US-12619893-B2 - Generation apparatus, generation method, and recording medium

US12619893B2US 12619893 B2US12619893 B2US 12619893B2US-12619893-B2

Abstract

A generation apparatus is configured to access a set of pieces of learning data each being a combination of a value of an explanatory variable and a value of an objective variable, a function family list including, of functions each indicating a physical law and an attribute of each of the functions, at least the functions, and search range limiting information for limiting a search range of the function family list, wherein the processor is configured to execute: first generation processing of generating a first prediction expression by setting a first parameter for the explanatory variable to a first function included in the function family list; first calculation processing of calculating, based on the search range limiting information, a first conviction degree relating to the first prediction expression; and first output processing of outputting the first prediction expression and the first conviction degree.

Inventors

Hiroyuki Namba
Masaki Hamamoto
Masashi Egi

Assignees

HITACHI, LTD.

Dates

Publication Date: 20260505
Application Date: 20220907
Priority Date: 20220218

Claims (20)

1 . A generation apparatus, comprising: a processor configured to execute a program; and a storage device configured to store the program, the generation apparatus being configured to access: a set of pieces of learning data each being a combination of a value of an explanatory variable and a value of an objective variable; a function family list including, of functions each indicating a physical law and an attribute of each of the functions, at least the functions; and search range limiting information for limiting a search range of the function family list, wherein the generation apparatus is configured to generate interpretable prediction expressions by constraining a search space to physically meaningful functions from the function family list that indicate physical laws, wherein the function family list is pre-configured based on domain-specific knowledge of physical laws applicable to a target prediction domain, to thereby address a technical problem of black-box machine learning models by producing prediction rules that are both accurate and explainable, wherein the processor is configured to execute: first generation processing of generating a first prediction expression that is interpretable by setting a first parameter for the explanatory variable to a first function included in the function family list, wherein the first function indicates a physical law, and wherein generating the first prediction expression comprises constraining the search space to the physically meaningful functions from the function family list; first calculation processing of calculating, based on the search range limiting information, a first conviction degree relating to the first prediction expression generated through the first generation processing, wherein the first conviction degree is calculated as a measure of consistency between the first prediction expression and domain-specific knowledge represented by the search range limiting information, wherein calculating the first conviction degree comprises evaluating conformity of the first prediction expression to physical law constraints specified in the search range limiting information, and wherein the first conviction degree is calculated independently of prediction accuracy of the first prediction expression, wherein the domain-specific knowledge comprises at least one of physical laws and theoretical expressions specified in the search range limiting information; and first output processing of outputting the first prediction expression and the first conviction degree calculated through the first calculation processing only when the first prediction expression satisfies both (i) a precision requirement based on prediction accuracy measured against the objective variable and (ii) a conviction degree threshold indicating that the first prediction expression conforms to the physical law constraints within a predetermined tolerance, wherein the precision requirement and the conviction degree threshold are independently evaluated.
2 . The generation apparatus according to claim 1 , wherein the search range limiting information is a specific function included in the function family list, and wherein, in the first calculation processing, the processor is configured to calculate the first conviction degree based on the specific function and the first function of the first prediction expression.
3 . The generation apparatus according to claim 1 , wherein the function family list includes the attribute of each of the functions, wherein the search range limiting information is a specific attribute included in the function family list, and wherein, in the first calculation processing, the processor is configured to calculate the first conviction degree based on the specific attribute and an attribute of the first function of the first prediction expression.
4 . The generation apparatus according to claim 3 , wherein, in the first output processing, the processor is configured to output the specific attribute.
5 . The generation apparatus according to claim 1 , wherein the search range limiting information includes a range of the value of the explanatory variable and a theoretical expression which holds within the range, and wherein, in the first calculation processing, the processor is configured to acquire specific learning data corresponding to the range of the value of the explanatory variable from the set of pieces of learning data, and to calculate, as the first conviction degree, similarity between the first prediction expression and the theoretical expression through use of the specific learning data.
6 . The generation apparatus according to claim 5 , wherein, in the first calculation processing, the processor is configured to obtain Taylor expansions of the first prediction expression and the theoretical expression to each of which the specific learning data is input, and to calculate, as the first conviction degree, similarity between a coefficient obtained from the Taylor expansion of the first prediction expression and a coefficient obtained from the Tayler expansion of the theoretical expression.
7 . The generation apparatus according to claim 6 , wherein, in the first output processing, the processor is configured to output the coefficient obtained from the Taylor expansion of the first prediction expression and the coefficient obtained from the Taylor expansion of the theoretical expression.
8 . The generation apparatus according to claim 1 , wherein the processor is configured to execute first optimization processing of calculating an objective function of the first prediction expression based on a precision of the first prediction expression obtained from a prediction value calculated by inputting the value of the explanatory variable to the first prediction expression and the value of the objective variable and on the first conviction degree, wherein the objective function combines the precision and the first conviction degree as separate weighted terms to balance prediction accuracy against conformity to physical law constraints, and updating the first parameters based on the objective function, wherein updating the first parameters comprises adjusting the first parameters to improve both the precision and the first conviction degree as reflected in the objective function, wherein, in the first generation processing, the processor is configured to set, in the first function, the first parameters that have been updated through the first optimization processing, to thereby update the first prediction expression, wherein, in the first calculation processing, the processor is configured to calculate a first conviction degree relating to the updated first prediction expression generated through the first generation processing based on the search range limiting information, and wherein, in the first output processing, the processor is configured to output the updated first prediction expression and the first conviction degree relating to the updated first prediction expression.
9 . The generation apparatus according to claim 8 , wherein the processor is configured to repeatedly execute the first generation processing and the first calculation processing until the objective function satisfies a predetermined condition.
10 . The generation apparatus according to claim 8 , wherein, in the first output processing, the processor is configured to output the updated first prediction expression and the first conviction degree relating to the updated first prediction expression when the objective function satisfies a predetermined condition.
11 . The generation apparatus according to claim 1 , wherein, in the first output processing, the processor is configured to output complexity of the first prediction expression.
12 . The generation apparatus according to claim 11 , wherein the complexity of the first prediction expression is a number of first parameters.
13 . The generation apparatus according to claim 1 , wherein the processor is configured to execute: second generation processing of generating a second prediction expression by setting a second parameter for the explanatory variable to a second function included in the function family list; second calculation processing of calculating, based on the search range limiting information, a second conviction degree relating to the second prediction expression generated through the second generation processing; and second output processing of outputting a polynomial including the first prediction expression and the second prediction expression and the second conviction degree calculated through the second calculation processing.
14 . The generation apparatus according to claim 1 , wherein the processor is further configured to: control a physical manufacturing process based on the first prediction expression by adjusting at least one manufacturing parameter corresponding to the explanatory variable to achieve a target value of the objective variable, wherein the manufacturing parameter comprises at least one of water content, cement content, or manufacturing date in a concrete manufacturing process, and wherein the target value of the objective variable comprises a target strength value for manufactured concrete.
15 . The generation apparatus according to claim 1 , wherein: the function family list is specific to a concrete manufacturing domain and includes functions representing physical relationships between manufacturing conditions and concrete strength; the search range limiting information specifies physical law constraints applicable to concrete manufacturing; and the processor is configured to generate the first prediction expression to predict concrete strength based on manufacturing conditions including water content and cement content, wherein the first prediction expression is constrained to conform to known physical laws governing concrete strength development.
16 . The generation apparatus according to claim 1 , wherein the processor is further configured to: validate the first prediction expression by comparing predicted values generated by the first prediction expression against actual measured values of the objective variable from a validation dataset distinct from the set of pieces of learning data; calculate a validation error metric quantifying deviation between the predicted values and the actual measured values; and output the first prediction expression only when the validation error metric satisfies a validation threshold, wherein the validation threshold is determined based on requirements for reliable prediction in a target application domain.
17 . The generation apparatus according to claim 1 , wherein: the function family list includes a plurality of distinct function families each representing a different physical law, wherein each function family comprises a differentiable mathematical function; the search range limiting information specifies at least one of: (i) a subset of the plurality of distinct function families to be searched, or (ii) a specific attribute tag associated with one or more of the plurality of distinct function families; and the processor is configured to, in the first generation processing, select the first function from the subset of the plurality of distinct function families specified by the search range limiting information, wherein the selection is based on maximizing the first conviction degree while maintaining the precision requirement.
18 . The generation apparatus according to claim 5 , wherein: the theoretical expression is a domain-specific physical law equation that relates the explanatory variable to the objective variable under specified conditions; and the processor is configured to, in the first calculation processing: obtain a Taylor expansion of the first prediction expression at a representative point within the range of the value of the explanatory variable; obtain a Taylor expansion of the theoretical expression at the representative point; calculate similarity between coefficients of the Taylor expansion of the first prediction expression and coefficients of the Taylor expansion of the theoretical expression; and set the first conviction degree based on the calculated similarity, wherein higher similarity results in a higher first conviction degree; and iteratively update the first parameters to increase both the precision and the first conviction degree until a combined objective function satisfies a convergence criterion.
19 . A generation method, which is executed by a generation apparatus, the generation apparatus including a processor configured to execute a program, and a storage device configured to store the program, the generation apparatus being configured to access: a set of pieces of learning data each being a combination of a value of an explanatory variable and a value of an objective variable; a function family list including, of functions each indicating a physical law and an attribute of each of the functions, at least the functions; and search range limiting information for limiting a search range of the function family list, wherein the generation method generates interpretable prediction expressions by constraining a search space to physically meaningful functions from the function family list that indicate physical laws, wherein the function family list is pre-configured based on domain-specific knowledge of physical laws applicable to a target prediction domain, to thereby address a technical problem of black-box machine learning models by producing prediction rules that are both accurate and explainable, the generation method comprising executing, by the processor: first generation processing of generating a first prediction expression that is interpretable by setting a first parameter for the explanatory variable to a first function included in the function family list, wherein the first function indicates a physical law, and wherein generating the first prediction expression comprises constraining the search space to the physically meaningful functions from the function family list; first calculation processing of calculating, based on the search range limiting information, a first conviction degree relating to the first prediction expression generated through the first generation processing, wherein the first conviction degree is calculated as a measure of consistency between the first prediction expression and domain-specific knowledge represented by the search range limiting information, wherein calculating the first conviction degree comprises evaluating conformity of the first prediction expression to physical law constraints specified in the search range limiting information, and wherein the first conviction degree is calculated independently of prediction accuracy of the first prediction expression, wherein the domain-specific knowledge comprises at least one of physical laws and theoretical expressions specified in the search range limiting information; and first output processing of outputting the first prediction expression and the first conviction degree calculated through the first calculation processing only when the first prediction expression satisfies both (i) a precision requirement based on prediction accuracy measured against the objective variable and (ii) a conviction degree threshold indicating that the first prediction expression conforms to the physical law constraints within a predetermined tolerance, wherein the precision requirement and the conviction degree threshold are independently evaluated.
20 . A computer-readable non-transitory recording medium having recorded thereon a generation program for causing a processor to generate a rule for predicting data, the processor being configured to access: a set of pieces of learning data each being a combination of a value of an explanatory variable and a value of an objective variable; a function family list including, of functions each indicating a physical law and an attribute of each of the functions, at least the functions; and search range limiting information for limiting a search range of the function family list, wherein the generation program causes the processor to generate interpretable prediction expressions by constraining a search space to physically meaningful functions from the function family list that indicate physical laws, wherein the function family list is pre-configured based on domain-specific knowledge of physical laws applicable to a target prediction domain, to thereby address a technical problem of black-box machine learning models by producing prediction rules that are both accurate and explainable, the generation program causing the processor to execute: first generation processing of generating a first prediction expression that is interpretable by setting a first parameter for the explanatory variable to a first function included in the function family list, wherein the first function indicates a physical law, and wherein generating the first prediction expression comprises constraining the search space to the physically meaningful functions from the function family list; first calculation processing of calculating, based on the search range limiting information, a first conviction degree relating to the first prediction expression generated through the first generation processing, wherein the first conviction degree is calculated as a measure of consistency between the first prediction expression and domain-specific knowledge represented by the search range limiting information, wherein calculating the first conviction degree comprises evaluating conformity of the first prediction expression to physical law constraints specified in the search range limiting information, and wherein the first conviction degree is calculated independently of prediction accuracy of the first prediction expression, wherein the domain-specific knowledge comprises at least one of physical laws and theoretical expressions specified in the search range limiting information; and first output processing of outputting the first prediction expression and the first conviction degree calculated through the first calculation processing only when the first prediction expression satisfies both (i) a precision requirement based on prediction accuracy measured against the objective variable and (ii) a conviction degree threshold indicating that the first prediction expression conforms to the physical law constraints within a predetermined tolerance, wherein the precision requirement and the conviction degree threshold are independently evaluated.

Description

CLAIM OF PRIORITY The present application claims priority from Japanese patent application JP 2022-23849 filed on Feb. 18, 2022, the content of which is hereby incorporated by reference into this application. BACKGROUND OF THE INVENTION This invention relates to a generation apparatus and a generation method which generate a rule for predicting data, and a recording medium. In a classification problem or a regression problem, there is known an issue of making a prediction rule consistent with knowledge of experts. For example, in a system which predicts strength of a product manufactured based on data relating to manufacturing conditions and manufacturing methods, when a prediction rule is not consistent with knowledge of experts, the system cannot be employed in a reliable manner. The knowledge of the experts is, for example, a physical characteristic that a specific explanatory variable and the strength are proportional to each other. As a technology relating to this issue, there exist, for example, JP 2020-42346 A, and Crabbe, J., Zhang, Y, Zame, W, and van der Schaar, M. (2020). “Learning outside the Black-Box: The pursuit of interpretable models.” In Neural Information Processing Systems (NeurIPS 2020), Volume 33, 17838-17849. A diagnosis support device as disclosed JP 2020-42346 A includes an identification part, an algorithm change part and a re-identification part. The identification part executes identification processing with medical information as an input, so as to output a first identification result and a first identification ground leading to the result. The algorithm change part changes an algorithm of the identification processing so as not to output the first identification ground, in response to a refusal instruction to the first identification ground. The re-identification part executes identification processing after the algorithm change with the medical information as an input so as to output a second identification result and a second identification ground leading to the result. The technology as disclosed in Crabbe, J., Zhang, Y, Zame, W, and van der Schaar, M. (2020). “Learning outside the Black-Box: The pursuit of interpretable models.” In Neural Information Processing Systems (NeurIPS 2020), Volume 33, 17838-17849 is a technology for efficiently searching functions which are simple and can be understood by experts for a function which best fits data. There is a case in which a learning model, that is, a prediction rule, in the classification problem or the regression problem is highly precise and simple, but is not consistent with knowledge of users, and hence cannot be relied on. SUMMARY OF THE INVENTION This invention has an object to increase consistency between a prediction rule and knowledge of a user. An aspect of the disclosure in the present application is a generation apparatus, comprising: a processor configured to execute a program; and a storage device configured to store the program, the generation apparatus being configured to access a set of pieces of learning data each being a combination of a value of an explanatory variable and a value of an objective variable, a function family list including, of functions each indicating a physical law and an attribute of each of the functions, at least the functions, and search range limiting information for limiting a search range of the function family list, wherein the processor is configured to execute: first generation processing of generating a first prediction expression by setting a first parameter for the explanatory variable to a first function included in the function family list; first calculation processing of calculating, based on the search range limiting information, a first conviction degree relating to the first prediction expression generated through the first generation processing; and first output processing of outputting the first prediction expression and the first conviction degree calculated through the first calculation processing. According to the representative embodiment of this invention, the consistency between the prediction rule and the knowledge of the user can be increased. Other objects, configurations, and effects than those described above are clarified by the following description of an embodiment. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram for illustrating a hardware configuration example of a computer. FIG. 2 is an explanatory diagram for illustrating an example of a learning DB in a first embodiment of this invention. FIG. 3 is an explanatory diagram for illustrating an example of a function family list in the first embodiment. FIG. 4 is an explanatory diagram for illustrating an example of search range limiting information in the first embodiment. FIG. 5 is a block diagram for illustrating a system configuration example of a prediction rule generation system in the first embodiment. FIG. 6 is an explanatory diagram for illustrating an example of an input screen on the