Patent Publication Number: US-2021192392-A1

Title: Learning method, storage medium storing learning program, and information processing device

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2019-229399, filed on Dec. 19, 2019, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to the learning technique. 
     BACKGROUND 
     The classification using a trained model by the machine learning (or, simply “learning”) technique has been known to solve the problem in the classification of data having the non-linear characteristics. In the application to the fields of human resource and finance that desire the interpretation of which logic is used to obtain the classification result, there has been known an existing technique of classifying the data having the non-linear characteristics by using a decision tree, which is a model having high interpretability in the classification result. 
     Related techniques are disclosed in, for example, Japanese Laid-open Patent Publication Nos. 2010-9177 and 2016-109495. 
     SUMMARY 
     According to an aspect of the embodiments, a learning method is executed by a computer. The method includes: obtaining a trained model in which learning data (or, training data) having non-linear characteristics is learned by supervised learning using a first teacher or teaching label; classifying the learning data by using the obtained trained model and calculating a score related to a factor of the obtainment of the classification result for the learning data; clustering the learning data based on the calculated score; applying a second teacher label based on clusters obtained from the clustering to the learning data; and executing supervised learning of a decision tree by using the learning data and the applied second teacher label. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram illustrating an example of a system configuration; 
         FIG. 2  is a flowchart illustrating operation examples of a host learning device and a client learning device; 
         FIG. 3  is an explanatory diagram describing a learning model of the supervised learning; 
         FIG. 4  is an explanatory diagram describing the data classification using the learning model; 
         FIG. 5  is a flowchart exemplifying clustering processing of learning data; 
         FIG. 6  is an explanatory diagram illustrating examples of a factor distance matrix and an error matrix; 
         FIG. 7A  is an explanatory diagram describing the evaluation of the degree of influence on the error matrix; 
         FIG. 7B  is an explanatory diagram describing the evaluation of the degree of influence on the error matrix; 
         FIG. 7C  is an explanatory diagram describing the data deletion according to the degree of influence on the error matrix; 
         FIG. 8  is an explanatory diagram describing the clustering of the learning data; 
         FIG. 9  is an explanatory diagram describing the creation of new learning data; 
         FIG. 10  is an explanatory diagram describing the creation of a decision tree; 
         FIG. 11  is an explanatory diagram describing the comparison between the existing technique and the present embodiment; 
         FIG. 12  is an explanatory diagram describing the comparison between the existing technique and the present embodiment; and 
         FIG. 13  is a block diagram illustrating an example of a computer that executes a program. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     In the related art, the classification using the decision tree in the above-described existing technique has a problem that the classification accuracy is lower than that of using other models such as a gradient boosting tree (GBT) and a neural network, although the interpretability is higher. 
     In one aspect, an object is to provide a learning method, a storage medium storing a learning program, and an information processing device capable of creating a decision tree having an excellent classification accuracy. 
     Hereinafter, a learning method, a learning program, and an information processing device according to embodiments are described with reference to the drawings. In embodiments, the same reference numerals are used for a configuration having the same functions, and repetitive description is omitted. The learning method, the learning program, and the information processing device described in the embodiments described below are merely illustrative and not intended to limit the embodiment. The following embodiments may be combined as appropriate to the extent not inconsistent therewith. 
       FIG. 1  is a block diagram illustrating an example of a system configuration. As illustrated in  FIG. 1 , an information processing system  1  includes a host learning device  2  and a client learning device  3 . In the information processing system  1 , the host learning device  2  and the client learning device  3  are used to perform the supervised learning with learning data  10 A and  11 A to which teacher or teaching labels  10 B and  11 B are applied. Then, in the information processing system  1 , a model obtained by the supervised learning is used to classify classification target data  12 , which is data having the non-linear characteristics, and obtain a classification result  13 . 
     Although this embodiment exemplifies the system configuration in which the host learning device  2  and the client learning device  3  are separated from each other, the host learning device  2  and the client learning device  3  may be integrated as a single learning device. Specifically, the information processing system  1  may be formed as a single learning device and may be, for example, an information processing device in which a learning program is installed. 
     In this embodiment, here is exemplified for description a case where the pass or fail of an examination such as an entrance examination is classified based on the performance of an examinee that is an example of the data having the non-linear characteristics. For example, the information processing system  1  inputs the performances of Japanese, English, and so on of an examinee to the information processing system  1  as the classification target data  12  and obtains the pass or fail of the examination such as an entrance examination of the examinee as the classification result  13 . 
     The learning data  10 A and  11 A are the performances of Japanese, English, and so on of examinees as samples. In this case, the learning data  11 A and the classification target data  12  have the same data format. For example, when the learning data  11 A is performance data (vector data) of English and Japanese of the sample examinees, the classification target data  12  is also the performance data (vector data) of English and Japanese of the subjects. 
     The data formats of the learning data  10 A and the learning data  11 A may be different from each other as long as the sample examinees are the same. For example, the learning data  10 A may be image data of examination papers of English and Japanese of the sample examinees, and the learning data  11 A may be the performance data (vector data) of English and Japanese of the sample examinees. In this embodiment, the learning data  10 A and the learning data  11 A are the completely same data. For example, the learning data  10 A and  11 A are both the performance data of English and Japanese of the sample examinees (examinee A, examinee B, examinee Z). 
     The host learning device  2  includes a hyperparameter adjustment unit  21 , a learning unit  22 , an inference unit  23 , a clustering execution unit  24 , and a creation unit  25 . 
     The hyperparameter adjustment unit  21  is a processing unit that adjusts hyperparameters related to the machine learning such as the batch size, the number of iterations, and the number of epochs to inhibit the machine learning using the learning data  10 A from being overlearning. For example, the hyperparameter adjustment unit  21  tunes the hyperparameters such as the batch size, the number of iterations, and the number of epochs by the cross-validation of the learning data  10 A or the like. 
     The learning unit  22  is a processing unit that creates a learning model that performs the classification by the machine learning using the learning data  10 A. Specifically, the learning unit  22  creates a learning model such as a gradient boosting tree (GBT) and a neural network by performing the publicly-known supervised learning based on the learning data  10 A and the teacher labels  10 B applied to the learning data  10 A as correct answers (for example, the pass or fail of the sample examinees). For example, the learning unit  22  is an example of an obtainment unit. 
     The inference unit  23  is a processing unit that performs the inference (the classification) using the learning model created by the learning unit  22 . For example, the inference unit  23  classifies the learning data  10 A by using the learning model created by the learning unit  22 . For example, the inference unit  23  inputs the performance data of the sample examinees in the learning data  10 A into the learning model created by the learning unit  22  to obtain the probability of the pass or fail of each examinee as a classification score. Then, based on the classification scores thus obtained, the inference unit  23  classifies the pass or fail of the sample examinees. 
     The inference unit  23  calculates a score (hereinafter, a factor score) of a factor of the obtainment of the classification result for the learning data  10 A. For example, the inference unit  23  calculates the factor score by using publicly-known techniques such as the local interpretable model-agnostic explanations (LIME) and the Shapley additive explanations (SNAP) which interpret that on what basis the classification by the machine learning model is performed. For example, the inference unit  23  is an example of a calculation unit. 
     The clustering execution unit  24  is a processing unit that clusters the learning data  10 A by using the factor score calculated by the inference unit  23 . For example, the clustering execution unit  24  gathers the learning data  10 A having similar factors according to the factor score calculated by the inference unit  23  and divides the learning data  10 A into multiple clusters. 
     The creation unit  25  is a processing unit that changes the teacher labels  10 B applied to the learning data  10 A as correct answers to the teacher labels  11 B based on the clusters obtained by the clustering by the clustering execution unit  24 . For example, the creation unit  25  creates the teacher labels  11 B by changing the teacher labels  10 B, which indicate correct answers (the pass or fail) applied to the respective sample examinees of the learning data  10 A, to labels indicating in which cluster out of the multiple clusters divided by the clustering execution unit  24  the data is included. The creation unit  25  creates label correspondence information  11 C that indicates a correspondence relationship before and after the change from the teacher labels  108  to the teacher labels  118 . 
     The client learning device  3  includes a hyperparameter adjustment unit  31 , a learning unit  32 , and an inference unit  33 . 
     The hyperparameter adjustment unit  31  is a processing unit that adjusts hyperparameters related to the machine learning such as the batch size, the number of iterations, and the number of epochs to inhibit the machine learning using the learning data HA from being overlearning. For example, the hyperparameter adjustment unit  21  tunes the hyperparameters such as the batch size, the number of iterations, and the number of epochs by the cross-validation of the learning data  11 A or the like. 
     The learning unit  32  is a processing unit that performs the publicly-known supervised learning related to a decision tree by using the learning data  11 A and the teacher labels  118  changed from the teacher labels  108 . Specifically, the decision tree learned by the learning unit  32  includes multiple nodes and edges coupling the nodes, and intermediate nodes are associated with branch conditions (for example, conditional expressions of a predetermined data item). Terminal nodes in the decision tree are associated with labels of the teacher labels  11 B or specifically the clusters obtained by the clustering by the clustering execution unit  24 . 
     Through the publicly-known supervised learning related to the decision tree, the learning unit  32  creates the decision tree by determining the branch conditions for the intermediate nodes so as to reach the terminal nodes associated with the labels applied to the teacher labels  11 B for the corresponding sample examinees of the learning data  11 A. 
     The learning unit  32  performs the replacement of the terminal nodes in the learned decision tree based on the label correspondence information  11 C indicating the correspondence relationship in the change from the teacher labels  10 B to the teacher labels  1113 . Specifically, the learning unit  32  replaces the terminal nodes associated with the labels of the teacher labels  11 B in the learned decision tree with the labels of the teacher labels  10 B (for example, the pass or fail of the examinees) according to the correspondence relationship indicated by the label correspondence information  11 C. Thus, with the classification using the learned decision tree, it is possible to obtain the classification result (for example, the pass or fail of the examinees) corresponding to the teacher labels  10 B by reaching the terminal nodes according to the branch conditions for the intermediate nodes. 
     The inference unit  33  is a processing unit that performs the inference (the classification) of the classification target data  12  using the decision tree learned by the learning unit  32 . For example, the inference unit  33  obtains the classification result  13  by following the edges of the conditions corresponding to the classification target data  12  out of the branch conditions for the intermediate nodes in the decision tree learned by the learning unit  32  until reaching the terminal nodes. 
       FIG. 2  is a flowchart illustrating operation examples of the host learning device  2  and the client learning device  3 . As illustrated in  FIG. 2 , once the processing is started, the learning unit  22  performs the supervised learning of the learning model by using the learning data  10 A and the teacher labels  10 B applied to the learning data  10 A as correct answers (S 1 ). 
       FIG. 3  is an explanatory diagram describing a learning r model of the supervised learning. The left side of  FIG. 3  illustrates distributions in a plane of a performance (x 1 ) of Japanese and a performance (x 2 ) of English for data d 1  of the sample examinees included in the learning data  10 A. “1” or “0” in the data dl indicates a label of the pass or fail applied as the teacher label  108 , while “1” indicates an examinee who passes, and “0” indicates an examinee who fails. 
     The learning unit  22  obtains a learning model M 1  by adjusting weights (a 1 , a 2 , . . . a N ) in the learning model M 1  so as to make a boundary k 1  closer to a true boundary k 2  in the learning model M 1  of a gradient boosting tree (GBT) that classifies the examinees into who passes and who fails, as illustrated in  FIG. 3 . 
     Referring back to  FIG. 2  and following S 1 , the inference unit  23  classifies the learning data  10 A by using the learning model M 1  created by the learning unit  22  and calculates the classification score of each of the sample examinees included in the learning data  10 A (S 2 ). 
       FIG. 4  is an explanatory diagram describing the data classification using the learning model M 1 . As illustrated in  FIG. 4 , the learning unit  22  inputs performances (Japanese) d 12  and performances (English) d 13  of corresponding examinees d 11 , which are the “examinee A”, the “examinee B”, . . ., the “examinee Z”, into the learning model M 1  to obtain outputs of fail rates d 14  and pass rates d 15  related to the classification of the pass or fail of the examinees d 11 . The learning unit  22  determines classification results d 16  based on the obtained fail rates d 14  and pass rates d 15 . For example, the learning unit  22  sets “1” indicating the pass as the classification result d 16  when the pass rate d 15  is greater than the fail rate d 14  and sets “0” indicating the fail as the classification result d 16  when the pass rate d 15  is not greater than the fail rate d 14 . 
     Referring back to  FIG. 2 , the inference unit  23  uses the publicly-known techniques such as the LIME and the SHAP that investigate the factor of the classification performed by the learning model M 1  to calculate the factor of the obtainment of the classification score (the factor score) (S 3 ). 
     For example, since the performance of the “examinee A” is (the performance of English, the performance of Japanese)=(6.5, 7.2), the “examinee A” is classified to the pass “ 1 ” with the performance being inputted in the learning model M 1 . With the publicly-known techniques such as the LIME and the SHAP, the inference unit  23  obtains the degrees of contribution of the performance of English and the performance of Japanese to the pass of the “examinee A” as the factor score indicating the factor of the classification. For example, the inference unit  23  obtains (the performance of English, the performance of Japanese)=(3.5, 4.5) as the degrees of contribution of the performance of English and the performance of Japanese to the pass of the “examinee A” as the factor score of the pass of the “examinee A”. Based on this factor score, it is possible to see that the performance of Japanese more contributes than the performance of English to the pass of the “examinee A”. 
     Then, the clustering execution unit  24  uses the factor score calculated by the inference unit  23  to execute the clustering of the learning data  10 A (S 4 ).  FIG. 5  is a flowchart exemplifying the clustering processing of the learning data  10 A. 
     As illustrated in  FIG. 5 , once the clustering processing is started, the clustering execution unit  24  defines a factor distance matrix and an error matrix (S 10 ). 
       FIG. 6  is an explanatory diagram illustrating examples of the factor distance matrix and the error matrix, As illustrated in  FIG. 6 , a factor distance matrix  40  is a matrix in which a distance (a factor distance) between the factor scores of one examinee as oneself and the other examinee out of the sample examinees (“examinee A”, “examinee B”. . .) in the learning data  10 A is arrayed. Specifically, the factor distance matrix  40  is a symmetric matrix in which the factor distance between the one examinee and oneself is “0”. In the factor distance matrix  40  in  FIG. 6 , the factor distance between the “examinee D” and the “examinee E” is “4”. The clustering execution unit  24  defines the factor distance matrix  40  by, for example, obtaining a distance between the vector data of oneself and the other examinee based on the vector data of the degrees of contribution of the performances of English and Japanese for each of the sample examinees. 
     An error matrix  41  is a matrix in which an error (for example, a distance between the classification scores of oneself and the other examinee) that occurs when the classification is performed with the classification score of the other examinee for each of the sample examinees (the “examinee A”, the “examinee B”. . .) in the learning data  10 A is arrayed. Specifically, the error matrix  41  is a symmetric matrix in which the error between the one examinee and oneself is “0”. In the error matrix  41  in  FIG. 6 , the error that occurs when the classification of the “examinee A” is performed with the classification score of the “examinee C” is “4”. The clustering execution unit  24  defines the error matrix  41  by, for example, obtaining the error based on the classification scores for each of the sample examinees, 
     Referring back to  FIG. 5  and following S 10 , the clustering execution unit  24  repeats loop processing until the number of the data (the representative data) as the representative of the dusters that remain without being deleted from the defined factor distance matrix  40  and error matrix  41  matches the number set in advance by a user or the like (S 11  to S 14 ). For example, the clustering execution unit  24  repeats the processing of S 12  and S 13  until the representative data of the number corresponding to the predetermined number of the clusters remain without being deleted from the factor distance matrix  40  and the error matrix  41 . 
     For example, once the loop processing is started, the clustering execution unit  24  evaluates the degree of influence on the error matrix  41  in the case of deleting arbitrary learning data from the factor distance matrix  40  (S 12 ). 
       FIG. 7A  and  FIG. 7B  are explanatory diagrams describing the evaluation of the degree of influence on the error matrix  41 . As illustrated in  FIG. 7A , here is assumed a case of excluding the “examinee A” from the factor distance matrix  40 , for example. Based on the factor distances to the “examinee A” in the factor distance matrix  40 , an examinee who has the factor closest to that of the “examinee A” is the “examinee B” with the factor distance of “1”. In this way, the clustering execution unit  24  identifies data of the factor close to that of the data as the target of the deletion from the factor distance matrix  40 . 
     Then, the clustering execution unit  24  refers to the error matrix  41  and evaluates the error (the degree of influence) of a case of performing the classification with a classification score of the closest factor (the classification score of the other examinee). For example, since the “examinee B” is the person who has the factor closest to that of the “examinee A”, it is possible to see that, when the “examinee A” is excluded from the factor distance matrix  40  and the classification score of the “examinee B” is used, the error (the degree of influence) is increased by “3” based on the error matrix  41 . 
     As illustrated in  FIG. 7B , here is assumed a case of excluding the “examinee B” from the factor distance matrix  40 , for example. Based on the factor distances to the “examinee B” in the factor distance matrix  40 , examinees who have the factor closest to that of the “examinee B” are the “examinee A” and the “examinee E” with the factor distance of “1”. In this way, the clustering execution unit  24  identifies data of the factor close to that of the data as the target of the deletion from the factor distance matrix  40 . 
     Then, the clustering execution unit  24  refers to the error matrix  41  and evaluates the error (the degree of influence) of a case of performing the classification with a classification score of the closest factor (the classification score of the other examinee). For example, since the “examinee A” and the “examinee E” are the people who have the factor closest to that of the “examinee B”, it is possible to see that, when the “examinee B” is excluded from the factor distance matrix  40  and the classification scores of the “examinee A” and the “examinee E” are used, the error (the degree of influence) is increased by at least “2” based on the error matrix  41 . 
     Referring back to  FIG. 5  and following S 12 , based on the degree of influence evaluated in S 12 , the clustering execution unit  24  deletes the learning data of the smallest degree of influence on the error matrix  41  from the factor distance matrix  40  and the error matrix  41  (S 13 ). 
       FIG. 7C  is an explanatory diagram describing the data deletion according to the degree of influence on the error matrix  41 . As illustrated in  FIG. 7C , the clustering execution unit  24  deletes the “examinee D” who has the smallest degree of influence “1” from the factor distance matrix  40  and the error matrix  41 . Consequently, the remains in the factor distance matrix  40  and the error matrix  41  are four people, the “examinee A”, the “examinee B”, the “examinee C”, and the “examinee E”. As described above, the clustering execution unit  24  repeats the loop processing until the number of the remains reaches the number of the clusters. 
     Referring back to  FIG. 5  and following the loop processing (S 11  to S 14 ), the clustering execution unit  24  executes the clustering such that each of the learning data (the data dl of the sample examinees) of the learning data  10 A belongs to a cluster represented by the representative data of the shortest distance (S 15 ). 
       FIG. 8  is an explanatory diagram describing the clustering of the learning data. In the loop processing (S 11  to S 14 ), the data dl of the four people, the “examinee A”, the “examinee B”, the “examinee C”, and the “examinee E”, remain as the representative data. As illustrated in  FIG. 8 , the clustering execution unit  24  clusters the data dl included in the learning data  10 A based on the factor distances such that each of the data dl belongs to a cluster represented by the representative data of the shortest distance. Consequently, each of the data dl included in the learning data  10 A belongs to any one of the clusters “A”, “B”, “C”, and “E”. 
     Referring back to  FIG. 2  and following S 4 , the creation unit  25  creates new learning data in which the teacher labels  106  applied as correct answers to the learning data  10 A are changed to the teacher labels  116 , based on the clusters obtained by the clustering execution unit  24  (S 5 ). 
       FIG. 9  is an explanatory diagram describing the creation of the new learning data. As illustrated in  FIG. 9 , in the original learning data (combinations of the learning data  10 A and the teacher labels  106 ), teacher labels c 11  indicating the pass or fail of the examination (pass=“1”/fail=“0”) are applied with the performances (Japanese) d 12  and the performances (English) d 13  for the examinees d 11 . 
     The creation unit  25  changes the teacher labels  106  to the teacher labels  116  based on the clusters obtained from the clustering by the clustering execution unit  24 . Consequently, in the new learning data (combinations of the learning data  11 A and the teacher labels  11 B), teacher labels c 12  indicating the clusters to which the examinees d 11  belong (for example, “A”, “B”, “C”, and “D”) are applied with the performances (Japanese) d 12  and the performances (English) d 13  for the examinees d 11 . 
     Referring back to  FIG. 2  and following S 5 , the learning unit  32  performs the publicly-known supervised learning by using the learning data  11 A and the teacher labels  11 B changed from the teacher labels  10 B, or using the new learning data, to create the decision tree (S 6 ). 
       FIG. 10  is an explanatory diagram describing the creation of the decision tree. As illustrated in  FIG. 10 , the learning unit  32  creates a decision tree M 2  by determining the branch conditions for intermediate nodes (n 1  to n 3 ) so as to reach terminal nodes (n 4  to n 7 ) associated with the labels (for example, “A”, “B”, “C”, and “D”) applied to the teacher labels  11 B. 
     Then, after the learning of the decision tree M 2  is completed, the learning unit  32  restores the labels of the terminal nodes (n 4  to n 7 ) (for example, “A”, “B”, “C”, and “D”) to the state before the conversion (for example, pass=“1”/fail=“0”). For example, the learning unit  32  performs the replacement of the terminal nodes (n 4  to n 7 ) in the learned decision tree M 2  based on the label correspondence information  11 C indicating the correspondence relationship in the change from the teacher labels  10 B to the teacher labels  11 B. 
     Referring back to  FIG. 2  and following  56 , the inference unit  33  makes the inference on the classification target data  12  by using the decision tree M 2  learned by the learning unit  32  and obtains the classification result  13  (S 7 ). 
     As described above, the information processing system  1  obtains the learning model M 1  by learning the learning data  10 A having the non-linear characteristics by the supervised learning using the teacher labels  106 . The information processing system  1  classifies the learning data  10 A by using the obtained learning model M 1  and calculates the scores related to the factors of the obtainment of the classification result for the learning data  10 A. The information processing system  1  clusters the learning data  10 A by using the calculated scores. The information processing system  1  applies the teacher labels  11 B based on the clusters obtained from the clustering to the learning data  10 A ( 11 A). The information processing system  1  performs the supervised learning of the decision tree M 2  by using the learning data  11 A and the applied teacher labels  11 B. 
     Thus, according to the information processing system  1 , since the teacher labels used for the learning of the decision tree M 2  are changed based on the clusters in which the learning data having the factors are gathered based on the scores related to the factors of the obtainment of the classification result, it is possible to improve the classification accuracy of the decision tree M 2 . Therefore, in the classification of the classification target data  12 , it is possible to obtain accurate classification result  13  while maintaining the high interpretability of the decision tree M 2 . 
       FIG. 11  and  FIG. 12  are explanatory diagrams describing the comparison between the existing technique and the present embodiment. In  FIG. 11 , the classification in a case El is performed by using a decision tree M 3  created by applying the existing technique, and the classification in a case E 2  is performed by using the decision tree M 2  created in this embodiment. The classification target data  12  in the cases E 1  and E 2  are the same and are, for example, the performances (Japanese (x 1 ), English (x 2 )) of an “examinee a”. 
     As illustrated in  FIG. 11 , comparing with a true boundary K 1  dividing the pass or fail of the examinees, the pass or fail of the “examinee a” is inverted in the case E 1  in which a boundary K 3  divides the pass or fail according to the decision tree M 3 . Consequently, although the “examinee a” is actually classified as the pass, the “examinee a” is classified as the fail in the classification using the decision tree M 3 . On the contrary, in the case E 2  in which the boundary K 3  divides the pass and fail according to the decision tree M 2 , the pass or fail of the “examinee a” matches (see “1” in “E” on the right side in  FIG. 10 ). Thus, in the classification using the decision tree M 2 , it is possible to perform the correct classification matching the actual pass or fail. In the classification using the decision tree M 2 , it is possible to maintain the high interpretability of the pass or fail based on the branch conditions for the intermediate nodes. 
       FIG. 12  exemplifies Experimental Examples F 1  to F 3  in which the free datasets of kaggle are used to obtain Accuracy, or area under the curve (AUC), which is an evaluation value of the machine learning. For example, evaluation values of a method according to this embodiment (present method), a method using only a decision tree (decision tree), and a method using only the LightGBM that is a kind of GBTs (LightGBM) are obtained and compared with each other for the free datasets. 
     Experimental Example F 1  is an experimental example using a free dataset of a binary classification problem designed to implement overlearning (www.kaggle.com/c/dont-overfit-ii/overview). Experimental Example F 2  is an experimental example using a free dataset of a binary classification problem related to the transaction prediction (www.kaggle.com/lakshmi25npathi/santander-customer-transaction-prediction-dataset). Experimental Example F 3  is an experimental example using a free dataset of a binary classification problem related to a heart disease (www.kaggle.com/ronitf/heart-disease-uci). In Experimental Examples F 1  to F 3 , the evaluation values are obtained based on an average value of ten trials of the learning and the inference. 
     As illustrated in  FIG. 12 , in any of Experimental Examples F 1  to F 3  with the present method, although some cases fall short of the LightGBM that is capable of making closer to the true boundary, it is possible to obtain the classification result with a higher accuracy than that using the decision tree. 
     The information processing system  1  obtains the representative data representing the clusters by deleting the learning data of a small degree of influence on the error from the learning data  10 A, based on the errors of the learning data  10 A in the case of the classification using the learning data having dose scores of the factors in the clustering. Then, the information processing system  1  dusters the learning data such that the learning data belongs to any one of the dusters represented by the representative data based on the scores. Thus, according to the information processing system  1 , it is possible to cluster the learning data having similar factors based on the representative data representing the clusters. 
     The information processing system  1  replaces the nodes associated with the teacher labels  11 B for the learned decision tree M 2  with the nodes associated with the teacher labels  106  based on the correspondence relationship in the change from the teacher labels  106  to the teacher labels  116 . Thus, according to the information processing system  1 , it is possible to obtain the classification result  13  corresponding to the original teacher labels  106  (for example, the pass or fail of the examination) for the classification target data  12 . 
     The components of parts illustrated in the drawings are not necessarily configured physically as illustrated in the drawings. For example, specific forms of dispersion and integration of the parts are not limited to those illustrated in the drawings, and all or part thereof may be configured by being functionally or physically dispersed or integrated in given units according to various loads, the state of use, and the like. For example, the hyperparameter adjustment unit  21  and the learning unit  22 , the clustering execution unit  24  and the creation unit  25 , or the hyperparameter adjustment unit  31  and the learning unit  32  may be integrated with each other. The order of processing illustrated in the drawings is not limited to the order described above, and the processing may be simultaneously performed or the order may be switched within the range in which the processing contents do not contradict one another. 
     All or any of the various processing functions performed in the devices may be performed on a central processing unit (CPU) (or a microcomputer, such as a microprocessor unit (MPU) or a microcontroller unit (MCU)). It is to be understood that all or any part of the various processing functions may be executed on programs analyzed and executed by the CPU (or the microcomputer such as the MPU or the MCU) or on hardware using wired logic. The various processing functions may be enabled by cloud computing in which a plurality of computers cooperate with each other. 
     The various processing described above in the embodiments may be enabled by causing a computer to execute a program prepared in advance. 
     An example of a computer configured to execute a program having the same functions as those of the above-discussed embodiments will be described below.  FIG. 13  is a block diagram illustrating an example of the computer that executes the program. 
     As illustrated in  FIG. 13 , a computer  100  includes a CPU  101  configured to execute various arithmetic processing, an input device  102  configured to receive data input, and a monitor  103 . The computer  100  includes a medium reading device  104  configured to read a program and the like from a storage medium, an interface device  105  to be coupled with various devices, and a communication device  106  to be coupled to another information processing device or the like by wired or wireless communication. The computer  100  also includes a RAM  107  configured to temporarily store various information, and a hard disk device  108 . The devices  101  to  108  are coupled to a bus  109 . 
     The hard disk device  108  stores a program  108 A having the functions similar to those of the processing units (for example, the hyperparameter adjustment units  21  and  31 , the learning units  22  and  32 , the inference units  23  and  33 , the clustering execution unit  24  and the creation unit  25 ) in the information processing system  1  illustrated in  FIG. 1 . The hard disk device  108  stores various data for implementing the processing units in the information processing system  1 . The input device  102  receives input of various kinds of information, such as operation information, from a user of the computer  100 , for example. The monitor  103  displays various kinds of screens, such as a display screen, for the user of the computer  100 , for example. To the interface device  105 , for example, a printing device is coupled. The communication device  106  is coupled to a network (not illustrated) and transmits and receives various kinds of information to and from another information processing device. 
     The CPU  101  executes various processing by reading out the program  108 A stored in the hard disk device  108 , loading the program  108 A on the RAM  107 , and executing the program  108 A. These processes may function as the processing units (for example, the hyperparameter adjustment units  21  and  31 , the learning units  22  and  32 , the inference units  23  and  33 , the clustering execution unit  24  and the creation unit  25 ) in the information processing system  1  illustrated in  FIG. 1 . 
     The above-described program  108 A may not be stored in the hard disk device  108 . For example, the computer  100  may read and execute the programs  108 A stored on a storage medium readable by the computer  100 . The recording medium readable by the computer  100  corresponds to, for example, a portable storage medium, such as a compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), or a Universal Serial Bus (USB) memory, a semiconductor memory, such as a flash memory, or a hard disk drive, The programs  108 A may be stored in a device coupled to a public network, the Internet, a LAN, or the like, and the computer  100  may read and execute the programs  108 A from the device. 
     All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.