidate explanatory variable not selected by the first explanatory variable selection means. [Disclosure 22] The second explanatory variable selection means is, A selected explanatory variable group creation means creates a plurality of selected explanatory variable groups, each including one or more explanatory variables selected by the first explanatory variable selection means, A means for creating a second learning model that creates multiple second learning models showing the relationship between the explanatory variables included in the selected explanatory variable group and the target variable, for each of the multiple selected explanatory variable groups, A model evaluation regression equation calculation means calculates estimated data for the target variable based on the data of the explanatory variables included in the selected explanatory variable group and the second learning model, and calculates a model evaluation regression equation which is a linear regression equation showing the relationship between the ground truth value, which is the value of the data of the target variable, and the estimated value, which is the value of the estimated data of the target variable calculated by the second learning model, using the estimated data of the target variable and the data of the target variable corresponding to the data of the explanatory variables. A second evaluation index calculation means that calculates a second evaluation index for evaluating the aforementioned second learning model for each of the plurality of second learning models, A second relationship calculation means calculates explanatory variable number-second evaluation index relationship information that shows the relationship between the number of explanatory variables included in the second learning model and the second evaluation index, Based on the aforementioned explanatory variable number-second evaluation index relationship information, an explanatory variable additional selection means selects an explanatory variable to be used for calculating the correlation index from the explanatory variables selected by the first explanatory variable selection means, calculates a correlation index representing the correlation between the selected explanatory variable and the candidate explanatory variable based on the data of the selected explanatory variable and the data of the candidate explanatory variable not selected by the first explanatory variable selection means, and selects an explanatory variable in the first learning model from the candidate explanatory variable based on the value of the correlation index. An apparatus according to any one of disclosures 19 to 21, having the following characteristics. [Disclosure 23] The first second evaluation index comprises a variability evaluation index and a gradient evaluation index. The aforementioned variability evaluation index is an index that represents the variability of the estimated data of the dependent variable from the regression equation for model evaluation. The gradient evaluation index is an index that represents the gradient of the regression equation for model evaluation, The processing apparatus according to disclosure 22, wherein the second evaluation index in the explanatory variable number-second evaluation index relationship information is the variability evaluation index. [Disclosure 24] The processing apparatus according to disclosure 22 or 23, wherein the explanatory variable addition selection means selects, among the second learning models having a number of explanatory variable candidates for which the increase or decrease of the second evaluation index changes in the explanatory variable number-second evaluation index relationship information, the candidate explanatory variable included in the second learning model used when calculating the explanatory variable number-second evaluation index relationship information, as the explanatory variable in the first learning model. [Disclosure 25] The explanatory variables include factors used in the processing process, The apparatus according to any one of disclosures 1 to 24, wherein the objective variable includes a factor obtained in the processing process by performing the processing using a factor used in the processing process. [Disclosure 26] The aforementioned treatment process is a process that treats the water to be treated using a group of microorganisms present in the water to be treated, which contains a specific substance. The aforementioned explanatory variables are factors relating to the quantity of the microbial community, The apparatus according to disclosure 25, wherein the objective variable is a factor relating to the rate of change of the amount of the specific substance. [Disclosure 27] A processing method for selecting explanatory variables in a first learning model that shows the relationship between one or more explanatory variables and the target variable explained by those explanatory variables, A first explanatory variable candidate group acquisition step, which acquires multiple first explanatory variable candidate groups, each including one explanatory variable candidate or multiple explanatory variable candidates, A frequency calculation step of calculating the frequency of occurrence of each candidate explanatory variable in the plurality of candidate groups of first explanatory variables, A second explanatory variable candidate group creation step, which creates multiple second explanatory variable candidate groups, each containing one explanatory variable candidate or multiple explanatory variable candidates, based on the frequency of occurrence; A first learning model candidate creation step is performed for each of the multiple second explanatory variable candidate groups to create a plurality of first learning model candidates that show the relationship between the explanatory variable candidates included in the second explanatory variable candidate group and the target variable, A first evaluation index calculation step is performed for each of the multiple candidates for the first learning model, which involves calculating a first evaluation index for evaluating the estimation accuracy of the candidate for the first learning model. The method includes a first relationship calculation step that calculates explanatory variable number-first evaluation index relationship information, which shows the relationship between the number of candidate explanatory variables included in the candidate first learning model and a first evaluation index for evaluating the estimation accuracy of the candidate first learning model. A processing method in which the aforementioned information relating the number of explanatory variables to the first evaluation index is used for selecting the explanatory variables in the first learning model. [Disclosure 28] A program for causing a computer to function as one of the means of the processing apparatus described in any one of disclosures 1 to 26. [Explanation of Symbols]

[0269] 20. Biological treatment equipment 20a Biological Processing Area 20b Subsidence area 21 Sponge carrier 22 Air aeration 23 Bulkhead 24. Water to be treated 25. Treated water 100 Processing Units 110 Unit for acquiring candidate group of first explanatory variables 120 Frequency Calculation Unit 130 Second Explanatory Variable Candidate Group Creation Section 140 First Learning Model Candidate Creation Unit 150 First Evaluation Index Calculation Unit 160 First Relationship Calculation Unit 170 Selection of the first explanatory variable 180 Output section 310a~310d Candidate group of the first explanatory variable 320 Frequency of appearance 330 Candidate explanatory variables after sorting 340a~340d Candidate group of second explanatory variables 350a~350c Candidates for the first learning model 360a~360d First evaluation index 370 Number of explanatory variables - Information related to the first evaluation indicator 371-375 Points showing information regarding the relationship between the number of explanatory variables and the first evaluation indicator. 1100 Number of explanatory variables - Information related to the first evaluation indicator 1101~1106 Points showing local peaks in the relationship between the number of explanatory variables and the first evaluation index. 1600 Number of explanatory variables - Information related to the first evaluation indicator Points 1601-1603 indicate candidate local peaks in the relationship information between the number of explanatory variables and the first evaluation index. 1900 Processing Unit 1910 Second explanatory variable selection section 1911 Selected explanatory variable group creation unit 1912 Second Learning Model Creation Department 1913 Model Evaluation Regression Equation Calculation Unit 1914 Second Evaluation Index Calculation Department 1915 Second Relationship Calculation Unit 1916 Additional Explanatory Variable Selection Section 2100 Number of explanatory variables - Information related to the first evaluation indicator 2101 Points indicating local peaks in the relationship between the number of explanatory variables and the first evaluation index. 2211 Regression equation for model evaluation 2221 Learning Model (Simple Regression Equation) 2300 Number of explanatory variables - Information related to the second evaluation indicator 2301 Number of explanatory variables - Second evaluation index Relationship information Variation Points where the increase or decrease of evaluation index changes

Claims

1. A processing device that performs the process of selecting explanatory variables in a learning model that shows the relationship between one or more explanatory variables and the target variable explained by those explanatory variables, A first explanatory variable candidate group acquisition means for acquiring multiple first explanatory variable candidate groups, each containing one or more explanatory variable candidate groups, A frequency calculation means for calculating the frequency of occurrence of each candidate explanatory variable in the plurality of candidate first explanatory variables, A means for creating a group of candidate second explanatory variables, each of which contains one candidate explanatory variable or multiple candidates explanatory variables, based on the frequency of occurrence. A first learning model candidate creation means that creates a plurality of first learning model candidates that show the relationship between the candidate explanatory variables included in the second explanatory variable candidate group and the target variable, for each of the plurality of second explanatory variable candidate groups, A first evaluation index calculation means calculates a first evaluation index for each of the plurality of candidate first learning models to evaluate the estimation accuracy of the candidate first learning model, The system includes a first relationship calculation means for calculating explanatory variable number-first evaluation index relationship information, which shows the relationship between the number of candidate explanatory variables included in the candidate first learning model and a first evaluation index for evaluating the estimation accuracy of the candidate first learning model. The aforementioned information relating the number of explanatory variables to the first evaluation index is used for the selection of the explanatory variables in the first learning model, in the processing unit.

2. The processing apparatus according to claim 1, wherein the means for creating the second group of candidate explanatory variables selects candidates for explanatory variables to be included in the second group of candidate explanatory variables such that there are more candidates for explanatory variables with relatively high occurrence frequencies than candidates for explanatory variables with relatively low occurrence frequencies.

3. The processing apparatus according to claim 2, wherein the means for creating the second explanatory variable candidate group selects m explanatory variable candidates in order from those with the highest frequency of occurrence, and creates the second explanatory variable candidate group including the selected m explanatory variable candidates, for each case where M is an integer of 2 or more, from 1 to M.

4. The processing apparatus according to any one of claims 1 to 3, wherein the means for creating the second explanatory variable candidate group is used to create a plurality of second explanatory variable candidate groups, which include only a portion of the explanatory variable candidates included in the first explanatory variable candidate group.

5. The processing apparatus according to any one of claims 1 to 3, further comprising a first explanatory variable selection means for selecting the explanatory variables in the first learning model based on the explanatory variable number-first evaluation index relationship information.

6. The processing apparatus according to claim 5, wherein the first explanatory variable selection means selects, in the relationship indicated by the number of explanatory variables - first evaluation index relationship information, a candidate for the first evaluation index that is included in the candidate for the first learning model that satisfies predetermined conditions, as the explanatory variable in the first learning model.

7. The apparatus according to claim 6, wherein the predetermined condition is a condition expressed using the peak of the first evaluation index in the relationship shown by the number of explanatory variables - first evaluation index relationship information.

8. The apparatus according to claim 6, wherein the predetermined condition is a condition expressed using the number of explanatory variables in the relationship shown by the number of explanatory variables - first evaluation index relationship information.

9. The first explanatory variable candidate group acquisition means calculates the plurality of first explanatory variable candidate groups based on the results of a regression analysis with a penalty that can reduce the regression coefficient to zero, which is performed as a regression analysis to calculate the regression coefficient of a regression equation showing the relationship between the explanatory variable and the objective variable, using the data of the explanatory variable and the data of the objective variable. The means for obtaining the first explanatory variable candidate group calculates multiple sets of multiple sets of the multiple first explanatory variable candidate group by using multiple values ​​as predetermined hyperparameter values ​​used in the penalty-based regression analysis, The frequency calculation means calculates the frequency of occurrence of each candidate explanatory variable in the plurality of candidate groups of first explanatory variables for each of the plurality of sets of candidate groups of first explanatory variables, thereby calculating a plurality of sets of frequency calculations. The means for creating the second explanatory variable candidate group creates multiple second explanatory variable candidate groups, each containing one explanatory variable candidate or multiple explanatory variable candidates, based on the frequency of occurrence, for each of the multiple sets of frequency of occurrence, thereby creating multiple sets of multiple second explanatory variable candidate group groups. The first learning model candidate creation means creates the plurality of first learning model candidates for each of the plurality of sets of plurality of second explanatory variable candidate groups, thereby creating a set of the plurality of sets of plurality of first learning model candidate groups. The first evaluation index calculation means calculates the first evaluation index for each of the multiple sets of candidate first learning models. The processing apparatus according to any one of claims 1 to 3, wherein the first relationship calculation means calculates the explanatory variable number - first evaluation index relationship information for each of the multiple sets of candidate first learning models.

10. The apparatus according to any one of claims 1 to 3, wherein the target variable is a categorical variable.

11. The apparatus according to claim 10, wherein the means for obtaining the candidate group of first explanatory variables calculates the plurality of candidate groups of first explanatory variables based on the results of a penalty-based logistic regression analysis that can reduce the regression coefficients to zero, as a regression analysis for calculating the regression coefficients of a regression equation showing the relationship between the explanatory variables and the objective variable.

12. The processing apparatus according to any one of claims 1 to 3, wherein the first learning model is created by performing supervised learning.

13. The processing apparatus according to any one of claims 1 to 3, wherein the means for obtaining the first explanatory variable candidate group creates data for noise explanatory variables, which are variables that simulate noise that may be included in the data of the explanatory variable candidate group, and using the explanatory variable candidate group data, the noise explanatory variable data and the target variable data, performs a regression analysis with a penalty that can reduce the regression coefficient to zero as a regression analysis for calculating the regression coefficient of a regression equation showing the relationship between the explanatory variable candidate group, the noise explanatory variable and the target variable, and calculates the plurality of first explanatory variable candidate groups based on the result of comparing the regression coefficient for the explanatory variable candidate group and the regression coefficient for the noise explanatory variable.

14. The processing apparatus according to claim 13, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variable using the data for the explanatory variable candidates.

15. The processing apparatus according to claim 14, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variables such that the correlation of the noise explanatory variables with respect to the objective variable is lower than the correlation of the candidate explanatory variables with respect to the objective variable.

16. The processing apparatus according to claim 14, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variable such that the statistical distribution of the noise explanatory variable is the same as the statistical distribution of the candidate explanatory variable or a statistical distribution based on the statistical distribution of the candidate explanatory variable.

17. The first learning model described above is a linear regression model, The processing apparatus according to claim 14, wherein the first explanatory variable candidate group acquisition means creates data for the noise explanatory variables such that the noise explanatory variables have conditional independence from the target variable, conditional on the candidate explanatory variables.

18. The processing apparatus according to claim 13, wherein the means for obtaining the first explanatory variable candidate group calculates a regression coefficient for each candidate explanatory variable as a regression coefficient for the noise explanatory variable, and calculates the plurality of first explanatory variable candidate groups based on the result of comparing the regression coefficient for the candidate explanatory variable with the regression coefficient for the noise explanatory variable that corresponds to the candidate explanatory variable.

19. A first explanatory variable selection means for selecting the explanatory variables in the first learning model based on the number of explanatory variables - first evaluation index relationship information, The processing apparatus according to claim 13, further comprising: a second explanatory variable selection means for calculating a correlation index representing the correlation between an explanatory variable and a candidate explanatory variable based on data for at least one explanatory variable selected by the first explanatory variable selection means and data for a candidate explanatory variable not selected by the first explanatory variable selection means, and for further selecting an explanatory variable in the first learning model from the candidate explanatory variable based on the value of the correlation index.

20. The apparatus according to claim 19, wherein the correlation is a rank correlation.

21. The processing apparatus according to claim 19, wherein the second explanatory variable selection means selects the explanatory variable in the first learning model from the candidate explanatory variable based on the correlation index and the data values ​​of the candidate explanatory variable not selected by the first explanatory variable selection means.

22. The second explanatory variable selection means is, A selected explanatory variable group creation means creates a plurality of selected explanatory variable groups, each including one or more explanatory variables selected by the first explanatory variable selection means, A means for creating a second learning model that creates multiple second learning models showing the relationship between the explanatory variables included in the selected explanatory variable group and the target variable, for each of the multiple selected explanatory variable groups, A model evaluation regression equation calculation means calculates estimated data for the target variable based on the data of the explanatory variables included in the selected explanatory variable group and the second learning model, and calculates a model evaluation regression equation which is a linear regression equation showing the relationship between the ground truth value, which is the value of the data of the target variable, and the estimated value, which is the value of the estimated data of the target variable calculated by the second learning model, using the estimated data of the target variable and the data of the target variable corresponding to the data of the explanatory variables. A second evaluation index calculation means that calculates a second evaluation index for evaluating the second learning model for each of the plurality of second learning models, A second relationship calculation means for calculating explanatory variable number-second evaluation index relationship information that shows the relationship between the number of explanatory variables included in the second learning model and the second evaluation index, Based on the aforementioned number of explanatory variables - second evaluation index relationship information, an explanatory variable additional selection means selects an explanatory variable to be used for calculating the correlation index from the explanatory variables selected by the first explanatory variable selection means, calculates a correlation index representing the correlation between the selected explanatory variable and the candidate explanatory variable based on the data of the selected explanatory variable and the data of the candidate explanatory variable not selected by the first explanatory variable selection means, and selects an explanatory variable in the first learning model from the candidate explanatory variable based on the value of the correlation index. The apparatus according to claim 19, having the following features.

23. The second evaluation index described above comprises a variability evaluation index and a gradient evaluation index. The aforementioned variability evaluation index is an index that represents the variability of the estimated data of the dependent variable from the regression equation for model evaluation. The gradient evaluation index is an index that represents the gradient of the regression equation for model evaluation, The processing apparatus according to claim 22, wherein the second evaluation index in the explanatory variable number-second evaluation index relationship information is the variation evaluation index.

24. The processing apparatus according to claim 22, wherein the explanatory variable addition selection means selects, among the second learning models having a number of explanatory variable candidates whose number of explanatory variables changes in the explanatory variable number-second evaluation index relationship information, the candidate explanatory variable included in the second learning model used when calculating the explanatory variable number-second evaluation index relationship information, as the explanatory variable in the first learning model.

25. The explanatory variables include factors used in the processing process, The apparatus according to any one of claims 1 to 3, wherein the objective variable includes a factor obtained in the processing process by performing the processing using a factor used in the processing process.

26. The aforementioned treatment process is a process that treats the water to be treated using a group of microorganisms present in the water to be treated, which contains a specific substance. The aforementioned explanatory variables are factors relating to the quantity of the microbial community, The apparatus according to claim 25, wherein the objective variable is a factor relating to the rate of change of the amount of the specific substance.

27. A processing method for selecting explanatory variables in a first learning model that shows the relationship between one or more explanatory variables and the target variable explained by those explanatory variables, A first explanatory variable candidate group acquisition step, which acquires a plurality of first explanatory variable candidate groups, each containing one or more explanatory variable candidate groups, A frequency calculation step of calculating the frequency of occurrence of each candidate explanatory variable in the plurality of candidate groups of first explanatory variables, A second explanatory variable candidate group creation step, which creates multiple second explanatory variable candidate groups, each containing one explanatory variable candidate or multiple explanatory variable candidates, based on the frequency of occurrence, A first learning model candidate creation step is performed for each of the multiple second explanatory variable candidate groups to create a plurality of first learning model candidates that show the relationship between the explanatory variable candidates included in the second explanatory variable candidate group and the target variable, A first evaluation index calculation step is performed for each of the plurality of candidate first learning models to calculate a first evaluation index for evaluating the estimation accuracy of the candidate first learning model, The method includes a first relationship calculation step for calculating explanatory variable number-first evaluation index relationship information, which shows the relationship between the number of candidate explanatory variables included in the candidate first learning model and a first evaluation index for evaluating the estimation accuracy of the candidate first learning model. A processing method in which the aforementioned information relating the number of explanatory variables to the first evaluation index is used for selecting the explanatory variables in the first learning model.

28. A program for causing a computer to function as one of the means of the processing apparatus according to any one of claims 1 to 3.

Images