Processing apparatus, processing method, and program

Abstract

To comprehensively derive the causal relationships between multiple factors. [Solution] The processing device 100 classifies a plurality of causal exploration factors, which include an influencing factor and influencing factors that may influence the influencing factor, into one of a plurality of hierarchy levels according to the causal order of the plurality of causal exploration factors, and derives the causal relationships of the causal exploration factors belonging to multiple hierarchy levels that are different from each other.

Description

[Technical Field]

[0001] This disclosure relates to an apparatus, a processing method, and a program. [Background technology]

[0002] In various fields, the estimation of influencing factors that affect affected factors is being carried out. One such technique is described in Patent Document 1.

[0003] Patent Document 1 discloses a method for estimating microbial communities involved in changes in the amount of a specific substance. In the technique described in Patent Document 1, first, a dataset is created from measurement results of a sample containing the specific substance and microorganisms, consisting of the rate of change in the amount of the specific substance and the content of the microbial community into which the microorganisms are classified. Next, multiple sets of samples are created from this dataset by resampling. Next, a first selection step is performed. In the first selection step, a penalty-based regression analysis is performed for each of the multiple sets of samples, with the content of the microbial community as the explanatory variable and the rate of change in the amount of the specific substance as the dependent variable, allowing the regression coefficient to be reduced to 0 (zero). In this way, a microbial community is selected for each of the multiple sets of samples. In the first selection step, a microbial community is selected in this manner.

[0004] Next, the second selection process takes place. In the second selection process, microbial groups are further selected from the microbial groups selected in the first selection process. First, in the second selection process, a confidence level is calculated from the selection frequency of the microbial groups selected in the first selection process. Next, based on this confidence level, microbial groups are selected from the microbial groups selected in the first selection process. If the total number of microbial groups is 1000, and a certain microbial group is selected 500 times in the first selection process, the confidence level is 0.5 (= 500 / 1000). In the second selection process, microbial groups with such a confidence level of 0.5 or higher are selected. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2020-36579 [Overview of the project] [Problems that the invention aims to solve]

[0006] However, the technology described in Patent Document 1 does not make it easy to comprehensively derive the causal relationships between multiple factors. For example, it is not easy to derive the causal relationships between factors defined as explanatory variables. Furthermore, for example, it is not easy to derive that a factor defined as an explanatory variable and a factor defined as an dependent variable are indirectly causally related through other factors. This disclosure is made in light of the above-mentioned problems and aims to enable the comprehensive derivation of causal relationships between multiple factors. [Means for solving the problem]

[0007] The apparatus of the present disclosure is an apparatus for deriving causal relationships between a plurality of factors, including an influencing factor and influencing factors that may influence the influencing factor, and comprises: classification means for classifying each of the plurality of factors into one of a plurality of hierarchies according to their respective causal order; and causal relationship deriving means for deriving causal relationships between the factors belonging to a plurality of mutually different hierarchies.

[0008] The processing method of the present disclosure is a processing method for deriving causal relationships between a plurality of factors, including an affected factor and an influencing factor that may affect the affected factor, comprising: a classification step of classifying each of the plurality of factors into one of a plurality of hierarchies according to their respective causal order; and a causal relationship derivation step of deriving causal relationships between the factors belonging to a plurality of mutually different hierarchies.

[0009] The program of this disclosure causes a computer to function as each of the means of the processing apparatus. [Effects of the Invention]

[0010] According to this disclosure, it is possible to comprehensively derive the causal relationships between multiple factors. [Brief explanation of the drawing]

[0011] [Figure 1] This figure shows an example of the functional configuration of the processing unit. [Figure 2A] This is a flowchart illustrating one example of a processing method. [Figure 2B] This flowchart provides a detailed explanation of an example of the process for selecting influencing factors. [Figure 3] This diagram illustrates one example of a method for selecting mediating influencing factors. [Figure 4] This figure shows the first example of mutual information and the difference between mutual information. [Figure 5] This figure shows a second example of mutual information and the difference between mutual information. [Figure 6] This figure shows a third example of mutual information and the difference between mutual information. [Figure 7] This figure shows an example of the classification results for causal exploration factors. [Figure 8] This figure shows an example of a linear regression model, its regression coefficients and intercept, and its robust p-value. [Figure 9] This is a diagram showing an example of a causal graph. [Figure 10] This figure shows an example of the configuration of a biological processing device in an application example. [Figure 11] This figure shows an example of the rate of nitrite production in an application example. [Figure 12A] This figure shows an example of pH in an application example. [Figure 12B] This figure shows an example of HRT in application examples. [Figure 13] This diagram illustrates one example of a method for creating a Bootstrap sample. [Figure 14] This figure illustrates an example of a method for obtaining a candidate group of influencing factors. [Figure 15]This diagram illustrates one example of a method for calculating frequency of occurrence. [Figure 16] This figure shows an example of the relationship between the number of influencing factors and evaluation indicators in an application example. [Figure 17] This figure shows an example of the frequency distribution of causal exploration factors in an application example, and an example of the results of the Shapiro-Wilk test. [Figure 18A] This figure shows the first example of the difference in mutual information in an application example. [Figure 18B] This figure shows a second example of the difference in mutual information in an application example. [Figure 18C] This figure shows a third example of the difference in mutual information in the application examples. [Figure 18D] This figure shows a fourth example of the difference in mutual information in the application examples. [Figure 18E] This figure shows a fifth example of the difference in mutual information in the application examples. [Figure 18F] This figure shows a sixth example of the difference in mutual information in the application examples. [Figure 19] This figure shows an example of the classification results of causal exploration factors in an application example. [Figure 20A] This figure shows the first example of the results of exploring causal factors in an application example. [Figure 20B] This figure shows a second example of the results of exploring causal factors in an application example. [Figure 20C] This figure shows a third example of the results of exploring causal factors in an application example. [Figure 20D] This figure shows a fourth example of the results of exploring causal factors in an application example. [Figure 20E] This figure shows the fifth example of the results of exploring causal factors in an application example. [Figure 20F] This figure shows the sixth example of the results of exploring causal factors in an application example. [Figure 21] This figure shows an example of a causal graph in an application example. [Modes for carrying out the invention]

[0012] Hereinafter, an embodiment of this disclosure will be described with reference to the drawings. Note that when the comparison objects are the same in terms of length, position, size, spacing, etc., this includes not only cases where they are exactly the same, but also cases where they differ to the extent that they do not deviate from the spirit of this disclosure (for example, differences within the tolerance range determined at the time of design).

[0013] 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 apparatus 100 of this embodiment derives causal relationships between multiple factors, including influenced factors and influencing factors which are factors that may influence the influenced factors. Influencing factors may include influencing factors that affect other influencing factors, or influencing factors that do not affect other influencing factors. The number of influenced factors is one or more (i.e., each influenced factor is one or more types of influenced factors). The number of influencing factors is two or more (i.e., each influencing factor is two or more types of influencing factors). The data for influencing factors and influenced factors are represented by at least one of quantitative data and qualitative data. The data for influenced factors and influencing factors may be obtained by measurement or calculation. Quantitative data is data expressed numerically. Qualitative data, on the other hand, is data that is not expressed numerically.

[0015] The influencing factors and influencing factors are not limited. For example, influencing factors may include factors used in the treatment process. Also, influencing factors 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 for water to be treated. In this case, influencing factors are, for example, factors relating to the amount of microbial communities present in the treatment process and used in the treatment process. Also, influencing factors are, for example, factors 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 influencing factors are, for example, physical quantities used as manipulated variables 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 influencing factors are, for example, the quality of the hot-rolled coil (e.g., tensile strength). In other words, the quality of the hot-rolled coil is affected by the physical quantities used as manipulated variables for the rolled material. Influencing factors may also be state factors that determine the characteristics of the affected factor during processing. These state factors may be uncontrollable or controllable. For example, the attributes (quantity, etc.) of an uncontrollable factor cannot be controlled in the processing process. Conversely, the attributes (quantity, etc.) of a controllable factor can be controlled in the processing process.

[0017] Furthermore, the influencing factors are not limited to the factors used in the processing of the treatment process. For example, the influencing factors may be factors relating to the number of various genes in a person or the number of microorganisms (e.g., bacteria) in the human body. In this case, the affected factors may be, for example, factors relating to test items for a specific human disease. That is, the values ​​of test items for a specific disease are affected by human genes and microorganisms in the human body.

[0018] In addition, any other factor that may influence the affected factor is acceptable; the influencing factors are not limited to those mentioned above.

[0019] Furthermore, the influencing factors may include manipulable influencing factors that can be artificially manipulated and mediating influencing factors. Manipulable influencing factors and mediating influencing factors are examples of influencing factors that may affect the affected factor. Manipulable influencing factors are factors that may affect mediating influencing factors. Mediating influencing factors are at least one of the following: factors that cannot be artificially manipulated and factors that cannot be artificially manipulated.

[0020] For example, an analyst can determine that a controllable influencing factor indirectly influences the affected factor through a mediating influencing factor if all of the following conditions (A) to (C) are met. (A) The processing device 100 derived that there is a causal relationship between the manipulable influencing factor and the mediating influencing factor. (B) The processing device 100 derived that there is a causal relationship between the mediating influencing factor and the affected factor. (C) The processing device 100 did not derive that there was a causal relationship between the manipulable influencing factor and the affected factor.

[0021] For example, in the aforementioned biological treatment process for water to be treated, factors relating to at least one of the pH and hydrological retention time (HRT) of the water to be treated are exemplified as manipulable influencing factors that can be artificially manipulated. Factors relating to the amount of microbial communities are exemplified as mediating influencing factors. Factors 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) are exemplified as affected factors. The amount of microbial communities can change by changing the pH or hydrological retention time (HRT) of the water to be treated. The amount of a specific substance in the water to be treated can change as a result of a change in the amount of microbial communities. Note that pH can be an affected factor that is influenced by manipulable influencing factors and mediating influencing factors, rather than being an artificially manipulable factor. In this case, pH should be treated as an affected factor, not as a manipulable influencing factor.

[0022] Furthermore, examples of manipulable influencing factors that can be artificially altered in the human body include factors related to the nutrients that humans ingest. Examples of mediating influencing factors include factors related to the number of various microbial communities (bacteria) in the human body. Examples of affected factors include factors related to test items for specific human diseases. Changing the nutrients that humans ingest can change the amount of microbial communities (bacteria) in the human body. Changes in the amount of microbial communities in the human body can change the values ​​of test items for specific diseases.

[0023] In Figure 1, this embodiment illustrates a case where the processing device 100 includes an acquisition unit 110, an influencing factor selection processing unit 120, a classification unit 130, a causal relationship derivation unit 140, and an output unit 150. Figure 2A is a flowchart illustrating an example of a processing method performed using the processing device 100. Figure 2B is a flowchart illustrating in detail an example of the influencing factor selection processing step S202 in Figure 2A. Below, the processing method of this embodiment will be explained with reference to the flowcharts in Figures 2A and 2B, along with an example of the functions of the processing device 100 shown in Figure 1. In the following explanation, examples will be given where the influencing factors include manipulable influencing factors and mediating influencing factors.

[0024] [Acquisition step (S201), acquisition unit 110] The acquisition unit 110 acquires information that the processing unit 100 needs to acquire in advance when deriving the causal relationship between the affected factor and the influencing factor. The acquisition unit 110 may acquire this information based on an input operation of the information to the user interface of the processing unit 100, may acquire this information by receiving it from an external device, or may acquire this information by reading it stored on a storage medium.

[0025] The acquisition unit 110 acquires, for example, multiple sets of training data as datasets, each set consisting of a data set containing data of an affected factor and data of multiple candidate influencing factors that may influence the affected factor. In this case, the data of the affected factor may be used as ground truth data (ground truth labels). The candidate influencing factors are candidates for influencing factors that will be used to derive causal relationships, as described later. In this embodiment, the example shows that the multiple influencing factors include multiple controllable influencing factors and multiple mediating influencing factors. The number of at least one of the controllable influencing factors and mediating influencing factors (number of items) may be 1. Also, in this embodiment, the example shows that the number of affected factors (number of items) is 1, but the number of affected factors may be multiple.

[0026] Furthermore, the acquisition unit 110 acquires values ​​that need to be pre-set as constants for processing in the influencing factor selection processing unit 120, the classification unit 130, and the causal relationship derivation unit 140, which will be described later.

[0027] [Influence factor selection process (S202), influence factor selection processing unit 120] The influence factor selection processing unit 120 performs processing to select influence factors from among multiple candidate influence factors that will be subject to the classification process (S203) and classification by the classification unit 130, as described later. In the following description, the targets of classification by the classification process (S203) and classification unit 130, as described later, will be referred to as classification targets as needed. Also, in the following description, the influence factors that will be subject to classification by the classification process (S203) and classification unit 130, as described later, will be referred to as classification target influence factors as needed.

[0028] When there are many types of influencing factors, such as in a microbial community, classifying all types of influencing factors increases the computational load. Furthermore, it increases the likelihood of deriving causal relationships from influencing factors that can be considered noise. Therefore, in this embodiment, the acquisition unit 110 acquires data including data on the affected factor and data on multiple candidate influencing factors that may be affected by the affected factor, and the influencing factor selection processing unit 120 selects (narrows down) the influencing factor to be classified from among the multiple candidate influencing factors. However, this is not always necessary. In this case, the influencing factor selection step (S202) and the influencing factor selection processing unit 120 may be omitted. Alternatively, in this case, the acquisition unit 110 may acquire data including data on the affected factor and data on multiple influencing factors that may be affected by the affected factor as training data.

[0029] Furthermore, in this embodiment, an example is given in which, among the manipulable influencing factors and mediating influencing factors, only mediating influencing factors are targeted for selection by the influencing factor selection processing unit 120. In this case, manipulable influencing factors are not targeted for selection by the influencing factor selection processing unit 120, and all types of manipulable influencing factors included in the learning data acquired by the acquisition unit 110 are targeted for classification. However, this is not necessarily required, and for example, manipulable influencing factors may be targeted for selection by the influencing factor selection processing unit 120 in addition to or instead of mediating influencing factors. Furthermore, in this embodiment, an example is given in which all types of affected factors included in the learning data acquired by the acquisition unit 110 are targeted for classification.

[0030] Furthermore, in this embodiment, an example is given in which the influence factor selection processing unit 120 performs a process to select a mediating influence factor to be classified from among a plurality of candidate mediating influence factors using a plurality of sets of training data acquired by the acquisition unit 110. This process may be a known method. For example, the influence factor selection processing unit 120 may select a mediating influence factor selected as described in Patent Document 1 as the mediating influence factor to be classified. Alternatively, the influence factor selection processing unit 120 may select a mediating influence factor selected by a known variable selection method such as the stepwise method as the mediating influence factor to be classified.

[0031] However, even when the frequency distribution of the data for each mediating influencing factor is non-normal and it is not easy to obtain a large amount of data, the influence factor selection processing unit 120 selects mediating influencing factors to be classified in a manner that allows for the selection of mediating influencing factors that may have a causal relationship with the affected factor as comprehensively as possible. The following is an example of how the influence factor selection processing unit 120 selects mediating influencing factors to be classified. Note that the following method is the method described in Japanese Patent Application No. 2024-77149.

[0032] In Figure 1, this embodiment illustrates a case where the influence factor selection processing unit 120 includes a first influence factor candidate group acquisition unit 121, an occurrence frequency calculation unit 122, a second influence factor candidate group creation unit 123, a learning model candidate creation unit 124, a model accuracy evaluation index calculation unit 125, a relationship calculation unit 126, and an influence factor selection unit 127. Figure 3 is a diagram illustrating an example of a method for selecting mediating influence factors. Below, an example of the functions of the influence factor selection processing unit 120 in this embodiment will be described with reference to the flowchart in Figure 2B and Figure 3. As mentioned above, this embodiment illustrates a case where the influence factors selected as the target of classification are mediating influence factors. Therefore, below, an example will be given in which the influence factor selection processing unit 120 selects the mediating influence factors to be classified.

[0033] [[First influencing factor candidate group acquisition step (S211), first influencing factor candidate group acquisition unit 121]] The first influence factor candidate group acquisition unit 121 acquires multiple first influence factor candidate groups, each containing either one candidate mediating influence factor or multiple candidate mediating influence factors. The first influence factor candidate group contains one or more candidates as mediating influence factors to be classified. In this embodiment, the case where the learning model is a linear regression equation as shown in equation (1) below is illustrated. However, the 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).

[0034]

number

[0035] In equation (1), x i0 x is the influencing factor as the dependent variable, ij β is a mediating factor as an explanatory variable, j x is the mediating factor x as an explanatory variable. ijThe regression coefficients are for β, where p is the number of mediating factors as explanatory variables. When p is 1, equation (1) is a simple regression equation; when p is 2 or greater, equation (1) is a multiple regression equation. 0i x is the intercept (constant term). i is a variable that identifies the learning model, and if the number of learning models (number of regression equations) is 1, i is not needed. For the sake of simplicity, the notation of the variable i will be omitted in the following explanation where necessary. In this case, the mediating influence factor as an explanatory variable is x j The dependent variable is x0, and the intercept is β. 0i These are represented by β0, respectively.

[0036] The number of candidate mediating factors (explanatory variables) included in multiple candidate groups of first influence factors only needs to be one or more. Furthermore, two or more candidate groups of first influence factors may include the same candidate mediating factors (explanatory variables). In this embodiment, we illustrate the case where the candidate mediating factors (explanatory variables) included in the candidate groups of first influence factors are selected from a predetermined set of candidate mediating factors. If the predetermined number of candidate mediating factors is p, then the candidate mediating factors are x1, x2, ... x p From this group, candidate mediating factors are selected from the first group of candidate influencing factors. For example, selecting a mediating factor may be represented by a regression coefficient for that mediating factor being non-zero. Not selecting a mediating factor may be represented by a regression coefficient for that mediating factor being zero.

[0037] Furthermore, in this embodiment, we illustrate a case in which the first influence factor candidate group acquisition unit 121 acquires training data from the acquisition unit 110. Figure 3 illustrates the following candidate groups of first influence factors: group 310a consisting of candidate mediating influence factor x1; group 310b consisting of candidate mediating influence factors x1 and x5; group 310c consisting of candidate mediating influence factors x2, x3, and x5; and group 310d consisting of candidate mediating influence factors x2, x4, x5, and x7.

[0038] The candidates for the mediating influence factors included in the plurality of first influence factor candidate groups 310a to 310d may be selected, for example, using the method described in Patent Document 1. In this case, for example, the first influence factor candidate group acquisition unit 121 creates a plurality of samples by resampling the learning data (dataset) acquired from the acquisition unit 110. The resampling method is, for example, the Bootstrap method, the Jackknife method, or the like.

[0039] Then, the first influence factor candidate group acquisition unit 121 extracts, from each resampled sample, a set of data of the influenced factor x0 (correct data) and candidate data of mediating influence factors x1, x2,... x p that may affect the influenced factor x0, and uses each of the plurality of sets of learning data as a dataset.

[0040] The first influence factor candidate group acquisition unit 121 performs penalized regression analysis that can shrink the regression coefficient to 0 for each sample using the extracted dataset. Then, the first influence factor candidate group acquisition unit 121 selects mediating influence factors whose regression coefficients do not become 0. The first influence factor candidate group acquisition unit 121 selects candidates for mediating influence factors to be included in each of the first influence factor candidate groups 310a to 310d by performing such selection of mediating influence factors for each sample. In this case, one of the first influence factor candidate groups 310a to 310d is obtained from one sample. The method of penalized regression analysis that can shrink the regression coefficient to 0 is, for example, a method that performs L1 regularization (regularization of the L1 norm), represented by Lasso (Least Absolute Shrinkage and Selection Operator), Elastic net, and SCAD (Smoothly Clipped Absolute Deviation). Also, the method of selecting candidates for mediating influence factors to be included in the plurality of first influence factor candidate groups is not limited to the method described in Patent Document 1. For example, the first influence factor candidate group acquisition unit 121 may randomly select candidates for mediating influence factors to be included in the first influence factor candidate group from among the candidate mediating influence factors x1, x2,... x p of.

[0041] Furthermore, the first influence factor candidate group acquisition unit 121 may acquire information indicating the first influence factor candidate group 310a to 310d from the acquisition unit 110 without performing the calculations described above. In this case, the acquisition unit 110 may acquire the information indicating the first influence factor candidate group 310a to 310d based on an input operation of the information to the user interface of the processing device 100, or by receiving the information from an external device, or by reading the information stored on a storage medium.

[0042] [[Appearance frequency calculation step (S212), appearance frequency calculation unit 122]] The frequency calculation unit 122 calculates the frequency of occurrence of candidate mediating influencing factors in multiple candidate groups of first influencing factors 310a to 310d, where x1, x2, ... x p This is done for each of them. For example, if there are B candidates for multiple primary influencing factors 310a to 310d, and a certain candidate for mediating influencing factor x r If (r=1, 2, ...p) is included in the G candidate group of first influencing factors, then the candidate x of the mediating influencing factor is r The 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 influence factors 310a to 310d were acquired by the first influence factor candidate group acquisition unit 121, then for example, the frequency of occurrence of candidate mediating influence factor x1 is 0.5 (=2 / 4), and the frequency of occurrence of candidate mediating influence factor x5 is 0.75 (=3 / 4). Also, for example, the number of resamplings N_rs mentioned above, and a candidate x of a certain mediating influence factor included in the sample obtained by re-evaluation. r The frequency of occurrence can also be defined as the ratio of the number of occurrences H to N_rs (=H / N_rs or =(H / N_rs)×100).

[0043] As described above, as shown in Figure 3, the candidate mediating influence factors are x1, x2, ... x p The frequency of occurrence for each of these is calculated (one by one), with a value of 320.

[0044] [[Process for creating candidate group of second mediating influence factors (S213), Second influence factor candidate group creation unit 123]] The second influence factor candidate group generation unit 123 generates candidate mediating influence factors x1, x2, ... x p Based on the frequency of occurrence 320 for each of the above, multiple candidate groups of second mediating factors are created, each containing either one candidate mediating factor or multiple candidate mediating factors. Candidate mediating factors with relatively high frequency of occurrence are more likely to be mediating factors that influence the affected factor x0 (explanatory variables that accurately explain the dependent variable) than candidates mediating factors with relatively low frequency of occurrence. Therefore, in this embodiment, we illustrate a case in which the second influence factor candidate group creation unit 123 selects candidate mediating factors to be included in the second mediating factor candidate group such that candidates mediating factors with relatively high frequency of occurrence 320 are included in more second mediating factor candidate groups than candidates mediating factors with relatively low frequency of occurrence 320.

[0045] In the example shown in Figure 3, for example, the second influence factor candidate group creation unit 123 may select candidate mediating factors to include in the second mediating factor candidate group such that candidate x5 of mediating factors is included in more second mediating factor candidate groups than candidate x1 of mediating factors. Alternatively, for example, the second influence factor candidate group creation unit 123 may select candidate mediating factors to include in the second mediating factor candidate group such that candidate x5 of mediating factors is included in more second mediating factor candidate groups than candidate x7 of mediating factors. Alternatively, for example, the second influence factor candidate group creation unit 123 may select candidate mediating factors to include in the second mediating factor candidate group such that candidate x1 of mediating factors is included in more second mediating factor candidate groups than candidate x7 of mediating factors.

[0046] Furthermore, the second influence factor candidate group creation unit 123 may select candidate mediating factors to be included in the second mediating factor candidate group such that there are more candidates for mediating factors with a relatively high frequency of occurrence 320 than candidates for mediating factors with a relatively low frequency of occurrence 320. In other words, the second mediating factor candidate group may be selected such that there are not more candidates for mediating factors with a relatively low frequency of occurrence 320 than candidates for mediating factors with a relatively high frequency of occurrence 320. In this way, the more likely a mediating factor is to explain the influenced factor x0 with good accuracy, the more candidates it can be included in the second mediating factor candidate group.Therefore, in this embodiment, we will illustrate the case in which the second influence factor candidate group creation unit 123 selects m candidate mediating factors in order from the highest frequency of occurrence and creates a second mediating factor candidate group containing the selected m candidate mediating factors, for each case in which M is an integer of 2 or more and m is changed from 1 to M.

[0047] When performing such processing, the second influence factor candidate group creation unit 123 generates candidate mediating influence factors x1, x2, ... x p These can also be sorted in descending order of frequency of occurrence. In this case, as shown in Figure 3, candidate mediating factors 330 sorted in descending order of frequency of occurrence are obtained. In the following explanation, candidate mediating factors sorted in descending order of frequency of occurrence will be referred to as sorted candidate mediating factors, as necessary.

[0048] In the example shown in Figure 3, when m=1, the second influence factor candidate group creation unit 123 creates a second mediating influence factor candidate group that includes only candidate x5, which is the first mediating influence factor in the sorted mediating influence factor candidate 330. When m=2, the second influence factor candidate group creation unit 123 creates a second mediating influence factor candidate group that includes candidate x1 and x5, which are the first and second mediating influence factors in the sorted mediating influence factor candidate 330. When m=3, the second influence factor candidate group creation unit 123 creates a second mediating influence factor candidate group that includes candidate x1, x5, and x7, which are the first to third mediating influence factors in the sorted mediating influence factor candidate 330. Similarly, when m=M, the second influence factor candidate group creation unit 123 creates a second mediating influence factor candidate group that includes candidate mediating influence factors from the first to the Mth in the sorted mediating influence factor candidate 330. The value of M is the candidate mediating factor x1, x2, ... x p The number of (=p) may be the same, and the candidate mediating influencers 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).

[0049] In Figure 3, the candidate group of second influencing factors 340 represents the candidate groups of second influencing factors 340a to 340c created as described above. Figure 3 also shows the names of the candidate mediating influencing factors included in each of the candidate groups of second influencing factors 340a to 340c, namely "x5", "x1,x5", and "x1,x5,x7", and their numbers, namely "1", "2", and "3".

[0050] It should be noted that the second influence factor candidate group creation unit 123 does not necessarily have to create the second mediating influence factor candidate group in the manner described above. For example, the second influence factor candidate group creation unit 123 may make the number of second mediating influence factor candidate groups that include the second and third highest mediating influence factor candidates with an occurrence frequency of 320 (x1 and x7 in the example shown in Figure 3) the same.

[0051] [[Training model candidate creation process (S214), training model candidate creation unit 124]] The learning model candidate creation unit 124 creates multiple learning model candidates for each of the multiple second influence factor candidate groups 340a to 340c, each showing the relationship between the mediating influence factor candidate included in the second mediating influence factor candidate group and the influenced factor. As mentioned above, this embodiment exemplifies the case where the learning model is a linear regression equation. Therefore, this embodiment exemplifies the case where the learning model candidate is also a linear regression equation. In this case, the learning model candidate creation unit 124 may create the learning model candidate by performing supervised learning using a known method such as the least squares method. In this case, the learning model candidate creation unit 124 may perform supervised learning using the aforementioned dataset or multiple samples obtained by resampling the dataset. In this embodiment, it is shown that the aforementioned dataset (training data) or multiple samples obtained by resampling the dataset are obtained by the first influence factor candidate group acquisition unit 121. Therefore, it is preferable for the learning model candidate creation unit 124 to create the learning model candidate by performing supervised learning. However, for example, the learning model candidate creation unit 124 may create learning model candidates by unsupervised learning.

[0052] Figure 3 shows three candidate learning models 350a to 350c. Candidate learning model 350a consists of five candidate mediating factors x included in the second candidate group of influencing factors 340a and the influenced factor x 01 This shows the relationship (x 01 =β5x5+β 01 ). Candidate learning model 350b is composed of candidate mediating factors x1, x5 and influenced factor x, which are included in candidate group 340b of the second influencing factor. 02 This shows the relationship (x 02 =β1x1+β5x5+β 02 ). Candidate learning model 350c is composed of candidate mediating factors x1, x5, x7 and influenced factor x, which are included in candidate group 340b of the second influencing factor. 03 This shows the relationship (x 03 =β1x1+β5x5+β7x7+β 03 ). Note that x 01 , x 02 , x 03 , β 01 , β 02 , β03 The subscripts 1, 2, and 3 indicate the first, second, and third candidate learning models, respectively.

[0053] [[Model accuracy evaluation index calculation process (S215), Model accuracy evaluation index calculation unit 125]] The model accuracy evaluation index calculation unit 125 calculates a model accuracy evaluation index for each of the multiple candidate learning models 350a to 350c. The model accuracy evaluation index is an index used to evaluate the estimation accuracy of the candidate learning models. Note that the model accuracy evaluation index is not limited to a specific index. For example, the model accuracy evaluation index may be the coefficient of determination, the adjusted coefficient of determination, the root mean squared error (RMSE), the Akaike Information Criterion (AIC), the multiple correlation coefficient, the p-value of the regression coefficient, or the absolute value of the regression coefficient. Note that the estimation accuracy is evaluated using, for example, the cross-validation method.

[0054] In Figure 3, although specific numerical values ​​are omitted, the model accuracy evaluation metrics for candidate learning models 350a, 350b, and 350c are 360a, 360b, and 360c, respectively. The coefficient of determination R is used as the model accuracy evaluation metric. 2 When using this, a larger value of the model accuracy evaluation metric indicates higher estimation accuracy for candidate learning models 350a to 350c. However, the model accuracy evaluation metric is not limited to those that show higher values ​​in relation to higher estimation accuracy for candidate learning models 350a to 350c. For example, the coefficient of determination R can be used as a model accuracy evaluation metric. 2 Alternatively, the value obtained by multiplying by (-1) may be used as the model accuracy evaluation index. In this case, the model accuracy evaluation index will show smaller values ​​(larger absolute values ​​for negative values) as the estimation accuracy of candidate learning models 350a to 350c increases.

[0055] [[Relationship calculation process (S216), Relationship calculation unit 126]] The relationship calculation unit 126 calculates the relationship information between the number of influencing factors and the evaluation index. This relationship information shows the relationship between the number of mediating influencing factors included in one candidate learning model 350a to 350c and the model accuracy evaluation index used to evaluate the estimation accuracy of the candidate learning model.

[0056] In Figure 3, the number of mediating influence factor candidates included in candidate learning model 350a is 1 (see the column for the number of mediating influence factor candidates in the second influence factor candidate group 340a). Therefore, the number of mediating influence factor candidates included in candidate learning model 350a (=1) and the value of the model accuracy evaluation index 360a for candidate learning model 350a are used to calculate the influence factor number-evaluation index relationship information. Similarly, the number of mediating influence factor candidates included in candidate learning model 350b (=2) and the value of the model accuracy evaluation index 360b for candidate learning model 350b are used to calculate the influence factor number-evaluation index relationship information. The number of mediating influence factor candidates included in candidate learning model 350c (=3) and the value of the model accuracy evaluation index 360c for candidate learning model 350c are used to calculate the influence factor number-evaluation index relationship information.

[0057] Figure 3 shows an example of the influencing factor number-evaluation index relationship information 370. Point 371, which represents the influencing factor number-evaluation index relationship information 370, is determined by the number of mediating influencing factor candidates included in learning model candidate 350a (=1) and the value of the model accuracy evaluation index 360a for learning model candidate 350a. Similarly, point 372 is determined by the number of mediating influencing factor candidates included in learning model candidate 350b (=2) and the value of the model accuracy evaluation index 360b for learning model candidate 350b. Point 373 is determined by the number of mediating influencing factor candidates included in learning model candidate 350c (=3) and the value of the model accuracy evaluation index 360c for learning model candidate 350c.

[0058] The relationship information between the number of influencing factors and the evaluation metric may be represented by a function that shows the relationship between the number of candidate mediating influencing factors included in candidate learning models 350a to 350c and the model accuracy evaluation metric used to assess the estimation accuracy of the candidate learning models. Alternatively, the relationship information between the number of influencing factors and the model accuracy evaluation metric may be represented by a table that stores the relationship between the number of candidate mediating influencing factors included in candidate learning models 350a to 350c and the model accuracy evaluation metric used to assess the estimation accuracy of the candidate learning models.

[0059] [[Selection process for mediating influencing factors (S217), Influencing factor selection unit 127]] The influencing factor selection unit 127, based on the influencing factor number-evaluation index relationship information, selects mediating influencing factors x1, x2, ..., x in the learning model. p This is selected as the mediating factor for classification. Note that if p=1, the only mediating factor in the learning model will be x1. Also, as mentioned above, the regression coefficient β for the selected mediating factor is... j Set a value other than 0 for the regression coefficient β for the mediating influence factors that are 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 mediating factors for this.

[0060] In this embodiment, we illustrate a case in which the influence factor selection unit 127 derives a model accuracy evaluation index that satisfies predetermined conditions in the relationship shown by the number of influence factors - evaluation index relationship information 370, and selects candidate mediating influence factors included in the candidate learning model corresponding to the model accuracy evaluation index as the mediating influence factors to be classified. Here, the candidate mediating influence factors included in the candidate learning model corresponding to the model accuracy evaluation index are the candidate mediating influence factors included in the candidate learning model from which the model accuracy evaluation index is calculated. For example, in Figure 3, the model accuracy evaluation index determined at point 373 is the model accuracy evaluation index 360c, the candidate learning model from which the model accuracy evaluation index 360c is calculated is the candidate learning model 350c, and the candidate mediating influence factors included in the candidate learning model 350c are candidate mediating influence factors x1, x5, and x7. Therefore, the candidate learning model corresponding to the model accuracy evaluation index determined at point 373 is the candidate learning model 350c, and the candidate mediating influence factors included in the candidate learning model are x1, x5, and x7.

[0061] Furthermore, the predetermined conditions may also be expressed using, for example, the peak value of the model accuracy evaluation index in the relationship shown by the number of influencing factors - evaluation index relationship information 370. For example, the model accuracy evaluation index may be one in which the value increases as the estimation accuracy of the candidate learning models 350a to 350c increases. For example, the influencing factor selection unit 127 may derive a model accuracy evaluation index that shows a maximum value in the relationship shown by the number of influencing factors - evaluation index relationship information 370. The influencing factor selection unit 127 may then select a candidate mediating influencing factor included in the candidate learning model corresponding to the model accuracy evaluation index that shows a maximum value as the mediating influencing factor to be classified. In this case, in Figure 3, the influencing factor selection unit 127 selects a candidate mediating influencing factor included in the candidate learning model corresponding to the model accuracy evaluation index at points 373 to 375 as the mediating influencing factor to be classified. Thus, the influencing factor selection unit 127 may select a candidate mediating influencing factor included in multiple candidate learning models as the mediating influencing factor to be classified. Furthermore, if the model accuracy evaluation index is one in which the value decreases as the estimation accuracy of the candidate learning models 350a to 350c increases, the influencing factor selection unit 127 may use the local minimum instead of the aforementioned local maximum. In the following explanation, the local maximum when using a model accuracy evaluation index that increases as the estimation accuracy of the candidate learning models 350a to 350c increases, and the local minimum when using a model accuracy evaluation index that decreases as the estimation accuracy of the candidate learning models 350a to 350c increases, will be referred to as local peaks, as necessary.

[0062] Furthermore, the influence factor selection unit 127 may select as the mediating influence factors to be classified the candidate mediating influence factors included in the candidate learning model with the smallest number of candidate mediating influence factors among the candidate learning models corresponding to the model accuracy evaluation index showing a local peak. In this way, for example, it is possible to suppress the selection of mediating influence factors from overfitted candidate learning models. In Figure 3, among the candidate learning models corresponding to the model accuracy evaluation index at points 373 to 375, the candidate learning model with the smallest number of candidate mediating influence factors is candidate learning model 350c corresponding to the model accuracy evaluation index at point 373. Therefore, the influence factor selection unit 127 selects candidate mediating influence factors x1, x5, and x7 included in candidate learning model 350c as the mediating influence factors to be classified. Thus, the influence factor selection unit 127 may select as the mediating influence factors to be classified any candidate mediating influence factors included in a single candidate learning model.

[0063] Furthermore, when selecting a candidate learning model with a larger absolute value of the model accuracy evaluation index, the influence factor selection unit 127 may select mediating influence factors that affect the affected factors, for example, as follows. First, the influence factor selection unit 127 derives a model accuracy evaluation index from among the candidate learning models corresponding to the model accuracy evaluation index that shows a local peak, in which the absolute value is greater than the threshold Th2 (Th2 is a positive number) defined for the relationship shown by the influence factor number-evaluation index relationship information 370. Then, the influence factor selection unit 127 selects the candidate mediating influence factors included in the candidate learning model corresponding to the model accuracy evaluation index as the mediating influence factors to be classified.

[0064] The threshold Th2 may be a predetermined fixed value or a variable value. For example, the influence factor selection unit 127 may calculate the threshold Th2 based on the influence factor number-evaluation index relationship information 370. More specifically, for example, the influence factor selection unit 127 may calculate the threshold Th2 based on a value (e.g., standard deviation σ) that represents the variability of the model accuracy evaluation index in the relationship shown in the influence factor number-evaluation index relationship information 370. In this case, for example, the influence factor selection unit 127 may calculate a threshold Th2 whose absolute value is obtained by subtracting or adding a positive integer multiple of σ (e.g., 1 × σ, 2 × σ) from the value of the model accuracy evaluation index at the local peak with the largest absolute value in the relationship shown in the influence factor number-evaluation index relationship information 370.

[0065] When using a model accuracy evaluation index that shows a larger value the higher the estimation accuracy of candidate learning models 350a to 350c, the influence factor selection unit 127 may select mediating influence factors that affect the affected factors, for example, as follows. First, the influence factor selection unit 127 derives the maximum value of the model accuracy evaluation index that shows the largest maximum value in the relationship shown in the influence factor number-evaluation index relationship information 370. Then, the influence factor selection unit 127 calculates a threshold Th2 by subtracting a positive integer multiple of σ (for example, 1 × σ, 2 × σ) from the maximum value of the model accuracy evaluation index. Then, the influence factor selection unit 127 selects candidate mediating influence factors included in the candidate learning models that correspond to the model accuracy evaluation index that is larger than the threshold Th2 as the mediating influence factors to be classified. On the other hand, when using a model accuracy evaluation index that shows a smaller value the higher the estimation accuracy of candidate learning models 350a to 350c, the influence factor selection unit 127 may select mediating influence factors that affect the affected factors, for example, as follows. First, the influence factor selection unit 127 derives the minimum value of the model accuracy evaluation index that shows the smallest local minimum in the relationship shown in the influence factor number-evaluation index relationship information 370. Then, the influence factor selection unit 127 calculates a threshold Th2 by adding a positive integer multiple of σ (for example, 1 × σ, 2 × σ) to the minimum value of the model accuracy evaluation index. Then, the influence factor selection unit 127 selects candidate mediating influence factors included in the candidate learning model corresponding to the model accuracy evaluation index smaller than the threshold Th2 as the mediating influence factors to be classified.

[0066] Furthermore, for example, if the number of influencing factors - evaluation index relationship information 370 is expressed as a function, the number of candidate mediating influencing factors corresponding to the model accuracy evaluation index showing a local peak may not be an integer in that function. In this case, the influencing factor selection unit 127 may select the point that is closest to the model accuracy evaluation index showing a local peak from among the points used when calculating the function (points determined by the model accuracy evaluation index and the number of candidate mediating influencing factors).

[0067] The candidate learning models corresponding to the local peaks in the model accuracy evaluation metrics in the relationship shown by the number of influencing factors - evaluation metric relationship information 370 can be said to be candidate learning models whose estimation accuracy is locally improved. By searching for candidate learning models that satisfy the conditions using such local peak model accuracy evaluation metrics, it is possible to search for candidate learning models that include candidate model accuracy evaluation metrics that accurately explain the influencing factors. However, it is not necessarily true that a larger absolute value of a model accuracy evaluation metric indicates higher estimation accuracy for the candidate learning model corresponding to that metric. For example, even if the absolute value of a model accuracy evaluation metric is large, if the number of candidate mediating influencing factors included in the candidate learning model corresponding to that metric is large, it may result in overfitting.

[0068] Based on the above, it is preferable for the influence factor selection unit 127 to use a condition expressed using the peak value of the model accuracy evaluation index in the relationship shown by the influence factor number-evaluation index relationship information 370 when selecting candidate mediating influence factors included in candidate learning models corresponding to model accuracy evaluation indices that satisfy predetermined conditions as mediating influence factors to be classified. However, the predetermined conditions are not limited to these conditions. For example, the influence factor selection unit 127 may select mediating influence factors that affect the influenced factors as follows. First, the influence factor selection unit 127 derives model accuracy evaluation indices whose absolute value is greater than or equal to the threshold Th3 in the relationship shown by the influence factor number-evaluation index relationship information 370. Then, the influence factor selection unit 127 derives a model accuracy evaluation index in which the number of candidate mediating influence factors corresponding to the model accuracy evaluation index is the smallest among the model accuracy evaluation indices whose absolute value is greater than or equal to the threshold Th3. Then, the influence factor selection unit 127 selects candidate mediating influence factors included in candidate learning models corresponding to the model accuracy evaluation index as mediating influence factors to be classified. The threshold Th3 can be the same value as the aforementioned threshold Th2, or it can be a different value.

[0069] In Figure 3, the model accuracy metrics showing local peaks are those at points 373–375. Among the model accuracy metrics at points 373–375, the candidate learning model corresponding to the model accuracy metric with the minimum number of candidate mediating factors is candidate learning model 350c, which corresponds to the model accuracy metric at point 373. Also in Figure 3, among the model accuracy metrics at points 373–375, the candidate learning models corresponding to the model accuracy metrics with a threshold of Th2 or higher are the candidate learning models corresponding to the model accuracy metrics at points 373 and 375. Furthermore, among the model accuracy metrics at points 373 and 375, the candidate learning model corresponding to the model accuracy metric with the minimum number of candidate mediating factors is candidate learning model 350c, which corresponds to the model accuracy metric at point 373.

[0070] Furthermore, when threshold Th3 is the same as threshold Th2, in Figure 3, among the model accuracy evaluation metrics that are greater than or equal to threshold Th2 (=Th3), the candidate learning model corresponding to the model accuracy evaluation metric with the smallest number of candidate mediating influence factors is candidate learning model 350c, which corresponds to the model accuracy evaluation metric at point 373.

[0071] Figure 3 illustrates the case where candidate mediating factors x1, x5, and x7 are selected as mediating factors to be classified (see the end of the arrow next to the number of influence factors - evaluation index relationship information 370). However, as mentioned above, for example, the influence factor selection unit 217 may select all of the mediating factors included in the candidate learning model corresponding to the model accuracy evaluation index that shows a local peak (model accuracy evaluation index at points 373 to 375). Although not shown in Figure 3, in this case, 11 candidate mediating factors, including candidate mediating factors x1, x5, and x7, are selected as mediating factors to be classified.

[0072] As described above, this embodiment illustrates a case in which the influence factor selection unit 217 selects mediating influence factors to be classified based on the influence factor number-evaluation index relationship information 370. However, if the influence factor number-evaluation index relationship information 370 is used for selecting explanatory variables in the learning model, the processing unit 100 does not necessarily have to spontaneously select mediating influence factors to be classified. A user (human) may select the mediating influence factors for which causal relationships are to be derived based on the influence factor number-evaluation index relationship information 370. In this case, the acquisition unit 110 may acquire information on the mediating influence factors for which causal relationships are to be derived, as selected by the user. In this case, the processing unit 100 (influence factor selection processing unit 120) does not necessarily have an influence factor selection unit 127.

[0073] [Classification process (S203), classification section 130] The classification unit 130 classifies each of the multiple factors, including the affected factors and the influencing factors, into one of several hierarchical levels according to their respective causal order. As described above, this embodiment exemplifies a case where the influencing factors include manipulable influencing factors and mediating influencing factors. Furthermore, this embodiment exemplifies a case where the classification unit 130 classifies only the mediating influencing factors selected as the target for classification by the influencing factor selection processing unit 120 from among the candidate mediating influencing factors.

[0074] The order of the causal order between two factors is determined, for example, such that the causal factor is higher in rank (earlier in the order) than the effect factor. The causal order may be calculated based on an independence evaluation index that assesses the independence of the explanatory variable with respect to the residuals calculated by performing a simple linear regression analysis with one of the two factors as the dependent variable and the other as the explanatory variable. The calculation of the causal order itself can be achieved using known techniques, for example, by using methods such as LiNGAM (Linear Non-Gaussian Acyclic Model) or Bayesian networks. In this embodiment, we illustrate a case where the classification unit 130 calculates the causal order of each of multiple factors, including influenced factors and influencing factors (manipulable influencing factors and mediating influencing factors), by using LiNGAM. In the following description, the factors for which causal relationships are derived will be referred to as causal exploration factors as needed.

[0075] First, the classification unit 130 performs the following (C) and (D) for all combinations of two causal exploration factors obtained from all causal exploration factors. (C) One of any two causal exploration factors x i Let x be the explanatory variable, and the other causal exploration factor x j By performing a simple linear regression analysis using the training data with the target variable r, the residuals r j (i) Calculate. (D) Mutual information I(x i ,r j (i) Calculate ).

[0076] The training data includes, for example, at least one of the training data acquired by the acquisition unit 110 and the samples resampled by the influencing factor selection processing unit 120. (Residual r) j (i)The mutual information I(X,Y) is expressed by equations (2) and (3) below, respectively. In LiNGAM, it is assumed that the data are non-normally distributed. In addition, in LiNGAM, the error term of the structural equation used in simple linear regression is assumed to be non-normally distributed and independent of other error terms. Therefore, if the frequency distribution of the data for each causal exploration factor (included in the aforementioned training data) is not non-normally distributed, it is preferable for the classification unit 130 to resample the causal exploration factor so that the frequency distribution of the data for the causal exploration factor becomes non-normally distributed. In this case, for example, the classification unit 130 includes the resampled data of the causal exploration factor in the training data and performs simple linear regression. The test to determine whether or not a causal exploration factor is non-normally distributed can be implemented using known techniques. For example, the classification unit 130 may determine whether or not a causal exploration factor is non-normally distributed by using the Shapiro-Wilk test or the KS (Kolmogorov-Smirnov) test, etc.

[0077]

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[0078] In equation (2), cov(x i ,x j ) is the causal exploration factor x i , x j This is the covariance of var(x). i ) is the causal exploration factor x i This is the variance of r. j (i) In equation (2), etc., r j This corresponds to the symbol with (i) above the j.

[0079] In equation (3), P(x,y) is the joint probability of the random variables x and y. P(x)P(y) is the marginal probability of the random variables x and y. In LiNGAM, if the mutual information I(X,Y) is 0, then X and Y are considered to be independent of each other. A certain causal search factor x i Regarding the causal exploration factor x, iLet x be the explanatory variable, and all other causal search factors x that are the target of the causal order search. j The total mutual information I(x) calculated when x is the dependent variable. i ,r j (i) If ) is 0, then the causal exploration factor x i This involves searching for all other causal search factors that are the target of the causal order search, and the target variable x j The residual r is calculated by performing a simple linear regression analysis. j (i) It is independent of the causal search factor x. Therefore, by LiNGAM's theorem, which is the contrapositive of the Darmois-Skitovic theorem, the causal search factor x i The causal order of is determined to be the highest-level causal order among the causal search factors being explored. In other words, causal search factor x i It is determined to be an exogenous variable (a variable that does not have a parent in the causal graph). The LiNGAM theorem states that for every pair of observed variables, when regression analysis is performed in two ways—one with one pair as the dependent variable and the other as the independent variable, and the other with the dependent variable and the other as the independent variable—the independent variable that is independent of the residuals in any pair can be the first in the causal order. In actual data applications, the mutual information I(X,Y) may not be zero. Therefore, instead of zero, the condition that it is below a positive threshold greater than zero may be adopted. For example, the threshold may be set in the range of 0.1 or less.

[0080] Here, we illustrate the case where the classification unit 130 calculates the causal order of five causal exploration factors x1 to x5. Note that x shown in this section (the section [Classification process (S203), Classification unit 130]) i , x j (x1~x5) The x1~x5 exemplified in the section [Influence Factor Selection Processing Step (S202), Influence Factor Selection Processing Unit 120] are not shown to correspond here. Here, we illustrate the case where x1, x3, and x4 are mediating influence factors, x5 is a controllable influence factor, and x2 is an influenced factor.

[0081] Furthermore, for the sake of simplicity, in the structural equation (4) shown below, we assume that the error variables e1 to e5 are uniformly distributed error variables in the unit interval [-1,1]. Also, we assume that the data for causal exploration factors x1 to x5 were generated with a sample size of 1000. Figure 4 shows the results obtained from the data for causal exploration factors x1 to x5 generated in this way.

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[0083] Figure 4(a) shows the mutual information I(x) calculated from two of the five causal exploration factors x1 to x5. i ,r j (i) This figure shows an example of the above. Here, as an example, when the threshold mentioned above is 0.09, Figure 4(a) shows the total mutual information I(x1,r2) calculated when the causal exploration factor x1 is the explanatory variable and all other causal exploration factors x2~x5 that are the target of the causal order exploration are the dependent variables. (1) ), I(x1,r3 (1) ), I(x1,r4 (1) ), I(x1,r5 (1) ) is 0. However, when the causal exploration factor x5 is used as the explanatory variable and all other causal exploration factors x1, x2~x4 that are the target of the causal order exploration are used as the dependent variables, the total mutual information I(x5,r1) is calculated. (5) ), I(x5,r2 (5) ), I(x5,r3 (5) ), I(x5,r4 (5) ) is also close to 0. Depending on the threshold mentioned above, the causal order of causal exploration factors such as causal exploration factor x5 may be lower in order. Therefore, in this embodiment, the classification unit 130 processes the causal exploration factor x as follows. i An example of determining the causal order is given.

[0084] First, as shown in Figure 4(a), the same causal exploration factor x i The mutual information I(x) is calculated when x is used as the explanatory and dependent variable. i, r i (i) ) becomes the diagonal component, and the mutual information I(x i , r j (i) ) is represented by a matrix. In Fig. 4(a), the mutual information I(x i , r j (i) ) with i (the causal exploration factor x i ) as the explanatory variable is made to correspond to the rows, and j (the causal exploration factor x j ) as the target variable is made to correspond to the columns is exemplified. The classification unit 130, in this matrix, as shown in the following equation (5), calculates the value obtained by subtracting the component (I(x i , r j (i) )) from the component at the transposed position with respect to the said component (I(x j , r i (j) )). In the following description, this value is referred to as the difference in mutual information as necessary. In the matrix storing the difference in mutual information calculated in this way for a certain causal exploration factor x i , if the values of the components other than the diagonal component are all negative, the classification unit 130 can determine that the causal order of the said causal exploration factor x i is a causal order higher than that of all other causal exploration factors for which the causal order is to be explored (note that the diagonal component of the matrix storing the difference in mutual information is 0). However, when the mutual information is extremely close to 0 or when the negative value of the difference in mutual information is minute, in numerical calculations, the difference in mutual information may be regarded as a value equal to or greater than 0. Therefore, the classification unit 130 sets a threshold value equal to or greater than 0 as the threshold value for the difference in mutual information. The threshold value may be, for example, a value of 0.2 or less, preferably a value of 0.1 or less. Also, the threshold value may be a negative value. Here, in the matrix storing the difference in mutual information calculated for a certain causal exploration factor x i , if the values of the components other than the diagonal component are all less than or equal to the threshold value, the said causal exploration factor x iThe causal order of is exemplified by the case where it is determined to be a higher causal order than all other causal search factors that are the target of the causal order search (i.e., the aforementioned negative value is set to be below the threshold). In this embodiment, mutual information and the difference of components other than the diagonal components of mutual information are examples of independence evaluation indicators. In the following description, in the matrix that stores the difference of mutual information, the values ​​of components other than the diagonal components will be referred to as the difference of components other than the diagonal components of mutual information, as necessary.

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[0086] Figure 4(b) shows the mutual information I(x) shown in Figure 4(a). i ,r j (i) This figure shows an example of the difference in mutual information calculated based on ). Here, the case where the threshold is 0.09 is shown as an example. In Figure 4(b), the difference I(x1,r) of mutual information other than the diagonal components calculated using causal exploration factors x1 and x5 is shown. j (1) )-I(x j ,r1 (j) ), I(x5,r j (5) )-I(x j ,r5 (j) All of the values ​​are below the threshold. Therefore, causal search factors x1 and x5 are determined to be the highest-ranking among the causal search factors x1 to x5 that are being searched for in terms of causal order.

[0087] Next, the classification unit 130 excludes causal search factors x1 and x5, which it determined to be the highest-ranking among the causal search factors x1 to x5 that are the targets of the causal order search, from the causal order search target (structural equation model), and makes the remaining causal search factors x2 to x4 the (new) targets of the causal order search.

[0088] Next, the classification unit 130 calculates the residual r2 from the remaining causal exploration factors x2 to x4, excluding the causal exploration factors x1 and x5 that were excluded from the causal order search target, by removing the influence of the excluded causal exploration factors x1 and x5. [1,5] , r3[1,5] , r5 [1,5] This is calculated using the following equation (2').

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[0090] Here, k = 2, 3, 4. Also, x in equation (2) i , x j Each of these, r i [1,5] , r j [1,5] Replace with the following. The classification unit 130 calculates the residual using the following equation (2'').

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[0092] In the following explanation, the residual r defined by equation (2) is used. j (i) This is referred to as the first residual, as needed. Also, the residual r defined in equation (2') k [1,5] This is referred to as the second residual, as needed. Also, the residual Δr defined by equation (2'') j (i)[1,5] This is referred to as the third residual, as needed.

[0093] Then, the classification unit 130 calculates the second residual r i [1,5] And the third residual Δr j (i)[1,5] The mutual information between and I(r i [1,5] ,Δr j (i)[1,5] Calculate ).

[0094] Then, the classification unit 130 selects one of the causal search factors x among the causal search factors that are the target of the causal order search. i And, among the causal search factors that are the target of the causal order search, there are other causal search factors x jThe difference I(r) of all mutual information amounts calculated using and i [1,5] ,Δr j (i)[1,5] )-I(r j [1,5] ,Δr i (j)[1,5] In a matrix that stores ( ), if the values ​​of components other than the diagonal components (the difference of the mutual information other than the diagonal components) are less than or equal to a threshold, then that one causal exploration factor x i The causal order is the same as all other causal exploration factors x j It is determined that this is a higher causal order. The classification unit 130 determines that one of the causal search factors x of the causal search factors that are the target of the causal order search is i And, among the causal search factors that are the target of the causal order search, other causal search factors x j The total mutual information I(r) calculated using and i [1,5] ,Δr j (i)[1,5] If ) is 0 or less than or equal to the threshold, then the one causal exploration factor x i The causal order is the same as all other causal exploration factors x j It may be determined that this is a higher causal order.

[0095] Figure 5(a) shows the mutual information I(r) calculated from two of the three causal exploration factors x2 to x4, excluding the top-level causal exploration factors x1 and x5 from the five causal exploration factors x1 to x5 shown in Figure 4. i [1,5] ,Δr j (i)[1,5] This figure shows an example of ). Also, Figure 5(b) shows the difference in mutual information I(r) calculated from two of the three causal exploration factors x2 to x4, excluding the top-level causal exploration factors x1 and x5 from the five causal exploration factors x1 to x5 shown in Figure 4. i [1,5] ,Δr j (i)[1,5] )-I(r j [1,5] ,Δr i (j)[1,5] An example of this is shown.

[0096] Figure 5 illustrates a case in which causal search factor x3 is determined to be the highest-ranking among the causal search factors x2 to x4 that are the target of the causal order search, as described above.

[0097] Next, the classification unit 130 excludes the causal search factor x2 to x4 that it has determined to be the highest-ranking among the causal search factors x2 to x4 that are the targets of the causal order search (structural equation model), and makes the remaining causal search factors the (new) targets of the causal order search. In the example shown in Figure 5, the causal search factor that has been determined to be the highest-ranking among the causal search factors x2 to x4 that are the targets of the causal order search is causal search factor x3. Also in the example shown in Figure 5, the remaining causal search factors are causal search factors x2 and x4.

[0098] Then, the classification unit 130 determines whether the (new) target causal exploration factors x2 and x4 are the highest-ranking factors, as described above. To this end, the classification unit 130 excludes the causal exploration factors x1, x3, and x5 that were excluded from the target of the causal order search, and then examines the remaining causal exploration factors x 2, The second residual r² is obtained by removing the effects of the excluded causal exploration factors x1, x3, and x5 from x4. [1,3,5] r4 [1,3,5] This is calculated using equation (2') below.

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[0100] Here, k=2,4. Also, x in equation (2) i , x j Each of these, r i [1,3,5] , r j [1,3,5] Replace with the following. The classification unit 130 calculates the third residual using the following equation (2'').

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[0102] In this manner, the process of determining whether a causal search factor is the highest-ranking factor in the causal order, and then excluding the highest-ranking causal search factor, is repeated until the causal order of all causal search factors is calculated.

[0103] Figure 6(a) shows the mutual information I(r) calculated from two causal exploration factors x2 and x4. i [1,3,5] ,Δr j (i)[1,3,5] This figure shows an example of ). Also, Figure 6(b) shows the difference in mutual information I(r) calculated from two causal exploration factors x2 and x4. i [1,3,5] ,Δr j (i)[1,3,5] )-I(r j [1,3,5] ,Δr i (j)[1,3,5] An example of this is shown. Figure 6 illustrates a case where, among the causal exploration factors x2 and x4 being explored, causal exploration factor x2 is determined to be the highest-ranking.

[0104] As shown above, in the examples in Figures 4 to 6, the causal order of causal exploration factors x1 and x5 is 1st, the causal order of causal exploration factor x3 is 2nd, the causal order of causal exploration factor x2 is 3rd, and the causal order of causal exploration factor x4 is 4th. Here, we have provided an example of searching for causal order using a method called Direct LiNGAM. However, the method for searching for causal order is not limited to Direct LiNGAM; for example, ICA LiNGAM (Independent component analysis LiNGAM) can also be used to search for causal order.

[0105] This embodiment illustrates a case in which the classification unit 130 calculates the causal order of multiple causal exploration factors (influenced factors and influencing factors (operable influencing factors and mediating influencing factors)) as described above. The classification unit 130 then classifies each of the multiple causal exploration factors into one of several hierarchical levels according to the causal order. This embodiment illustrates a case in which the classification unit 130 classifies causal exploration factors with the same causal order into the same hierarchical level. This embodiment also illustrates a case in which the classification unit 130 classifies causal exploration factors such that higher-ranking causal exploration factors belong to lower hierarchical levels. The classification unit 130 may, for example, classify causal exploration factors such that higher-ranking causal exploration factors belong to higher hierarchical levels. The classification unit 130 may also classify causal exploration factors with a causal order within a predetermined range into the same hierarchical level. For example, if the causal order from the 1st to the 10th is calculated, the classification unit 130 may classify the causal search factor with the first causal order at the same level, the causal search factors with the second to third causal orders at the same level, the causal search factors with the fourth to seventh causal orders at the same level, the causal search factors with the eighth to ninth causal orders at the same level, and the causal search factor with the tenth causal order at the same level.

[0106] Figure 7 shows an example of the results of classifying causal exploration factors x1 to x5 according to the causal order illustrated in Figures 4 to 6. As mentioned above, the causal order of causal exploration factors x1 and x5 is 1st, the causal order of causal exploration factor x3 is 2nd, the causal order of causal exploration factor x2 is 3rd, and the causal order of causal exploration factor x4 is 4th. Therefore, causal exploration factors x1 to x5 are classified such that causal exploration factors x1 and x5 belong to the lowest level 1, causal exploration factor x3 belongs to level 2, causal exploration factor x2 belongs to level 3, and causal exploration factor x4 belongs to the highest level 4.

[0107] [Causal relationship derivation process (S204), causal relationship derivation unit 140] The causal relationship derivation unit 140 derives causal relationships between causal exploration factors belonging to multiple mutually different hierarchies. For example, in LiNGAM, if there are no unknown observed factors, causal exploration factors with a continuous causal order are considered to have a causal relationship unconditionally. However, since it is usually difficult to observe all factors, causal exploration factors with a continuous causal order are not necessarily causally related. Furthermore, in LiNGAM, it is not easy to derive causal relationships between causal exploration factors with a non-contiguous causal order. For example, causal exploration factors x1 and x5 (causal exploration factors belonging to hierarchical level 1), which have the highest causal order, and causal exploration factor x2 (causal exploration factor belonging to hierarchical level 3), which has the third highest causal order, are separated by causal exploration factor x2 (causal exploration factor belonging to hierarchical level 2), which has the second highest causal order (i.e., conditional independence is satisfied). Therefore, in LiNGAM, it is not easy to determine whether there is a causal relationship between causal exploration factors x1 and x5 and causal exploration factor x2. Thus, in this embodiment, as described above, the classification unit 130 classifies each of the multiple causal exploration factors into one of several hierarchical levels according to the causal order, and the causal relationship derivation unit 140 derives the causal relationships of causal exploration factors belonging to multiple mutually different hierarchical levels. This allows, for example, the derivation of causal relationships between two adjacent causal exploration factors among the hierarchical levels into which the causal exploration factors are classified according to the causal order. Furthermore, the causal relationship derivation unit 140 may also derive causal relationships between causal exploration factors belonging to multiple hierarchical levels to which causal exploration factors with non-contiguous causal orders belong. Therefore, the causal relationships of causal exploration factors can be comprehensively derived.

[0108] Furthermore, the causal relationship derivation unit 140 may determine whether or not there is a causal relationship between a certain causal exploration factor and one or more causal exploration factors that have a higher causal order than that certain causal exploration factor, based on regression coefficients calculated by performing a regression analysis with the certain causal exploration factor as the dependent variable and one or more causal exploration factors that have a higher causal order than that certain causal exploration factor as independent variables. In this case, the causal relationship derivation unit 140 only needs to determine whether or not there is a causal relationship between a certain causal exploration factor and at least some of the causal exploration factors that have a higher causal order than that certain causal exploration factor. For example, the causal relationship derivation unit 140 may determine whether there is a causal relationship between a certain causal search factor and one or more causal search factors that belong to one or more hierarchical levels that are not adjacent to the level to which the certain causal search factor belongs, among the causal search factors that are higher in causal order than the certain causal search factor. This allows for a more comprehensive derivation of the causal relationships of the causal search factors. Alternatively, for example, the causal relationship derivation unit 140 may determine whether there is a causal relationship between a certain causal search factor and all causal search factors that are higher in causal order than the certain causal search factor. In this way, the causal relationships of the causal search factors can be derived even more comprehensively. In this embodiment, an example is given in which the causal relationship derivation unit 140 determines whether there is a causal relationship between a certain causal search factor and all causal search factors that are higher in causal order than the certain causal search factor.

[0109] The causal relationship derivation unit 140 may use a significance evaluation index to assess the statistical significance of the regression coefficients calculated as described above when determining whether or not there is a causal relationship between the causal exploration factors, as described above. For example, a p-value that does not assume that the frequency distribution of the data is normally distributed (a so-called robust p-value) may be used as an example of a significance evaluation index. The robust p-value itself can be calculated using a known technique. For example, a robust p-value calculated by the t-test method using the Huber-White Sandwich Estimator, as described in "Hampel, FR, Ronchetti, EM, Rousseeuw, PJ, & Stahel, WA (1986). Robust Statistics: The Approach Based on Influence Functions. New York: Wiley," may be used as an example of a significance evaluation index. In this case, the causal relationship derivation unit 140 may determine that the null hypothesis that the regression coefficient is 0 is rejected if the robust p-value of the regression coefficient is less than or equal to a threshold (e.g., 0.05), and that the causal exploration factor for the regression coefficient is statistically significant with respect to the causal exploration factor used as the dependent variable.

[0110] Furthermore, the causal relationship derivation unit 140 may derive causal relationships between causal exploration factors belonging to multiple mutually different hierarchical levels by using the magnitude of the regression coefficient calculated as described above, in addition to or instead of the significance evaluation index. The magnitude of the regression coefficient may be expressed, for example, as the absolute value of the regression coefficient. In this case, the causal relationship derivation unit 140 may determine that a causal exploration factor for a regression coefficient whose absolute value exceeds a threshold (e.g., 0.1) is influencing the causal exploration factor that is the dependent variable.

[0111] In this embodiment, we illustrate a case in which the causal relationship derivation unit 140 determines the presence or absence of a causal relationship using the robust p-value and absolute value of the regression coefficient. Specifically, in this embodiment, we illustrate a case in which the causal relationship derivation unit 140 determines that there is a causal relationship between the causal exploration factor for the regression coefficient and the causal exploration factor used as the dependent variable when the robust p-value of the regression coefficient is less than or equal to a threshold (=0.05) and the absolute value of the magnitude of the regression coefficient exceeds a threshold (=0.1). In this case, if the causal relationship derivation unit 140 does not satisfy at least one of the following conditions, the robust p-value of the regression coefficient is less than or equal to a threshold (=0.05) and the absolute value of the magnitude of the regression coefficient exceeds a threshold (=0.1), then it determines that there is no causal relationship between the causal exploration factor for the regression coefficient and the causal exploration factor used as the dependent variable.

[0112] In this case, for example, if the robust p-value of the regression coefficient exceeds a threshold (e.g., 0.05) and the absolute value of the regression coefficient also exceeds a threshold (e.g., 0.1), the causal relationship derivation unit 140 determines that there is no causal relationship between the causal exploration factor for the regression coefficient and the causal exploration factor that becomes the dependent variable. However, in this case, from the perspective of the absolute value of the regression coefficient, it can also be said that the causal exploration factor for the regression coefficient has a causal relationship with the causal exploration factor that becomes the dependent variable. Therefore, in this case, for example, the causal relationship derivation unit 140 may determine that there is a possibility that the causal exploration factor for the regression coefficient and the causal exploration factor that becomes the dependent variable are causally related through an influencing factor that is not included in the causal relationship search target. Similarly, the causal relationship derivation unit 140 may determine, for example, that if the robust p-value of the regression coefficient is less than or equal to a threshold (e.g., 0.05) and the absolute value of the regression coefficient is less than or equal to a threshold (e.g., 0.1), then the causal search factor for the regression coefficient and the causal search factor that becomes the dependent variable may be causally related through influencing factors not included in the causal relationship search target.

[0113] Figure 8 shows an example of a linear regression model, its regression coefficients and intercept, and the robust p-values ​​for those coefficients and intercept. The dependent variable of this linear regression model is a single causal exploration factor. The independent variables of this linear regression model are all causal exploration factors that have a higher causal order than that single causal exploration factor. The regression coefficients and intercept are calculated by performing a regression analysis using this linear regression model. Specifically, the dependent variable of the linear regression model shown in Figure 8(a) is the causal exploration factor x4. The independent variables of the linear regression model shown in Figure 8(a) are the causal exploration factors x1 to x3 and x5 that have a higher causal order than causal exploration factor x4. The regression coefficients calculated by performing a regression analysis using this linear regression model are b1, b2, b3, and b5. The intercept calculated by performing a regression analysis using this linear regression model is b0. This figure shows an example of robust p-values ​​p1, p2, p3, p5, and p0 for regression coefficients b1, b2, b3, b5 and intercept b0. The dependent variable of the linear regression model shown in Figure 8(b) is the causal exploration factor x2. The independent variables of the linear regression model shown in Figure 8(b) are causal exploration factors x1, x3, and x5, which have a higher causal order than causal exploration factor x2. The regression coefficients calculated by performing regression analysis using this linear regression model are b1, b3, and b5. The intercept calculated by performing regression analysis using this linear regression model is b0. The robust p-values ​​for regression coefficients b1, b3, b5 and intercept b0 are p1, p3, p5, and p0. Note that ε is the error term.

[0114] In the example shown in Figure 8(a), the robust p-value of regression coefficient b2 is less than or equal to the threshold (=0.05), and the absolute value of the magnitude of regression coefficient b2 is greater than the threshold (=0.1). Therefore, it is determined that there is a causal relationship between causal exploration factor x2 and causal exploration factor x4. In the example shown in Figure 8(b), the robust p-values ​​of regression coefficients b1, b3, and b5 are less than or equal to the threshold (=0.05), and the absolute values ​​of the magnitudes of regression coefficients b1, b3, and b5 are greater than the threshold (=0.1). Therefore, it is determined that there is a causal relationship between causal exploration factors x1, x3, and x5 and causal exploration factor x2.

[0115] The causal relationship derivation unit 140 determines which of the two causal exploration factors is the causal factor based on the causal order of the two causal exploration factors that are in a causal relationship. For example, the causal relationship derivation unit 140 determines that the causal exploration factor with the higher (first) causal order is the causal factor, and the causal exploration factor with the lower (later) causal order is the consequence factor that results from that causal factor. In the example shown in Figure 8(a), the causal exploration factor x2 with the third causal order (the causal exploration factor used as the explanatory variable in the linear regression model described above) is determined to be the causal factor. In addition, the causal exploration factor x4 with the lowest causal order (the causal exploration factor used as the dependent variable in the linear regression model described above) is determined to be the consequence factor that results from that causal factor. Similarly, in the example shown in Figure 8(b), the causal exploration factors x1, x3, and x5, which are the first and second highest causal order factors (the causal exploration factors used as explanatory variables in the linear regression model described above), are determined to be causal factors. In addition, the causal exploration factor x2, which is the third highest causal order factor (the causal exploration factor used as the dependent variable in the linear regression model described above), is determined to be the consequence factor resulting from the said causal factors.

[0116] Figure 9 shows an example of a causal graph (causal diagram). The causal graph shown in Figure 9 is created by determining the presence or absence of causal relationships for causal exploration factors x1 to x5, which are classified into levels 1 to 4 as shown in Figure 7, as shown in Figure 8. As shown in Figure 9, it can be seen that the causal relationships of the structural equation (4), which is the basis for the data of causal exploration factors x1 to x5 exemplified in this embodiment, can be reproduced. Here, in order to search for the causal factors for causal exploration factor x4, which is the lowest causal level, we search for causal exploration factor x2, which is causally related to causal exploration factor x4 (see Figure 8(a)), and then we exemplify the case where we search for causal exploration factors x1, x3, and x5, which are causally related to the discovered causal exploration factor x2 (see Figure 8(b)). However, the causal exploration factors that are subject to the determination of the presence or absence of causal relationships can be any one or more causal exploration factors from among the causal exploration factors classified by level by the classification unit 130. For example, the causal relationship derivation unit 140 may determine whether or not there is a causal relationship for all two causal exploration factors that can be selected from the causal exploration factors classified hierarchically by the classification unit 130. Alternatively, as illustrated in Figure 9, the causal relationship derivation unit 140 may determine whether or not there is a causal relationship for some of the two causal exploration factors that can be selected from the causal exploration factors classified hierarchically by the classification unit 130. In this case, it is preferable to make at least one of the affected factors the target of the determination of whether or not there is a causal relationship. In this case, the causal relationship derivation unit 140 may continue to determine whether or not there is a causal relationship until no more causal exploration factors that are directly causally related to the affected factor, or causal exploration factors that are indirectly causally related to the affected factor through other causal exploration factors, are found.

[0117] When the causal relationship derivation unit 140 determines whether or not there is a causal relationship for some of the two causal relationship derivation units selected from all two causal relationship derivation units that have been classified hierarchically by the classification unit 130, it may identify the causal relationship derivation unit for which the causal relationship is to be determined, for example, based on an input operation to specify the causal relationship derivation unit to the user interface of the processing unit 100. Note that the factors to be classified may include factors other than affected factors and influencing factors (operable influencing factors and mediating influencing factors). For example, factors that are clearly not causally related to affected factors and influencing factors may be included in the causal relationship derivation units. In this case, the factor may be included in the causal relationship derivation units in order to confirm that the factor is not causally related to affected factors and influencing factors.

[0118] [Output process (S205), output unit 150] The output unit 150 outputs information indicating the causal relationships between causal exploration factors (influenced factors and influencing factors) derived by the causal relationship derivation unit 140. The information indicating causal relationships includes, for example, information identifying the causal exploration factors that are in a causal relationship (e.g., the names of the causal exploration factors) and information identifying whether two causal exploration factors in a causal relationship are causal factors or consequence factors. The information indicating causal relationships may also include, for example, a causal graph as illustrated in Figure 9. The output form of the information indicating causal relationships 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] As described above, in this embodiment, the processing device 100 classifies each of the multiple causal exploration factors, which include an affected factor and an influencing factor that influences the affected factor, into one of several hierarchical levels according to the causal order of the multiple causal exploration factors. The processing device 100 then derives the causal relationships of the causal exploration factors belonging to multiple mutually different hierarchical levels. Therefore, the causal relationships of the causal exploration factors can be comprehensively derived without distinguishing between affected factors and influencing factors. For example, the processing device 100 can derive the causal relationships of factors with discontinuous causal orders.

[0119] Furthermore, in this embodiment, the processing device 100 calculates regression coefficients by performing regression analysis with a certain causal exploration factor as the dependent variable and one or more causal exploration factors that are higher in causal order than the certain causal exploration factor as independent variables. Then, based on the regression coefficients, the processing device 100 determines whether or not there is a causal relationship between the certain causal exploration factor and one or more causal exploration factors that are higher in causal order than the certain causal exploration factor. Thus, the presence or absence of a causal relationship between causal exploration factors can be determined based on a quantitative indicator. As such an indicator, for example, at least one of the following may be used: a significance evaluation index for evaluating the statistical significance of the regression coefficients and the magnitude of the regression coefficients.

[0120] Furthermore, in this embodiment, the processing unit 100 performs a process to select the influencing factors to be classified from among a plurality of candidate influencing factors, and classifies the selected influencing factors into one of a plurality of hierarchical levels based on this process. Therefore, the computational load can be reduced when there are many types of influencing factors. In addition, it is possible to suppress the derivation of causal relationships of influencing factors that can be considered as noise.

[0121] For example, the processing unit 100 may perform the following processing as a process for selecting influencing factors to be classified. First, the processing unit 100 calculates the frequency of occurrence 320 of the candidate influencing factors in a plurality of candidate first influencing factor groups 310a to 310d for each candidate influencing factor. Next, the processing unit 100 creates a plurality of candidate second influencing factor groups 340a to 340c based on the frequency of occurrence 320. Next, the processing unit 100 creates a plurality of candidate learning models 350a to 350c for each of the plurality of candidate learning models 350a to 350c. Next, the processing unit 100 calculates model accuracy evaluation indices 360a to 360c for each of the plurality of candidate learning models 350a to 350c to evaluate the estimation accuracy of the candidate learning model. The processing unit 100 then calculates influence factor number-evaluation index relationship information 370, which shows the relationship between the number of candidate influencing factors included in candidate learning models 350a to 350c and an evaluation index for evaluating the estimation accuracy of the candidate learning models, as information used for selecting the influencing factors to be classified. In this way, it is possible to select influencing factors (explanatory variables) that may affect the affected factor (dependent variable) with higher accuracy than when explanatory variables are selected by comparing the frequency of occurrence of explanatory variables with a threshold, as in the confidence level described in Patent Document 1. Furthermore, the processing unit 100 may (automatically) select the influencing factors to be classified based on the influence factor number-evaluation index relationship information 370.

[0122] Furthermore, the influencing factors may include manipulable influencing factors that can be artificially manipulated, and mediating influencing factors. The manipulable influencing factors may also be factors that have the potential to influence the mediating influencing factors. In this way, the causal relationships between each of the manipulable influencing factors, mediating influencing factors, and affected factors can be derived. For example, information can be obtained on which mediating influencing factors are affected by manipulating the manipulable influencing factors, and which affected factors are then affected by those affected mediating influencing factors.

[0123] Furthermore, in this embodiment, the processing device 100 calculates the causal order of the causal search factors based on an independence evaluation index that evaluates the independence of the explanatory variable with respect to the residuals calculated by performing a simple regression analysis with one of the two causal search factors as the dependent variable and the other causal search factor as the explanatory variable.Therefore, the causal order can be calculated based on a quantitative index. Furthermore, in this embodiment, the processing device 100 does not derive causal relationships between multiple causal exploration factors classified at the same hierarchical level. Therefore, multiple causal exploration factors classified at the same hierarchical level can be treated as having no causal relationship.

[0124] [Examples of application] As mentioned above, the affected and influencing factors are not limited, but specific application examples of this embodiment are shown below. In this application example, the rate of change in the amount of a specific substance before and after treatment in a biological wastewater treatment process was used as the affected factor. In this application example, the microbial species was used as the mediating influencing factor. In this application example, the pH and hydrological residence time (HRT) of the treated water were used as controllable influencing factors.

[0125] <Acquiring training data> (1) Operation of the biological wastewater treatment process, water quality analysis, calculation of decomposition rate, 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).

[0126] [Table 1]

[0127] The rate of change in the amount of a specific substance was collected using an integrated biological treatment apparatus 20, as shown in Figure 10, in which a biological treatment area 20a and a sedimentation area 20b are separated from each other by a partition wall 23 within a single tank, and are connected below this partition wall 23.

[0128] A sponge carrier 21 (fluidized carrier (AQ-1 manufactured by Kanto Inoac)) measuring 10 mm × 10 mm × 10 mm was added to the biological treatment area 20a of the biological treatment apparatus 20 at 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 prepared in this manner, and activated sludge was added as a microbial inoculation source. The water to be treated 24 was introduced so that its hydrological residence time (HRT) was 24, 18, 12, 8, 6, 4, 2, and 3 hours. In addition, the water to be treated 24 in each biological treatment apparatus 20 was aerated with air 22, and the treatment was continued until day 190 while adjusting the pH to around 7.5 using a 5 wt% sodium hydroxide aqueous solution.

[0129] 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 and nitrite ions. Monitoring was performed approximately every 7 days. Furthermore, the pH and HRT of the treated water within the biological treatment area 20a of each biological treatment device 20 were measured to monitor the pH value and HRT. In the above biological treatments, the daily rate of nitrite production per operating day was calculated according to the following equation (6).

[0130]

number

[0131] Figure 11 shows an example of the nitrite production rate per day of operation. Figure 12A shows an example of the pH per day of operation. Figure 12B shows an example of the HRT per day of operation.

[0132] (2) Collection of microbial community content DNA extraction, sequencing, determination of microbial communities, and sampling of microbial community content were performed in this order. Note that the method for sampling microbial community content can be achieved using known techniques, as described in Patent Document 1, and is not limited to the method described in this section. 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 apparatus 20 were performed by outsourcing (Nippon Steel Environmental Co., Ltd.). At each time point corresponding to the measurement of the rate of change in the amount of a specific substance, a sponge carrier 21 to which microorganisms were attached was collected. After dividing the collected sponge carrier 21 into four parts, DNA extraction and purification were performed using Extra Soil DNA Plus ver.2 (Nippon Steel Environmental Co., Ltd.).

[0133] The DNA concentration in 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 of eubacteria was performed using the primers shown in Table 2 below.

[0134] [Table 2]

[0135] The PCR products were analyzed using a next-generation sequencer (MiSeq) to determine their base sequences. The obtained nucleotide sequences were analyzed using QIIME (Quantitative Insights Into Microbial Ecology). 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, highly similar sequences (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 indicating the presence and quantity of a single microbial community. These OTUs varied in that some were detected multiple times in each sample, while others were detected in only one sample. Furthermore, the relative proportion of each OTU to the total OTU was calculated from the number of times each OTU was detected. The number of genes in eubacteria attached to the sponge carrier 21 was quantified using the QP-PCR method (Nippon Steel Environmental Co., Ltd.), a real-time PCR method. Specifically, after appropriately diluting the purified DNA solution described above, a reaction solution was prepared using the primers and QProbe shown in Table 3 below, and the number of genes was quantified using Rotor-Gene Q (QIAGEN).

[0136] [Table 3]

[0137] The total amount of microorganisms attached to the sponge carrier 21 differs depending on the sampling date. Therefore, in order to accurately understand 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 ratio of each OTU to the total OTU, as described above, by the number of genes of eubacteria attached to the sponge carrier 21.

[0138] <Selection of Influencing Factors> <<Acquisition of candidate group of primary influencing factors>> As mentioned above, the major OTUs involved in nitrite production were estimated by statistically analyzing 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.

[0139] The values ​​for each OTU in the dataset used for estimation were obtained by collecting data at time points corresponding to the measurement reference point for the nitrite production rate data (for example, using data on the nitrite production 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).

[0140] However, while there were 23 data points for the rate of nitrite production, 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.

[0141] Therefore, we performed the analysis using the Lasso method. Here, we created 1000 bootstrap samples and applied the Lasso method to these samples, thereby artificially increasing the number of datasets obtained through measurement. Using these datasets, we estimated the microbial community through regression analysis. When bootstrap samples are created, it is preferable to include them in the training data because it increases the number of training data points.

[0142] 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 11 illustrates an example of a method for creating Bootstrap samples from a dataset (training data) using the Bootstrap method. In Figure 11, t represents time (in this case, the number of operating days). In Figure 11, 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 duplicates. For example, in the first set shown in Figure 7, t=1 is sampled twice. In Figure 11, B represents the set number. In the example above, B=1000.

[0143] The Lasso method allows for the reduction of regression coefficients to zero. Therefore, it is possible to simultaneously select the variables (microbial communities) and estimate the constant term and regression coefficients.

[0144] In the Lasso method, for example, the parameter β that minimizes the value of the cost function expressed by equation (7) below is used. jWe search for the (regression coefficient). The second term of equation (7) 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 (7) 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 (8) below is... j We search for the regression coefficients. The second term in equation (8) below is the regularization term of the L2 norm. Also, λ2 is the regularization coefficient (hyperparameter).

[0145]

number

[0146] Figure 14 illustrates an example of a method for obtaining a candidate group of first influencing factors by performing Lasso analysis on each of the Bootstrap samples from group B. From the first group of Bootstrap samples in Figure 14, three denovos (number of microbial communities) were selected as denovo1, denovo3, and denovo9, corresponding to the mediating influencing factors for which the regression coefficient value was not zero. These three denovo1, denovo3, and denovo9 constitute one of the candidate groups of first influencing factors. Similarly, from the Bootstrap samples of group B, two denovo1 and denovo2 were selected. These two denovo1 and denovo2 constitute another candidate group of first influencing factors. As shown here, when each Bootstrap sample is analyzed using Lasso, the types of denovos selected are not necessarily the same, nor are the number of denovos selected. Note that denovo represents the type of microbial community, and the number after denovo represents the number of microbial communities.

[0147] <<Calculation of frequency of occurrence>> The frequency of occurrence of each mediating influencing factor (denovo (number of microbial communities)) candidate in the multiple candidate groups of first influencing factors obtained as described above was calculated. The frequency of occurrence is expressed, for example, by the confidence level described in Patent Document 1. Since one example of the 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 15 is a diagram illustrating one example of the method for calculating the frequency of occurrence.

[0148] In Figure 15, one candidate group of primary influencing factors is obtained from each of the Bootstrap samples in group B. The number of times each candidate explanatory variable is selected for the mediating influencing factor (denovo (number of microbial communities)) in the first candidate group of primary influencing factors obtained in this way is calculated. In the example shown in Figure 15, denovo1 was selected 988 times and denovo2 was selected 675 times. Here, we illustrate the case where the number of Bootstrap sample sets (=B) is 1000 sets, so the frequency of occurrence of denovo1 is 988 / 1000 = 0.988 and the frequency of occurrence of denovo2 is 675 / 1000 = 0.675.

[0149] <<Creation of candidate group for the second influencing factor>> Based on the frequency of occurrence of candidate mediating factors (denovo (number of microbial communities)), multiple candidate groups of secondary influencing factors were created, each containing either one candidate mediating factor or multiple candidate mediating factors.

[0150] First, the candidates for each mediating factor (denovo (number of microbial communities)) were sorted in descending order of frequency. For each mediating factor, starting with the candidates with the highest frequency, an integer was assigned that increased by 1, with an initial value of 0.

[0151] Then, m candidate mediating factors (denovo (number of microbial communities)) were selected in order of frequency of occurrence, and a second group of candidate influencing factors containing the selected m candidate mediating factors was created. 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 group of candidate influencing factors were created. Here, we illustrate the case where the value of M is less than the number of candidate mediating factors included in the first group of candidate influencing factors. However, the value of M may be the same as the total number of candidate influencing factors (in this case, mediating factors) included in the first group of candidate influencing factors.

[0152] <<Creating candidate learning models>> For each of the M (20 in the example above) candidate groups of second influencing factors, we created multiple candidate learning models that show the relationship between the mediating influencing factors (denovo (number of microbial communities)) included in that candidate group of second influencing factors and the target variable. Here, we created 20 linear regression equations as candidate learning models by performing linear regression. In addition, for the linear regression, we used a portion of the 1000 Bootstrap samples described in the section "<<Acquisition of Candidate Groups of First Influencing Factors>>" as training data.

[0153] <<Calculation of Model Accuracy Evaluation Metrics>> For each of the M (20 in the example above) candidate learning models (linear regression equations), a model accuracy evaluation index was calculated to assess the estimation accuracy of the candidate learning model. Here, a portion of the remaining 1000 Bootstrap samples described in the section "<<Acquisition of the First Influence Factor Candidate Group>>" was used as training data (test data). The coefficient of determination R was used as the model accuracy evaluation index. 2 I used it.

[0154] <<Calculation of relationship information between the number of influencing factors and evaluation indicators, selection of influencing factors>> The number of candidate mediating factors (denovo (number of microbial communities)) included in a candidate learning model (linear regression equation), and the coefficient of determination R for the candidate learning model. 2Information showing the relationship between and was calculated as an example of the relationship between the number of influencing factors and the evaluation index. Then, the coefficient of determination R, which shows a maximum value in the relationship between the number of influencing factors and the evaluation index, was calculated. 2 Candidate mediating factors corresponding to this were selected as explanatory variables in the learning model.

[0155] Figure 16 shows an example of the relationship between the number of influencing factors and the evaluation index. In Figure 16, five local peaks 1601-1605 (maximum values) were obtained. The coefficient of determination R for these six local peaks 1601-1605 2 All of the corresponding mediating factors (denovo (number of microbial communities)) may also be used as the mediating factors for classification.

[0156] However, in this case, a threshold Th2 was calculated to further narrow down the mediating influencing factors to be classified. The threshold Th2 was calculated from the value of the evaluation index at local peak 1602, which has the largest absolute value among the five local peaks 1601 to 1605, using the coefficient of determination R in the influencing factor number-evaluation index relationship information shown in Figure 16. 2 This is the value obtained by subtracting the standard deviation of 1 × σ. And, among the five local peaks 1601 to 1606, the coefficient of determination R 2 Local peak 1602 was selected because its value was above the threshold Th2 and it had the smallest number (content) of microbial communities. The coefficient of determination for local peak 1602 was R 2 Candidate mediating factors corresponding to this were selected as the mediating factors to be classified.

[0157] R-squared at local peak 1602 2The candidate mediating influencing factors corresponding to this were 12 species: denovo2997, denovo5159, denovo2724, denovo2261, denovo7386, denovo5641, denovo12939, denovo4946, denovo7905, denovo3791, denovo6781, and denovo5881. Therefore, denovo2997, denovo5159, denovo2724, denovo2261, denovo7386, denovo5641, denovo12939, denovo4946, denovo7905, denovo3791, denovo6781, and denovo5881 were selected as microbial species that influence the rate of change in the amount of specific substances (nitrite production rate) before and after treatment in the biological wastewater treatment process.

[0158] <Classification of causal exploration factors> As described above, the microbial species selected as mediating influencing factors (denovo2997, denovo5159, denovo2724, denovo2261, denovo7386, denovo5641, denovo12939, denovo4946, denovo7905, denovo3791, denovo6781, denovo5881), along with the manipulateable influencing factors pH and hydrological residence time, and the affected factor nitrite production rate, were used as causal exploration factors, totaling 15 types of factors. The causal order of these 15 causal exploration factors was calculated using Direct LiNGAM. The aforementioned Bootstrap sample was used as training data. Furthermore, the Shapiro-Wilk test was performed to determine whether the frequency distribution of the training data was non-normal. Figure 17 shows an example of the frequency distribution of each causal exploration factor and an example of the results of the Shapiro-Wilk test. In Figure 17, "Shapiro-Wilk p" is the p-value calculated by the Shapiro-Wilk test (the p-value of the theoretical standard normal distribution), and "Spherical Symmetry p" is the p-value calculated by the KS (Kolmogorov-Smirnov) test (the p-value of the distribution of distances from the center point of the data). Here, if "Shapiro-Wilk p" is less than 0.05, it was assumed that the distribution was non-normal. For all causal exploration factors, "Shapiro-Wilk p" was less than 0.05, confirming that the frequency distribution of the data for each causal exploration factor was non-normal.

[0159] Figures 18A to 18F show an example of the difference in mutual information between two of the 15 types of causal exploration factors. Here, the threshold for the difference in mutual information was set to 0.09. Figure 18A corresponds to Figure 4(b). In this application example, a certain causal exploration factor x i If the difference in mutual information calculated in this way is all 0.09 or less, then the causal exploration factor x iThis example illustrates a case where the causal order of a factor is determined to be higher in rank than all other causal search factors being investigated. Therefore, as shown in Figure 18A, denovo5159, denovo2724, denovo5641, denovo12939, denovo4946, denovo7905, and denovo5881 become the highest-ranking causal search factors among the 12 types of causal search factors. In other words, the causal order of denovo5159, denovo2724, denovo5641, denovo12939, denovo4946, denovo7905, and denovo5881 is the highest (1st) in rank.

[0160] Figures 18B to 18E correspond to Figures 5(b) and 6(b). As shown in Figure 18B, denovo3791 is the highest-ranking causal exploration factor among the eight factors remaining after excluding denovo5159, denovo2724, denovo5641, denovo12939, denovo4946, denovo7905, and denovo5881 from the 15 causal exploration factors. In other words, denovo3791 has the second highest causal order. Similarly, as shown in Figures 18C, 18D, and 18E, the causal orders of denovo2997, denovo7386, and HRT, denovo2261 and pH, and nitrite production rate are the third, fourth, and fifth, respectively. And, as shown in Figure 18F, the remaining denovo6781 has the lowest (sixth) causal order. Furthermore, as shown in Figure 18D, if the maximum value of the difference in mutual information of the target variable, nitrite production rate (=0.06306), is smaller than the threshold (=0.09), the threshold used to determine the subsequent causal order is changed to that maximum value.

[0161] Then, according to the causal order calculated as described above, the causal exploration factors were classified such that causal exploration factors with the same causal order belong to the same hierarchical level, and that causal exploration factors with a higher (earlier) causal order belong to a lower hierarchical level. Figure 19 shows an example of the results of classifying 15 types of causal exploration factors according to the causal orders exemplified in Figures 18A to 18F.

[0162] As illustrated in Figure 19, in this application example, denovo5159, denovo2724, denovo5641, denovo12939, denovo4946, denovo7905, and denovo5881 belonged to the lowest level 1, to which the causal exploration factor with the highest causal order belongs. Denovo3791 belonged to level 2. Denovo2997, denovo7386, and HRT belonged to level 3. Denovo2261 and pH belonged to level 4. Nitrite production rate belonged to level 5. Denovo6781 belonged to level 6, to which the causal exploration factor with the lowest causal order belongs.

[0163] <Derivation of causal relationships> Regression coefficients were calculated by performing regression analysis with one causal exploration factor, which was the target of the causal relationship derivation, as the dependent variable, and all causal exploration factors higher in causal order than that causal exploration factor as independent variables. If the robust p-value of the regression coefficient was less than or equal to the threshold (0.05), it was determined that there was a causal relationship between the causal exploration factor with respect to that regression coefficient and the causal exploration factor used as the dependent variable.

[0164] First, we determined whether there was a causal relationship between the nitrite production rate, one of the influencing factors, and all the causal exploration factors belonging to higher levels 1-4 in Figure 19. Figures 20A-20F show an example of the results of searching for causal exploration factors that are causally related to the nitrite production rate. As illustrated in Figure 20A, in this application example, denovo2997, denovo2724, denovo7386, denovo3791, and HRT were derived as causal exploration factors that are causally related to the nitrite production rate.

[0165] Next, the causal relationship between denovo2997, which was derived to have a causal relationship with the nitrous acid generation rate, and all causal exploration factors belonging to hierarchical levels 1 to 2 higher than denovo2997 in FIG. 19 was determined. FIG. 20B shows an example of the results of exploring causal exploration factors that have a causal relationship with denovo2997. As illustrated in FIG. 20B, in this application example, denovo2724 and denovo3791 were derived as causal exploration factors having a causal relationship with denovo2024.

[0166] Next, the causal relationship between denovo7386, which was derived to have a causal relationship with the nitrous acid generation rate, and all causal exploration factors belonging to hierarchical levels 1 to 2 higher than denovo7386 in FIG. 19 was determined. FIG. 20C shows an example of the results of exploring causal exploration factors that have a causal relationship with denovo7386. As illustrated in FIG. 20C, in this application example, denovo12939 and denovo3791 were derived as causal exploration factors having a causal relationship with denovo7386.

[0167] Next, the causal relationship between denovo3791, which was derived to have a causal relationship with the nitrous acid generation rate, and all causal exploration factors belonging to hierarchical level 1 higher than denovo3791 in FIG. 19 was determined. FIG. 20D shows an example of the results of exploring causal exploration factors that have a causal relationship with denovo3791. As illustrated in FIG. 20D, in this application example, denovo12939 and denovo2926 were derived as causal exploration factors having a causal relationship with denovo3791.

[0168] Next, the causal relationship between denovo6781, which was derived to have a causal relationship with the nitrous acid generation rate, and all causal exploration factors belonging to hierarchical levels 1 to 5 higher than denovo6781 in FIG. 19 was determined. FIG. 20E shows an example of the results of exploring causal exploration factors that have a causal relationship with denovo6781. As illustrated in FIG. 20E, in this application example, denovo7386, denovo12939, and the nitrous acid generation rate were derived as causal exploration factors having a causal relationship with denovo6781.

[0169] Finally, the presence or absence of a causal relationship between denovo2261, which was derived to have a causal relationship with the production rate of nitrite, and all causal exploration factors belonging to hierarchical levels 1 to 3 higher than denovo2261 in FIG. 19 was determined. FIG. 20F shows an example of the results of exploring causal exploration factors that have a causal relationship with denovo2261. As illustrated in FIG. 20F, in this application example, denovo2724, denovo12939, and HRT were derived as causal exploration factors having a causal relationship with denovo2261.

[0170] FIG. 21 shows a causal graph showing the causal relationships of the causal exploration factors shown in FIGS. 20A to 20F. Note that, for causal exploration factors other than the above-described causal exploration factors, causal exploration factors having a causal relationship with the causal exploration factors may also be explored.

[0171] (Other Embodiments) Note that the embodiments of the present disclosure described above can be realized by a computer executing a program. Also, a computer-readable recording medium recording the program and a computer program product such as the program can also be applied as embodiments of the present disclosure. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a non-volatile memory card, a ROM, etc. can be used. Also, the embodiments of the present disclosure may be realized by a PLC (Programmable Logic Controller) or may be realized by dedicated hardware such as an ASIC (Application Specific Integrated Circuit). Also, the embodiments of the present disclosure described above are merely examples of concretization in implementing the present disclosure, and the technical scope of the present disclosure should not be construed in a limited manner by these. That is, the present disclosure can be implemented in various forms without departing from its technical idea or its main features.

[0172] Furthermore, the disclosure of the above embodiments is as follows, for example. [Disclosure 1] A processing device for deriving causal relationships between multiple factors, including an influencing factor and influencing factors that may influence the said influencing factor, A classification means for classifying each of the aforementioned multiple factors into one of several hierarchy levels according to their respective causal order, A processing apparatus comprising: causal relationship derivation means for deriving causal relationships between factors belonging to a plurality of mutually different hierarchical levels. [Disclosure 2] The causal relationship derivation means derives a causal relationship of factors whose causal order is not consecutive, as described in Disclosure 1. [Disclosure 3] The apparatus according to disclosure 1 or 2, wherein the causal relationship derivation means determines whether or not there is a causal relationship between the factor and the factor that has a higher causal order than the factor in question, based on regression coefficients calculated by performing a regression analysis with the factor in question as the dependent variable and the factor that has a higher causal order than the factor in question as the independent variables. [Disclosure 4] The causal relationship derivation means determines whether or not there is a causal relationship between the factor used as the dependent variable and the factor used as the explanatory variable, based on at least one of the following: a significance evaluation index for evaluating the statistical significance of the regression coefficient calculated by performing a regression analysis with the factor used as the dependent variable and the factor having a higher causal order than the dependent variable as the explanatory variable, and the magnitude of the regression coefficient. [Disclosure 5] The system further comprises an influence factor selection processing means for performing a process to select the influence factor to be classified by the classification means from among a plurality of candidate influence factors, The processing apparatus according to any one of disclosures 1 to 4, wherein the classification means classifies each of the influence factors selected based on processing by the influence factor selection processing means into one of a plurality of hierarchy levels. [Disclosure 6] The aforementioned influencing factor selection processing means is A means for obtaining a group of candidate first influence factors, each of which includes one candidate influence factor or multiple candidate influence factors, A frequency calculation means for calculating the frequency of occurrence of each of the candidate influencing factors in the plurality of candidate first influencing factors, A means for creating a group of candidate second influencing factors, which creates a group of candidate second influencing factors, each of which includes one candidate influencing factor or multiple candidates influencing factors, based on the frequency of occurrence. A learning model candidate creation means that creates a plurality of learning model candidates that show the relationship between the candidate influencing factors included in the plurality of candidate second influencing factors and the influenced factors, for each of the plurality of candidate second influencing factors, A model accuracy evaluation index calculation means calculates a model accuracy evaluation index for each of the multiple candidate learning models to evaluate the estimation accuracy of the candidate learning model, The system includes a relationship calculation means for calculating relationship information between the number of candidate influencing factors included in the candidate learning model and the model accuracy evaluation index used to evaluate the estimation accuracy of the candidate learning model, The apparatus according to disclosure 5, wherein the influencing factor number-evaluation index relationship information is used for selecting the influencing factors to be classified by the classification means. [Disclosure 7] The aforementioned influencing factor selection processing means is The apparatus according to disclosure 6, further comprising an influence factor selection means for selecting the influence factors to be classified by the classification means based on the influence factor number-evaluation index relationship information. [Disclosure 8] The aforementioned influencing factors include manipulable influencing factors that can be artificially manipulated and mediating influencing factors. The apparatus according to any one of disclosures 1 to 7, wherein the operable influencing factor includes a factor that may affect the mediating influencing factor. [Disclosure 9] The processing apparatus according to any one of disclosures 1 to 8, wherein the classification means calculates the causal order of the factors based on an independence evaluation index that evaluates the independence of the explanatory variable with respect to the residuals calculated by performing a simple regression analysis with one of the two factors as the dependent variable and the other factor as the explanatory variable. [Disclosure 10] The apparatus according to any one of disclosures 1 to 9, wherein the causal relationship derivation means does not derive causal relationships between multiple factors classified at the same hierarchical level by the classification means. [Disclosure 11] The aforementioned influencing factors include factors used in the processing of the processing process, The apparatus according to any one of disclosures 1 to 10, wherein the influencing factor includes a factor obtained in the processing process by performing the processing using a factor used in the processing process. [Disclosure 12] A method for deriving causal relationships between multiple factors, including an influencing factor and influencing factors that may influence the said influencing factor, A classification step of classifying each of the aforementioned multiple factors into one of several hierarchy levels according to their respective causal order, A processing method comprising: a causal relationship derivation step of deriving causal relationships between factors belonging to multiple mutually different hierarchical levels. [Disclosure 13] 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 11. [Explanation of Symbols]

[0173] 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 Acquisition Department 120 Influence Factor Selection Processing Unit 121 First influence factor candidate group acquisition unit 122 Appearance frequency calculation unit 123 Second influence factor candidate group creation unit 124 Learning model candidate creation unit 125 Model accuracy evaluation index calculation unit 126 Relationship calculation unit 127 Influence factor selection unit 130 Classification unit 140 Causal relationship derivation unit 150 Output unit 310a~310d First influence factor candidate group 320 Appearance frequency 330 Sorted candidate of mediating influence factors 340a~340d Second influence factor candidate group 350a~350c Learning model candidates 360a~360d Evaluation indexes 370 Influence factor number - evaluation index relationship information 371~375 Points indicating influence factor number - evaluation index relationship information 1601~1605 Points indicating local peaks of influence factor number - evaluation index relationship information

Claims

1. A processing device for deriving causal relationships between multiple factors, including an influencing factor and influencing factors that may influence the said influencing factor, A classification means for classifying each of the aforementioned multiple factors into one of multiple hierarchies according to their respective causal order, A processing apparatus comprising: causal relationship derivation means for deriving causal relationships between factors belonging to a plurality of mutually different hierarchical levels.

2. The apparatus according to claim 1, wherein the causal relationship derivation means derives a causal relationship of factors whose causal order is not consecutive.

3. The apparatus according to claim 1 or 2, wherein the causal relationship derivation means determines whether or not there is a causal relationship between the factor and the factor that has a higher causal order than the factor in question, based on regression coefficients calculated by performing a regression analysis with the factor in question as the dependent variable and the factor that has a higher causal order than the factor in question as the independent variables.

4. The apparatus according to claim 3, wherein the causal relationship derivation means determines whether or not there is a causal relationship between the factor used as the dependent variable and the factor used as the explanatory variable, based on at least one of the following: a significance evaluation index for evaluating the statistical significance of the regression coefficient calculated by performing a regression analysis with the factor used as the dependent variable and the factor having a higher causal order than the dependent variable as the explanatory variable, and the magnitude of the regression coefficient.

5. The system further comprises an influence factor selection processing means for performing a process to select the influence factor to be classified by the classification means from among a plurality of candidate influence factors, The processing apparatus according to claim 1 or 2, wherein the classification means classifies each of the influence factors selected based on the processing by the influence factor selection processing means into one of a plurality of hierarchy levels.

6. The aforementioned influencing factor selection processing means is A means for obtaining a group of candidate first influence factors, each of which includes one candidate influence factor or multiple candidate influence factors, A frequency calculation means for calculating the frequency of occurrence of each of the candidate influencing factors in the plurality of candidate first influencing factors, A means for creating a group of candidate second influencing factors, which creates a group of candidate second influencing factors, each of which includes one candidate influencing factor or multiple candidate influencing factors, based on the frequency of occurrence. A learning model candidate creation means that creates a plurality of learning model candidates that show the relationship between the candidate influencing factors included in the plurality of candidate second influencing factors and the influenced factors, for each of the plurality of candidate second influencing factor groups, A model accuracy evaluation index calculation means calculates a model accuracy evaluation index for each of the multiple candidate learning models to evaluate the estimation accuracy of the candidate learning model, The system includes a relationship calculation means for calculating relationship information between the number of candidate influencing factors included in the candidate learning model and the model accuracy evaluation index used to evaluate the estimation accuracy of the candidate learning model, The apparatus according to claim 5, wherein the influencing factor number-evaluation index relationship information is used for selecting the influencing factors to be classified by the classification means.

7. The aforementioned influencing factor selection processing means is The apparatus according to claim 6, further comprising an influence factor selection means for selecting the influence factors to be classified by the classification means based on the relationship information between the number of influence factors and the evaluation index.

8. The aforementioned influencing factors include manipulable influencing factors that can be artificially manipulated and mediating influencing factors. The apparatus according to claim 1 or 2, wherein the operable influencing factor includes a factor that may affect the mediating influencing factor.

9. The processing apparatus according to claim 1 or 2, wherein the classification means calculates the causal order of the factors based on an independence evaluation index that evaluates the independence of the explanatory variable with respect to the residuals calculated by performing a simple regression analysis with one of the two factors as the dependent variable and the other factor as the explanatory variable.

10. The apparatus according to claim 1 or 2, wherein the causal relationship derivation means does not derive causal relationships between a plurality of factors classified at the same hierarchical level by the classification means.

11. The aforementioned influencing factors include factors used in the processing of the processing process, The apparatus according to claim 1 or 2, wherein the influencing factor includes a factor obtained in the processing process by performing the processing using a factor used in the processing process.

12. A method for deriving causal relationships between multiple factors, including an influencing factor and influencing factors that may influence the said influencing factor, A classification step of classifying each of the aforementioned multiple factors into one of multiple hierarchies according to their respective causal order, A processing method comprising: a causal relationship derivation step of deriving causal relationships between factors belonging to multiple mutually different hierarchical levels.

13. A program for causing a computer to function as each means of the processing apparatus according to claim 1 or 2.

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