Information processing device, information processing method, and program

Abstract

To construct a more appropriate model for analyzing production systems and other related aspects. [Solution] The information processing device includes a processing unit. The processing unit calculates the number of data points for each of the multiple categories using n input data points (n is an integer of 2 or more) each containing a categorical variable that represents one of the multiple categories, and a plurality of explanatory variables, each containing a categorical variable. For multiple combinations, each containing two categories from the multiple categories, the processing unit calculates weights based on the number of data points between the two categories included in the combination. The processing unit learns a first regression model that estimates the target variable from the plurality of explanatory variables using a loss function that includes a regularization term whose regularization strength changes according to the weight.

Description

[Technical Field]

[0001] Embodiments of the present invention relate to an information processing device, an information processing method, and a program. [Background technology]

[0002] Production systems such as factories (e.g., semiconductor factories) and plants (e.g., chemical plants) mass-produce various types of products. In recent years, it has become possible to acquire large amounts of process data from sensors installed in each manufacturing process at short intervals (e.g., daily). Furthermore, by analyzing the accumulated data, it is possible to implement measures to reduce variations in quality. Such measures lead to improvements in productivity and yield.

[0003] One such measure employs regression analysis using models (regression models) constructed through machine learning. A regression model is a model in which process data such as sensor values, setpoints, and control values ​​are used as explanatory variables, and quality characteristics are used as the dependent variable. By using a regression model, it becomes possible to analyze the factors (causes) of variability in quality characteristics and to estimate future quality characteristics. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] By Ryan J. Tibshirani and Jonathan Taylor, “THE SOLUTION PATH OF THE GENERALIZED LASSO.” The Annals of Statistics. 2011, Vol. 39, No. 3, 1335-1371. [Non-Patent Document 2] Mineaki Ohishi, et al., “Optimizations for Categorizations of Explanatory Variables in Linear Regression via Generalized Fused Lasso.”, 2021. [Non-Patent Document 3] Shota Katayama, "Support recovery of adaptive generalized lasso under high-dimensionality," 2017, Symposium on "Theory and Methodology of Large-Scale Complex Data and its Application to Related Fields," Grants-in-Aid for Scientific Research, FY2017. [Overview of the project] [Problems that the invention aims to solve]

[0005] The present invention aims to provide an information processing device, an information processing method, and a program that can construct a more appropriate model for analyzing production systems and the like. [Means for solving the problem]

[0006] The information processing device of this embodiment includes a processing unit. The processing unit calculates the number of data points, which is the number of input data points for each of the multiple categories, using n input data points (n is an integer of 2 or more) each containing a categorical variable that contains one of the multiple categories as an explanatory variable. For multiple combinations each containing two categories that are included in the multiple categories, the processing unit calculates weights based on the number of data points between the two categories included in the combination. The processing unit learns a first regression model that estimates the target variable from the multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the weight. [Brief explanation of the drawing]

[0007] [Figure 1] A block diagram of an information processing system including an information processing device of an embodiment. [Figure 2]Flowchart of the model building process in the first embodiment. [Figure 3] Block diagram of the information processing device of the second embodiment. [Figure 4] Flowchart of the model building process in the second embodiment. [Figure 5] A diagram illustrating the procedure for determining Cmin and Cmax. [Figure 6] Block diagram of the information processing device of the third embodiment. [Figure 7] Flowchart of the model building process in the third embodiment. [Figure 8] This figure shows an example of the output of the regression coefficient estimation results. [Figure 9] Hardware configuration diagrams of the information processing devices of the first to third embodiments. [Modes for carrying out the invention]

[0008] A preferred embodiment of the information processing device according to this invention will be described in detail below with reference to the attached drawings.

[0009] In factor analysis using regression models, highly interpretable models such as linear models, decision trees, and additive models are frequently used. For each explanatory variable, a quantity representing the degree of influence that the model's parameters have on the model's output is calculated. By using this calculated quantity, it becomes possible to identify the factors that can explain the variability in quality characteristics.

[0010] Model parameters include, for example, regression coefficients and importance values ​​in a regression model. Below, we will mainly explain examples using a regression model as the model and coefficients (regression coefficients) as the model parameters. The applicable models and model parameters are not limited to these.

[0011] Data in production systems and other applications can change rapidly. To always grasp the latest trends, regular model updates using the most up-to-date data are necessary. However, using only the most recent data results in a smaller data set, making the effects of noise more pronounced.

[0012] In particular, products belonging to new categories (such as new varieties) derived from existing categories (such as varieties) may be produced in small quantities, making it highly likely that the estimation of regression coefficients for the new categories will be unstable. In such cases, it is possible to collect data from all categories, convert the categorical variables representing the categories into dummy variables, and perform estimation by modeling as shown in equation (1) below.

number

[0013] A categorical variable is, for example, a variable that can take values ​​representing each of multiple categories. Such a categorical variable can be converted into dummy variables equal to the number of categories. Each dummy variable is, for example, a variable that indicates whether or not a product belongs to the corresponding category. In equation (1), the second row 1 カテゴリ (a) corresponds to the dummy variable that corresponds to category "a". A, B, etc. are examples of category values. Also, "temperature" in equation (1) refers to the explanatory variable that represents temperature.

[0014] In the method using equation (1), β 温度 While the estimation accuracy of regression coefficients for variables common to multiple categories (explanatory variables representing temperature) is improved, β A or β B The estimation accuracy of regression coefficients (category-specific intercepts) for variables representing category-specific characteristics (dummy variables) is often not improved.

[0015] Therefore, as a method to improve estimation accuracy, a method of performing estimation while integrating regression coefficients for each category (hereinafter referred to as Method EMA) has been proposed (for example, Patent Document 1). In Method EMA, the loss function including the regularization term is minimized. When there are three categories {A, B, C}, by setting a design matrix D that satisfies the following equation (2), the regression coefficients β for each category can be calculated. A , β B , β C These can be integrated. Equation (3) is an example of an equation that represents the minimization of the loss function.

number

number

[0016] Furthermore, a method using a weighted regularization term (hereinafter referred to as Method EMB) has also been proposed (for example, Patent Documents 2 and 3). When the three categories {A, B, C} are included, it is possible to set the design matrix WD to satisfy equation (4) below. Equation (5) is an example of an equation that represents the minimization of the loss function in Method EMB.

number

number

[0017] In the EMB method, the values ​​of the weights w are set using the initial estimator β~ obtained by normal linear regression, as shown in equation (6) below. Equation (6) is: w AB An example of the settings is shown below.

number

[0018] When estimation is performed using a weighted regularization term, such as in the EMB method, the regression coefficients for each category are merged. In this process, referring to the results of a normal linear regression makes it easier to merge the regression coefficients of two categories with similar values.

[0019] In manufacturing within production systems, advancements in manufacturing technology and the diversification of product specifications are leading to the continuous emergence of new product categories. In the initial stages of mass production, only small quantities of products are produced, and it may be difficult to secure sufficient data for model construction. When the amount of data is small, even using methods such as EMB, the estimation of the initial estimator β~ for small-volume production categories becomes unstable, and the calculated weights w also become unstable. Furthermore, integrating the regression coefficients of categories based on unstable weights w increases the likelihood of obtaining incorrect estimation results.

[0020] On the other hand, products in a new category are derivative products that have been improved based on products in an existing category (parent products), and often have similar characteristics to products in the existing category that are mass-produced. Therefore, in the following embodiment, this relationship is utilized to set the value of the weight w so that the regression coefficient of the small-volume production category is more easily integrated by the regression coefficient of the mass-production category.

[0021] This results in passive integration of two categories with sufficient data for both, or two categories with insufficient data for both, while actively integrating two categories with abundant data for one and insufficient data for the other. In other words, the regression coefficients of unstable derivatives (products in a new category) are more easily integrated into the regression coefficients of the more stable parent product.

[0022] (First Embodiment) The following describes an embodiment of a model that can be used for quality control in production systems. As described above, production systems employ measures to improve yield by suppressing variations and fluctuations in quality characteristics and reducing defects. Regression models, for example, are used to clarify the factors causing variations in quality characteristics and to estimate future quality characteristics.

[0023] Products become finished products through numerous manufacturing processes. When analyzing the factors causing variations in the quality characteristics of finished products, a model is constructed using information such as the type of manufacturing equipment used in each manufacturing process and sensor values ​​detected by sensors installed on the manufacturing equipment as explanatory variables. Furthermore, information such as the type of manufacturing equipment and sensor values ​​can be interpreted as feature quantities that represent the characteristics of the subject of analysis, such as the production system.

[0024] As manufacturing equipment deteriorates over time, the trends in the acquired process data also change. Furthermore, tasks such as periodic maintenance and parts replacement may be performed that affect the trends in process data. Therefore, for example, models are updated to reflect changes in the trends of process data.

[0025] In the model of this embodiment, for example, the objective variable may be a quality characteristic, a defect rate, or a variable indicating whether a product is good or defective. The objective variable may also be a sensor value detected by a sensor. The explanatory variables may be other sensor values, setpoints, control values, or product type information (category information). The explanatory variables may be preprocessed beforehand. Preprocessing may include, for example, standardization, normalization, transformation by a specific function, addition of interaction terms, time lag, time lead, dummy variable creation, encoding, outlier handling, and missing value handling.

[0026] Figure 1 is a block diagram showing an example of the configuration of an information processing system including the information processing device of this embodiment. As shown in Figure 1, the information processing system has a configuration in which the information processing device 100 and the management system 200 are connected via a network 300.

[0027] The information processing device 100 and the management system 200 can each be configured, for example, as server devices. The information processing device 100 and the management system 200 may be implemented as multiple physically independent devices (systems), or their respective functions may be configured within a single physical device. In the latter case, a network 300 may not be provided. At least one of the information processing device 100 and the management system 200 may be built on a cloud environment.

[0028] Network 300 is, for example, a LAN (Local Area Network) and the Internet. Network 300 may be either a wired network or a wireless network. The information processing device 100 and the management system 200 may send and receive data using direct wired or wireless connections between components without going through Network 300.

[0029] The management system 200 is a system for managing data used for model training (construction, updating) and analysis. The management system 200 comprises a storage unit 221 and a communication control unit 201.

[0030] The storage unit 221 stores various information used in various processes performed by the management system 200. For example, the storage unit 221 stores data including target variables and explanatory variables (such as process data). The storage unit 221 can be made up of any commonly used storage medium such as flash memory, memory card, RAM (Random Access Memory), HDD (Hard Disk Drive), and optical disc.

[0031] The communication control unit 201 controls communication with external devices such as the information processing device 100. For example, the communication control unit 201 transmits process data to the information processing device 100.

[0032] Each of the above components (communication control unit 201) may be implemented by, for example, one or more processors. For example, each of the above components may be implemented by having a processor such as a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit) execute a program, i.e., by software. Each of the above components may also be implemented by a dedicated IC (Integrated Circuit) or other processor, i.e., by hardware. Each of the above components may also be implemented by using a combination of software and hardware.

[0033] The information processing device 100 includes a storage unit 121, an input device 131, a display 132, a communication control unit 101, an acquisition unit 102, a data count calculation unit 103, a weight calculation unit 104, a regularization term configuration unit 111, a construction unit 112, and an output control unit 113.

[0034] The storage unit 121 stores various types of information used in various processes performed by the information processing device 100. For example, the storage unit 121 stores information (such as process data) acquired from the management system 200 via the communication control unit 101 and the acquisition unit 102, as well as parameters (coefficients) of models constructed by the construction unit 112. The storage unit 121 can be made up of any commonly used storage medium such as flash memory, memory card, RAM, HDD, and optical disc.

[0035] The input device 131 is a device for inputting information by a user or other party. The input device 131 is, for example, a keyboard and a mouse. The display 132 is an example of an output device that outputs information, for example, a liquid crystal display. The input device 131 and the display 132 may be integrated, for example, as a touch panel.

[0036] The communication control unit 101 controls communication with external devices such as the management system 200. For example, the communication control unit 101 receives process data from the management system 200. The communication control unit 101 also sends requests to the management system 200 to send process data for a specified period.

[0037] The acquisition unit 102 acquires various types of information. For example, the acquisition unit 102 acquires process data received from the management system 200 via the communication control unit 201.

[0038] For example, the acquisition unit 102 acquires process data for a specified period, or a specified number of process data, from the management system 200 via the communication control unit 101 as data to be analyzed (input data). In this embodiment, the input data consists of n data points (where n is an integer of 2 or more) each containing multiple explanatory variables, including categorical variables.

[0039] The acquisition unit 102 may acquire information indicating the category that is designated as the category for which a weight is set, from among multiple categories. There are no other methods for specifying the category, but for example, the output control unit 113 can output the names of multiple categories, and the acquisition unit 102 can select from the output names. For example, the acquisition unit 102 acquires information indicating the category corresponding to the name selected from the output names.

[0040] The data count calculation unit 103 uses n input data to calculate the data count, which is the number of input data for each of the multiple categories. If the acquisition unit 102 acquires information indicating the categories to which weights will be set, the data count calculation unit 103 may calculate the data count for the specified categories.

[0041] The weight calculation unit 104 calculates the weights of the regularization terms. These weights correspond to the weights added to weighted regularization terms, such as the EMB method described above. For example, the weight calculation unit 104 calculates weights based on the number of data points between two categories for multiple combinations, each containing two categories that are included in multiple categories. The weights based on the number of data points between two categories are, for example, the difference in the number of data points between the two categories, or the ratio (proportion) of the number of data points between the two categories.

[0042] The weight calculation unit 104 may perform scaling on the weights. Scaling is, for example, the following process. • Calculate weights such that they are between 0 and 1 (inclusive). • Calculate weights such that the sum of the weights for multiple combinations equals 1.

[0043] If the acquisition unit 102 acquires information indicating the categories to be designated as the categories for which weights are to be set, the weight calculation unit 104 may calculate weights for multiple combinations that each include any two of the designated categories.

[0044] The regularization term component 111 constitutes a regularization term to which weights calculated by the weight calculation unit 104 are added. The weighted regularization term can be interpreted as a regularization term in which the strength of regularization changes according to the weight.

[0045] The construction unit 112 learns (constructs) a regression model MA (first regression model) that estimates the target variable from multiple explanatory variables, using a loss function that includes a regularization term constructed by the regularization term constructor 111. Through learning, the regression coefficients of the regression model MA are obtained.

[0046] The output control unit 113 controls the output of various types of information used by the information processing device 100. For example, the output control unit 113 displays information (accuracy, coefficients, etc.) of the regression model MA constructed by the construction unit 112 on the display 132. This allows, for example, an expert to determine whether the estimated coefficients are within the expected range.

[0047] At least a portion of each of the above components (communication control unit 101, acquisition unit 102, data count calculation unit 103, weight calculation unit 104, regularization term configuration unit 111, construction unit 112, and output control unit 113) may be implemented by one or more processing units. Each of the above components may be implemented by, for example, one or more processors. For example, each of the above components may be implemented by having a processor such as a CPU and a GPU execute a program, i.e., by software. Each of the above components may be implemented by a processor such as a dedicated IC, i.e., by hardware. Each of the above components may be implemented by using both software and hardware. When multiple processors are used, each processor may implement one of the above components, or two or more of the above components.

[0048] Next, the model construction process by the information processing device 100 of the first embodiment will be described. Figure 2 is a flowchart showing an example of the model construction process in the first embodiment.

[0049] The acquisition unit 102 acquires categorical variables, for example, specified by the user (step S101). The data count calculation unit 103 calculates the number of data points for each category represented by the acquired categorical variables (step S102). The weight calculation unit 104 calculates the weights of the regularization term using the calculated data counts (step S103). The regularization term configuration unit 111 configures a regularization term that includes the calculated weights (step S104). The construction unit 112 constructs a regression model MA by optimizing the loss function that includes the regularization term (step S105), and then terminates the model construction process.

[0050] Next, we will further explain the details of the processing performed by each part of the information processing device 100.

[0051] Hereinafter, it is assumed that there are a total of n (n is an integer greater than or equal to 2) pieces of data (input data, process data) acquired by the acquisition unit 102, and each piece of data includes numerical values representing h (h is an integer greater than or equal to 1) explanatory variables and one target variable. That is, the data is (x i , y i ), where x i ∈R h , y i ∈R, and i = 1, ···, n. x i is an h-dimensional vertical vector of explanatory variables. y i is a scalar target variable.

[0052] For example, in the case of a linear regression model, the construction unit 112 solves an optimization problem of minimizing the loss function represented by the following equation (7) using the acquired data, thereby estimating the parameters of the regression model MA, that is, the regression coefficients for each explanatory variable.

Equation

[0053] G represents a set of indices of dummy variables representing categories. w jk represents the weight for the combination of category j and category k. The weight w jk takes a larger value when the difference in the number of data between two categories is large. β represents the regression coefficient. λ represents a hyperparameter that adjusts the balance between the sum of squared errors and the regularization term.

[0054] The dummy variable conversion of the categorical variable may be performed by the acquisition unit 102 when the input data is acquired, or may be performed by other component parts (such as the regularization term construction unit 111, the construction unit 112, etc.).

[0055] The categorical variables used as dummy variables may be one or more. These dummy categorical variables may be specified in advance by the user, or they may be selected from multiple explanatory variables based on the characteristics of the data. For example, explanatory variables that are discrete rather than continuous may be selected as categorical variables.

[0056] Set G is a set of indices that identify dummy variables converted from categorical variables. The following primarily describes the case where there is only one categorical variable to be converted into a dummy variable.

[0057] The first term on the right-hand side of equation (7) includes the sum of squared errors. The sum of squared errors is smaller, for example, when the regression coefficients of the category corresponding to a derivative are integrated with the regression coefficients of the category corresponding to a parent product with similar characteristics to that derivative, than when they are integrated with the regression coefficients of other categories with different characteristics.

[0058] The second term on the right-hand side of equation (7) includes a regularization term composed of the regularization term component 111. The regularization term in equation (7) is a regularization term in which the L1 norm between regression coefficients for each category is weighted based on the number of data points between the two categories. For example, if the difference in the number of data points between two categories (category j, category k) is large, a larger penalty is given. This causes the regression coefficients of these two categories to be actively integrated.

[0059] The two effects of the first and second terms result in an estimation where the regression coefficients of derivative products with a small amount of data are integrated with the regression coefficients of the parent product with a large amount of data.

[0060] In equation (7), the L1 norm is used, but other forms of norms, such as those specified by the user, may be used instead of the L1 norm. That is, the norm is L p It may also be a norm (where p is a non-negative real number).

[0061] If there are multiple categorical variables to be made into dummy variables, the second term of equation (7) may be transformed into equation (8) below.

number

[0062] T represents the set of categorical variables considered in the regularization term. i represents the identifier (index) that identifies the categorical variables included in the set T. α i represents a parameter that adjusts the influence of each categorical variable. G represents a set of indices of dummy variables that are transformed from each of the multiple categorical variables.

[0063] The regularization term component 111 may construct the regularization term as shown in equation (9) below. The weights in equation (9) are values ​​s, which are statistics that reflect the effect of the number of data points. jk This corresponds to the weight calculated by raising to the power of τ. For example, the weight calculation unit 104 calculates such a weight as a weight based on the number of data points between two categories. SE(·) represents the standard error.

number

[0064] value s jk This may be calculated using, for example, the variance, standard deviation, expected value, median, test, p-value of the test, and probability density for the test for the data or initial estimator. For example, the value s in equation (9) jk This corresponds to the value calculated from the t-test for the difference in the initial estimators of the regression coefficients.

[0065] In addition to the regularization term described above, the loss function may also include penalties (regularization terms) for each β, such as Ridge, Lasso (Least absolute shrinkage and selection operator), SCAD (Smoothly Clipped Absolute Derivation), MCP (Minimax Concave Penalty), Lq norm (0≦q<1), and Elastic Net.

[0066] Furthermore, while equation (7) uses a loss function based on the squared error (sum of squared errors), the loss function is not limited to this. For example, the loss function may be an absolute value loss, quantile loss, Hoover loss, cross-entropy loss, epsilon sensitivity loss, logistic loss, 0-1 loss, exponential loss, hinge loss, or smoothed hinge loss. Alternatively, a loss function in which the first term is weighted according to the confidence level and date / time of each data point may be used.

[0067] Furthermore, the models to which this embodiment can be applied are not limited to linear regression models; any model that can be expressed using parameters may be used. For example, logistic regression models, Poisson regression models, generalized linear models, generalized additive models, decision trees, and neural networks may be used.

[0068] Next, the weight w calculated by the weight calculation unit 104 jk Let's explain an example of how to calculate this. The weight calculation unit 104 calculates a value representing the difference in the number of data points for each of the multiple combinations that include two categories, for example, as shown in equation (10) below.

number

[0069] N j and N k This is the number of data points included in categories j and k. For example, N A >N B In this case, the above equation is 1-N B / N A This results in a value equivalent to scaling the proportion of small-batch production categories to mass-production categories to a range between 0 and 1.

[0070] The weight calculation unit 104 calculates the denominator of equation (10) to max(N A ,N B Values ​​that do not use ) i.e., values ​​without scaling, weight w jk It can also be calculated as follows: In the denominator, max(N A ,N B ) instead of min(N A ,N B ) may be used. In the numerator, any other norm of the difference may be used instead of the absolute value of the difference in the number of data points.

[0071] As described above, the weight calculation unit 104 calculates max(N A ,N B ) / min(N A ,N B Weight w is a value that represents a proportion like ). jk You may calculate this.

[0072] The weight calculation unit 104 calculates the weight w using one of the above methods, for example, a value τ set by the user. jk The value obtained by raising this to the power of τ is the final weight w jk It may also be calculated as follows. τ may be a real number.

[0073] Next, an example of output from the output control unit 113 will be described. After the regression model MA is constructed by the construction unit 112, the output control unit 113 outputs the regression coefficients for each explanatory variable.

[0074] The output control unit 113 may output the regression coefficient corresponding to the λ with the smallest error. For example, the construction unit 112 estimates regression coefficients for multiple λs by cross-validation or generalized cross-validation. The output control unit 113 outputs the regression coefficient corresponding to the λ with the smallest error among the multiple λs. The output control unit 113 may output the regression coefficient corresponding to the λ selected from the multiple λs according to a predetermined rule (such as the One Standard Error Rule). The output control unit 113 may output the regression coefficient corresponding to a specified λ from among the multiple λs.

[0075] The output control unit 113 may output the regression coefficients for categorical variables separately from the regression coefficients for explanatory variables other than categorical variables.

[0076] The output control unit 113 may output both the regression coefficients (regression model) estimated using a loss function that includes a regularization term and the regression coefficients estimated using a loss function that does not include a regularization term. For example, in addition to constructing the regression model MA using the loss function that includes a regularization term as described above, the construction unit 112 also constructs a regression model MB (second regression model) using a loss function that does not include a regularization term, which is constructed by the regularization term constructor 111. The loss function that does not include a regularization term, which is constructed by the regularization term constructor 111, is, for example, a loss function that does not include the second term on the right-hand side of equation (7). The output control unit 113 outputs, for example, two regression models MA and MB estimated by the two estimation methods in a comparable manner.

[0077] Thus, in this embodiment, for example, in data analysis of mass production of multi-category products, regression coefficients can be estimated while integrating the regression coefficients between categories, taking into account the number of data points for each category. According to this embodiment, the regression coefficients of derivative products produced in small quantities are integrated with the regression coefficients of parent products produced in large quantities, thus stabilizing the estimation of the regression coefficients of derivative products. In other words, a more reasonable model can be constructed as a model for analyzing production systems, etc. Furthermore, the integrated regression coefficients can be presented to experts, for example. This can improve the experts' confidence in the estimation results.

[0078] (Second embodiment) In the first embodiment, the regression coefficients between derivatives and parent products are integrated by providing a regularization term that combines the regression coefficients between categories while considering the number of data points in each category. In the second embodiment, a restriction is placed on the number of data points in calculating the weight w added to the regularization term. This makes it possible to obtain weights that are more realistic.

[0079] Figure 3 is a block diagram showing an example of the configuration of the information processing device 100-2 according to the second embodiment. As shown in Figure 3, the information processing device 100-2 includes a storage unit 121, an input device 131, a display 132, a communication control unit 101, an acquisition unit 102, a data count calculation unit 103, a weight calculation unit 104-2, a range determination unit 105-2, a regularization term configuration unit 111, a construction unit 112, and an output control unit 113.

[0080] In the second embodiment, the functions of the weight calculation unit 104-2 and the range determination unit 105-2 are added, which differ from the first embodiment. The other configurations and functions are the same as those in Figure 1, which is a block diagram of the information processing device 100 of the first embodiment, so the same reference numerals are used and their explanation is omitted here.

[0081] The range determination unit 105-2 determines the range within which the number of data points is limited. For example, the range determination unit 105-2 determines the lower and upper limits of the range for the number of data points. Details of the method for determining the range will be described later.

[0082] Furthermore, the range determination unit 105-2 performs a correction process to adjust the number of data points according to the determined range. For example, for each of the multiple categories, the range determination unit 105-2 performs a correction process to adjust the number of data points to the upper limit if the number of data points is greater than or equal to the upper limit, and to adjust the number of data points to the lower limit if the number of data points is less than or equal to the lower limit.

[0083] The weight calculation unit 104-2 calculates weights based on the number of data points using the corrected number of data points.

[0084] Next, the model construction process by the information processing device 100-2 of the second embodiment will be explained using Figure 4. Figure 4 is a flowchart showing an example of the model construction process in the second embodiment.

[0085] Steps S201 to S202 are the same as steps S101 to S102 in the information processing device 100 of the first embodiment, so their explanation will be omitted.

[0086] The range determination unit 105-2 modifies the number of data calculated in step S202 according to the range of the number of data (step S203). The range of the number of data may be determined before the model construction process or during the model construction process.

[0087] The weight calculation unit 104-2 calculates the weights of the regularization term using the corrected number of data points (step S204).

[0088] Steps S205 to S206 are the same as steps S104 to S105 in the information processing device 100 of the first embodiment, so their explanation will be omitted.

[0089] Next, we will explain further about the limitations (corrections) on the number of data points.

[0090] The accuracy of estimating regression coefficients in each category improves as the amount of data for that category increases. Therefore, for parent products as well, the larger the amount of data, the greater the benefit of integrating the regression coefficients of small-volume derivatives into the regression coefficients of the parent product.

[0091] Consider an example of integrating regression coefficients across three categories of data {A, B, C}. The number of data points for each category A, B, and C is N. A , N B , N C is, N A =500, N B =100, N C Assume that = 1000. In this example, the number of data points for categories A and C is sufficiently large, while the number of data points for category B is small. As a relationship between multiple categories, assume that category B is a derivative of category A. Under this assumption, it is desirable that the regression coefficients for category B be integrated into the regression coefficients for category A.

[0092] For the above example, if we calculate the weight using the typical calculation formula shown in the first embodiment, for example, w AB =0.8, w BC = 0.9. The weight w for the combination of Category B and Category C. BC Because the latter is larger, a regularization term is constructed that more aggressively integrates the regression coefficients of categories B and C. Thus, even though sufficient data is available for category A, the larger number of data points for category C results in weights that are not realistic, bringing category B closer to category C.

[0093] Therefore, in this embodiment, the range determination unit 105-2 modifies the number of data points using a cutoff function as shown in equation (11) below. Equation (11) corresponds to an equation that represents a modification using an upper limit value for the number of data points.

number

[0094] According to equation (11), the number of data points N is equal to the upper limit C. max If the number of data points N is greater than (for example, 500), then the number of data points N is C max It will be corrected to the number of data points N when using the cutoff function. C (=1000) is corrected to 500. As a result, the weight calculation unit 104-2 calculates w as the weights for categories B and C. AB =w BC This calculates to =0.8. As a result, the regression coefficients of derivative products (Category B) are more actively integrated with the regression coefficients of products (Category A) that result in a smaller term of the sum of squared errors.

[0095] In addition, along with the correction of the number of data points as described above, w was used as the weight for Category A and Category C. AC =0 is calculated. This helps to suppress unnecessary mergers between categories A and C, where the amount of data is sufficiently large.

[0096] The range determination unit 105-2 may perform a correction using a lower limit of the number of data points. For example, the range determination unit 105-2 may perform a correction of the number of data points using a cutoff function such as equation (12) below. Equation (12) corresponds to an equation that represents a correction using a lower limit of the number of data points. According to equation (12), when the number of data points N is lowered to the lower limit C min If smaller, the number of data points N is C min It will be corrected to:

number

[0097] The range determination unit 105-2 may perform modifications using both an upper and lower limit for the number of data points. For example, the range determination unit 105-2 may perform modifications to the number of data points using a cutoff function such as equation (13) below. According to equation (13), the number of data points N is [C min ,C max It will be modified to fall within the range of ].

number

[0098] Next, the range of the number of data [C min ,C max This section details how to determine [C]. For example, C min and C max This may be specified by the user. That is, the range determination unit 105-2 determines the C specified by the user. min and C max Accordingly, range [C min ,C max Determine the ].

[0099] C min and C max This may be determined according to a value stored in the memory unit 121 or the like. For example, the acquisition unit 102 may determine C min and C max The value of is read from the storage unit 121. The range determination unit 105-2 reads the value of C min and C max Accordingly, range [C min ,C max Determine the ].

[0100] The range determination unit 105-2 is C min Set C to ∞, or max By setting to -∞, equation (13) can be used as a cutoff function that restricts only one of the upper or lower limits.

[0101] Furthermore, the range determination unit 105-2 determines C from the input data using the following procedure. min and C max You may decide that. 1. For each of the multiple categories, generate multiple subsets, each containing the same number of input data points (data points) from the multiple input data sets that include categorical variables. 2. Calculate the statistical values ​​of the target variable included in the multiple subsets generated. 3. The upper limit is calculated based on the minimum number of data points in categories where the variability of multiple statistical values ​​is less than the threshold THA (first threshold). 4. Calculate the maximum value of the number of data in the category where the variation of a plurality of statistical values is greater than the threshold THB (the second threshold) as the lower limit value.

[0102] More specifically, the range determination unit 105-2 determines C, for example, according to the following procedure. min and C max are determined. (S1) Using bootstrap sampling, for each category, sample a plurality of subsets with the same number of data. (S2) Calculate the average value of the target variable of the data included in each subset for each category. (S3) If the standard deviation of the average value of the target variable in each subset is less than the threshold THA, and the number of data in the corresponding category is less than the current C max then update it as C max . (S4) If the standard deviation of the average value of the target variable in each subset is greater than the threshold THB, and the number of data in the corresponding category is greater than the current C min then update it as C min . (S5) Repeat steps S3 and S4 for all categories.

[0103] In the above example, the average value is used as the statistical value, but the statistical value is not limited to this. For example, other indicators such as the median may be used. Also, the indicator showing the variation is not limited to the standard deviation, and other indicators such as the variance may be used.

[0104] FIG. 5 is a diagram showing an overview of the determination procedure of C min and C max as described above. The above procedure can be interpreted as aiming to determine C min and C max so that all the following conditions are satisfied for all categories. · Condition: Since the estimation is stable when the number of data is C max or more, the magnitude of the number of data is not distinguished when it is C max or more. · Condition: When the number of data is C minSince the estimation becomes unstable when it is assumed to be as follows, C min Hereinafter, the magnitude of the number of data is not distinguished.

[0105] As shown in FIG. 5, the standard deviation is such that the larger the value, the more unstable the estimation becomes, while the number of data is such that the smaller the value, the more unstable the estimation becomes.

[0106] The above S3 corresponds to searching for the smallest number of data as the upper limit value C while satisfying the criterion that the standard deviation is smaller than the threshold value THA. In this way, C max is not obtained. For example, assume that the value of the number of data 504 in category 4 is determined as C max . In this case, a situation may occur where the number of data 503 in category 3 is not cut off even though it is stable. max

[0107] The above S4 corresponds to searching for the largest number of data as the lower limit value C while satisfying the criterion that the standard deviation is larger than the threshold value THB. In this way, C min is not obtained. For example, assume that the value of the number of data 501 in category 1 is determined as C min . In this case, a situation may occur where the number of data 502 in category 2 is not cut off even though it is unstable. min

[0108] As described above, in the second embodiment, by using a cut-off function with respect to the number of data, it is possible to avoid the situation where categories with a very large or very small number of data have an unrealistic impact on the estimation of the regression coefficient.

[0109] (Third Embodiment) The information processing apparatus according to the third embodiment uses not only regularization including a weight based on the number of data but also a regularization term including a weight based on the distance between categories other than the number of data.

[0110] Figure 6 is a block diagram showing an example of the configuration of the information processing device 100-3 according to the third embodiment. As shown in Figure 6, the information processing device 100-3 includes a storage unit 121, an input device 131, a display 132, a communication control unit 101, an acquisition unit 102, a data count calculation unit 103, a weight calculation unit 104, a distance calculation unit 106-3, a regularization term configuration unit 111-3, a construction unit 112-3, and an output control unit 113.

[0111] In the third embodiment, a distance calculation unit 106-3 is added, and the functions of the regularization term constructor 111-3 and the construction unit 112-3 differ from those of the first embodiment. Other configurations and functions are the same as those in Figure 1, which is a block diagram of the information processing device 100 of the first embodiment, so they are denoted by the same reference numerals and their description is omitted here.

[0112] The distance calculation unit 106-3 calculates the distance between two categories included in each of several combinations, each containing two categories that are included in multiple categories.

[0113] The regularization term component 111-3 further comprises a regularization term whose strength of regularization changes according to the distance.

[0114] The construction unit 112-3 learns the regression model MA using a loss function that further includes a regularization term in which the strength of regularization changes according to distance.

[0115] Next, the model construction process by the information processing device 100-3 of the third embodiment will be explained using Figure 7. Figure 7 is a flowchart showing an example of the model construction process in the third embodiment.

[0116] Steps S301 to S303 are the same as steps S101 to S103 in the information processing device 100 of the first embodiment, so their explanation will be omitted.

[0117] The distance calculation unit 106-3 calculates the distance between two categories included in each of the multiple combinations (step S304). The regularization term configuration unit 111-3 configures a regularization term that includes the weights calculated by the weight calculation unit 104, as well as a regularization term that includes the distance calculated by the distance calculation unit 106-3 (step S305). The construction unit 112-3 constructs the regression model MA by optimizing the loss function including the regularization term (step S306), and then terminates the model construction process.

[0118] Next, we will further explain the distance between categories and the regularization term, whose strength of regularization changes depending on the distance.

[0119] In this embodiment, the loss function represented by equation (14) below is used. In the loss function of equation (14), a third term is newly added to the right-hand side.

number

[0120] weight w jk This represents the weight calculated based on the number of data points. -1 jk This is the distance d between category j and category k, calculated from information other than the number of data points. jk It represents the reciprocal of [the given value].

[0121] The distance calculation unit 106-3 calculates the reciprocal of the distance d -1 jk β can also be calculated as shown in equation (15) below. j ~ and β k ~ represents the regression coefficients of categories j and k, which are initial estimators obtained from the results of a standard linear regression.

number

[0122] By adding a third term, the effect of making categories j and k more likely to be merged when they are similar in terms of factors other than the number of data points is further enhanced. The adjustment between the merging effect due to the number of data points and the merging effect due to distance can be performed using the hyperparameters λ(λ1, λ2).

[0123] distance d jk The calculation method is not limited to the above, and any other method may be used. Examples of other calculation methods are listed below. • From the estimation results of the model constructed at a past point in time, the distance d jk Calculate. • A quantitative value representing the difference in category names is the distance d. jk It is calculated as follows. • Distance d is a value that quantifies the relationship between categories based on domain knowledge. jk It is calculated as follows.

[0124] The distance calculation unit 106-3 calculates the distance d using one of the methods described above. jk The value obtained by raising this to the power of τ is the final distance d jk It may also be calculated as follows.

[0125] The regularization term component 111-3 may constitute a single regularization term by integrating the second and third terms on the right-hand side of equation (15). For example, the second and third terms on the right-hand side of equation (15) are λ1w jk +λ2d -1 jk It can be constructed as a single regularization term with weights λ1w. jk +λ2d -1 jk However, this can be interpreted as a weight for a single regularization term.

[0126] The weights of the regularization terms to be unified are given by the function f(w jk d -1 jk It may also be calculated as the output of ). The function f is w jk and d -1 jk (or d jk It can be any function that takes a value as input and outputs a value corresponding to the weight.

[0127] Thus, in the third embodiment, it becomes possible to integrate regression coefficients that take into account not only the number of data points but also the relationships between categories that can be utilized.

[0128] (Example output) Other examples of output methods for estimation results (regression coefficients) are described below. The following describes an example of outputting estimation results in a way that more clearly shows the integration process of regression coefficients. While the explanation uses the first embodiment as an example, similar procedures can be applied to the second and third embodiments.

[0129] For example, the construction unit 112 changes the hyperparameter λ in equation (7) above to multiple values ​​and calculates the regression coefficients of the regression model MA for each of the multiple λ values. In other words, the construction unit 112 constructs multiple regression models MA (regression coefficients) by learning by changing the hyperparameter λ, which controls the strength of the regularization term, to multiple values.

[0130] The output control unit 113 outputs information showing the changes in multiple regression model MAs for multiple values ​​of λ. For example, the output control unit 113 outputs the values ​​of the regression coefficients for λ on a coordinate system with λ on the horizontal axis and the regression coefficients on the vertical axis. The changes in the regression coefficients for λ can be interpreted as corresponding to the solution paths.

[0131] Figure 8 shows an example of the output of the regression coefficient estimation results using input data containing products from four categories: A, B, C, and D. Figure 8 shows the number of data points N for each category A, B, C, and D. A , N B , N C , N D However, N A =19, N B =77, N C =198, N D Here's an example where the value is 906.

[0132] As shown in Figure 8, as λ increases, a series of events can be observed in which the regression coefficients are integrated into categories that are close to the category with a large number of data points, starting from categories with fewer data points, and finally merging into a single regression coefficient.

[0133] The relationships between categories in actual mass production can be more complex. Experts can understand the relationships between categories from the data by examining the solution paths shown in Figure 8.

[0134] As explained above, according to the first to third embodiments, a more appropriate model can be constructed for analyzing production systems and the like.

[0135] Next, the hardware configuration of the information processing device according to the first to third embodiments will be described using Figure 9. Figure 9 is an explanatory diagram showing examples of the hardware configuration of the information processing device according to the first to third embodiments.

[0136] The information processing devices of the first to third embodiments include a control device such as a CPU (Central Processing Unit) 51, a storage device such as a ROM (Read Only Memory) 52 and a RAM (Random Access Memory) 53, a communication interface 54 for communication via a network, and a bus 61 for connecting the various parts.

[0137] The programs to be executed in the information processing devices of the first to third embodiments are provided pre-installed in a ROM 52 or the like.

[0138] The programs executed by the information processing devices of the first to third embodiments may be configured to be provided as computer program products by recording them in an installable or executable file format onto a computer-readable recording medium such as a CD-ROM (Compact Disk Read Only Memory), a flexible disk (FD), a CD-R (Compact Disk Recordable), or a DVD (Digital Versatile Disk).

[0139] Furthermore, the information processing device of the first to third embodiments may be configured to store the program on a computer connected to a network such as the Internet and provide it by allowing download via the network. Alternatively, the information processing device of the first to third embodiments may be configured to provide or distribute the program via a network such as the Internet.

[0140] The programs executed in the information processing apparatus of the first to third embodiments can cause the computer to function as a part of the information processing apparatus described above. This computer can read the program from a computer-readable storage medium onto the main memory and execute it using the CPU 51.

[0141] An example of the configuration of the embodiment is described below. (Configuration Example 1) Using n input data points (where n is an integer greater than or equal to 2), each containing a categorical variable representing one of several categories, the number of data points for each of the aforementioned categories is calculated. For multiple combinations, each containing two of the aforementioned categories, a weight is calculated based on the number of data points between the two categories included in the combination. A first regression model is trained that estimates the target variable from multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the aforementioned weights. Processing unit, An information processing device equipped with the following features. (Configuration example 2) The regularization term is the weight and the difference L of the regression coefficients of the first regression model between the two categories included in the combination. p The norm (where p is a non-negative real number) and the multiplication of The information processing device described in Configuration Example 1. (Configuration Example 3) The aforementioned processing unit, The weight is calculated as the difference in the number of data points of the two categories included in the combination. An information processing device as described in Configuration Example 1 or 2. (Configuration example 4) The aforementioned processing unit, The weight is calculated as the ratio of the number of data points between the two categories included in the combination. An information processing device as described in any one of Configuration Examples 1 to 3. (Configuration example 5) The aforementioned processing unit, The weights are calculated to be values ​​between 0 and 1, or values ​​such that the sum of the weights for multiple combinations of the weights is 1. An information processing device as described in any one of Configuration Examples 1 to 4. (Configuration example 6) The aforementioned processing unit, The weight is calculated to be the power of τ of the value based on the number of data points between the two categories included in the combination. An information processing device as described in any one of Configuration Examples 1 to 5. (Configuration example 7) The aforementioned processing unit, For each of the multiple categories, if the number of data points is greater than or equal to the upper limit, the number of data points is corrected to the upper limit; if the number of data points is less than or equal to the lower limit, a correction process is performed to correct the number of data points to the lower limit. An information processing device as described in any one of Configuration Examples 1 to 6. (Configuration example 8) The aforementioned processing unit, The correction process is performed using the specified upper limit and the specified lower limit. The information processing device described in Configuration Example 7. (Configuration example 9) Each of the multiple input data includes a target variable corresponding to each of the multiple explanatory variables, The aforementioned processing unit, For each of the multiple categories, multiple subsets are generated, each containing the same number of input data, which is a portion of the multiple input data containing the categorical variable representing the category; and statistical values ​​of the target variable included in the multiple subsets that are generated are calculated. The minimum number of data points in the category where the variability of multiple statistical values ​​is less than the first threshold is calculated as the upper limit. The maximum number of data points in the category where the variability of multiple statistical values ​​is greater than the second threshold is calculated as the lower limit. The information processing device described in Configuration Example 7. (Configuration example 10) The aforementioned processing unit, The distance between the two categories included in the above combination is calculated, The first regression model is trained using the loss function which further includes a regularization term whose regularization strength changes according to the distance. An information processing device as described in any one of Configuration Examples 1 to 9. (Configuration Example 11) The aforementioned processing unit, For multiple combinations, each containing two of the aforementioned categories selected from the multiple aforementioned categories, the weights are calculated. An information processing device as described in any one of Configuration Examples 1 to 10. (Configuration Example 12) The aforementioned processing unit, Output the names of multiple categories, and calculate the weights for multiple combinations of the outputted names, each containing two categories corresponding to a specified name. An information processing device as described in any one of Configuration Examples 1 to 11. (Configuration Example 13) The aforementioned processing unit, A second regression model is trained that estimates the target variable from multiple explanatory variables using a loss function that does not include the regularization term. Output the first regression model and the second regression model. An information processing device as described in any one of Configuration Examples 1 to 12. (Configuration Example 14) The aforementioned processing unit, Multiple first regression models are constructed by learning in which the parameter controlling the strength of the regularization term is varied to multiple values. Outputs information showing the changes in multiple first regression models for multiple aforementioned values. An information processing device as described in any one of Configuration Examples 1 to 13. (Configuration example 15) An information processing method performed by an information processing device, A step of calculating the number of data points, which is the number of input data points for each of the multiple categories, using n input data points (where n is an integer of 2 or more) each containing a categorical variable that represents one of the multiple categories, and a multiple explanatory variable, For multiple combinations, each containing two of the aforementioned categories, the step of calculating a weight based on the number of data points between the two aforementioned categories included in the combination; The steps include: learning a first regression model that estimates the target variable from multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the aforementioned weights; Information processing methods including (Configuration Example 16) On the computer, A step of calculating the number of data points, which is the number of input data points for each of the multiple categories, using n input data points (where n is an integer of 2 or more) each containing a categorical variable that represents one of the multiple categories, and a multiple explanatory variable, For multiple combinations, each containing two of the aforementioned categories, the step of calculating a weight based on the number of data points between the two aforementioned categories included in the combination; The steps include: learning a first regression model that estimates the target variable from multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the aforementioned weights; A program to execute.

[0142] While several embodiments of the present invention have been described, these embodiments are presented as examples only and are not intended to limit the scope of the invention. These novel embodiments can be carried out in a variety of other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their variations are included in the scope and spirit of the invention, as well as in the claims of the invention and its equivalents. [Explanation of symbols]

[0143] 100, 100-2, 100-3 Information Processing Device 101,201 Communication Control Unit 102 Acquisition Department 103 Data Count Calculation Unit 104,104-2 Weight calculation unit 105-2 Range Determination Unit 106-3 Distance Calculation Unit 111,111-3 Regularization term component 112,112-3 Construction Section 113 Output Control Unit 121,221 Storage section 131 Input Devices 132 displays 200 Management Systems 300 Networks

Claims

1. Using n input data (where n is an integer of 2 or more) each containing a categorical variable representing one of several categories, the number of data points, which is the number of input data points for each of the several categories, is calculated. For multiple combinations, each containing two of the aforementioned categories, a weight is calculated based on the number of data points between the two categories included in the combination. A first regression model is trained that estimates the target variable from multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the aforementioned weights. Processing unit, An information processing device equipped with the following features.

2. The regularization term is the weight and L, which is the difference between the regression coefficients of the first regression model between the two categories included in the combination. ｐ The norm (where p is a non-negative real number) and the multiplication of The information processing apparatus according to claim 1.

3. The aforementioned processing unit, The weight is calculated as the difference in the number of data points of the two categories included in the combination. The information processing apparatus according to claim 1.

4. The aforementioned processing unit, The weight is calculated as the ratio of the number of data points between the two categories included in the combination. The information processing apparatus according to claim 1.

5. The aforementioned processing unit, The weights are calculated to be values ​​between 0 and 1, or values ​​such that the sum of the weights for multiple combinations of the weights is 1. The information processing apparatus according to claim 1.

6. The aforementioned processing unit, The weight is calculated to be the power of τ of the value based on the number of data points between the two categories included in the combination. The information processing apparatus according to claim 1.

7. The aforementioned processing unit, For each of the multiple categories, if the number of data points is greater than or equal to the upper limit, the number of data points is corrected to the upper limit; if the number of data points is less than or equal to the lower limit, a correction process is performed to correct the number of data points to the lower limit. The information processing apparatus according to claim 1.

8. The aforementioned processing unit, The correction process is performed using the specified upper limit and the specified lower limit. The information processing apparatus according to claim 7.

9. Each of the multiple input data includes a target variable corresponding to each of the multiple explanatory variables, The aforementioned processing unit, For each of the multiple categories, multiple subsets are generated, each containing the same number of input data, which is a portion of the multiple input data containing the categorical variable representing the category; and statistical values ​​of the target variable included in the multiple subsets that are generated are calculated. The minimum number of data points in the category where the variability of multiple statistical values ​​is less than the first threshold is calculated as the upper limit. The maximum number of data points in the category where the variability of multiple statistical values ​​is greater than the second threshold is calculated as the lower limit. The information processing apparatus according to claim 7.

10. The aforementioned processing unit, The distance between the two categories included in the above combination is calculated, The first regression model is trained using the loss function which further includes a regularization term whose regularization strength changes according to the distance. The information processing apparatus according to claim 1.

11. The aforementioned processing unit, For multiple combinations, each containing two of the aforementioned categories selected from the multiple aforementioned categories, the weights are calculated. The information processing apparatus according to claim 1.

12. The aforementioned processing unit, Output the names of multiple categories, and calculate the weights for multiple combinations of the outputted names, each containing two categories corresponding to a specified name. The information processing apparatus according to claim 1.

13. The aforementioned processing unit, A second regression model is trained that estimates the target variable from multiple explanatory variables using a loss function that does not include the regularization term. Output the first regression model and the second regression model. The information processing apparatus according to claim 1.

14. The aforementioned processing unit, Multiple first regression models are constructed by learning in which the parameter controlling the strength of the regularization term is varied to multiple values. Outputs information showing the changes in multiple first regression models for multiple values. The information processing apparatus according to claim 1.

15. An information processing method performed by an information processing device, A step of calculating the number of data points, which is the number of input data points for each of the multiple categories, using n input data points (where n is an integer of 2 or more) each containing a categorical variable that represents one of the multiple categories, and a multiple explanatory variable, For multiple combinations, each containing two of the aforementioned categories, the step of calculating a weight based on the number of data points between the two aforementioned categories included in the combination; The steps include: learning a first regression model that estimates the target variable from multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the aforementioned weights; Information processing methods including

16. On the computer, A step of calculating the number of data points, which is the number of input data points for each of the multiple categories, using n input data points (where n is an integer of 2 or more) each containing a categorical variable that represents one of the multiple categories, and a multiple explanatory variable, For multiple combinations, each containing two of the aforementioned categories, the step of calculating a weight based on the number of data points between the two aforementioned categories included in the combination; The steps include: learning a first regression model that estimates the target variable from multiple explanatory variables using a loss function that includes a regularization term whose strength of regularization changes according to the aforementioned weights; A program to execute.

Images