Training data generation program, training data generation method, and information processing device

Abstract

The present invention: calculates, for each of a first value and a second value of a first attribute among a plurality of attributes included in data, the probability of occurrence of a value of a second attribute among the plurality of attributes other than the first attribute; selects one or more second attributes from among the plurality of attributes on the basis of a loss function that includes a parameter representing the difference between the probabilities of occurrence calculated respectively for the first value and the second value; and generates training data on the basis of the one or more attributes, thereby making it possible to generate training data taking fairness into account.

Description

[Technical field]

[0001] The present invention relates to a technique for generating training data that takes fairness into consideration. [Background technology]

[0002] When dealing with high-dimensional data in machine learning models (clustering, classification, etc.), the accuracy of the model often deteriorates and it becomes unstable due to noise in the data and high computational complexity. For this reason, feature selection, which reduces the dimensionality of the data in advance, is being actively researched. In feature selection, only those features necessary to provide a good approximation of the information content of the high-dimensional data are selected.

[0003] One method for achieving feature selection is dimensionality reduction, which multiplies each dimension of the original feature by a continuous weight to generate new low-dimensional features. Note that a new interpretation is required for the generated features.

[0004] Feature selection selects features by multiplying each dimension of the original features by a (sparse) weight of 0 or 1. No new interpretation is required for the selected features.

[0005] Since the data after feature selection has a lower dimension than the original data, it is possible to reduce the amount of calculation and remove noise. In addition, the data after feature selection has high interpretability.

[0006] In recent years, machine learning models (clustering, classification, etc.) have been implemented in society and are now used in many decision-making processes (medical decisions, loan screening, university entrance exams, crime area prediction, etc.). In these situations, in addition to the model's predictive accuracy, it is necessary to consider fairness in order to comply with laws and ethics.

[0007] Fairness in machine learning is defined as the fairness of predictions of machine learning models for each protected group based on the protected attributes of the data. Protected attributes are attributes that should not be discriminated against based on law or expertise, such as race or gender. Protected groups are groups obtained by dividing data by protected attributes.

[0008] Fairness techniques for unsupervised learning have not yet been developed as much as fairness techniques for supervised learning, but unsupervised learning has a wide range of applications and a large social impact.

[0009] For example, large-scale data rarely contains supervised labels, making it difficult to apply supervised fairness. There are also many types of machine learning that do not use supervised labels (unsupervised learning). Examples of this include clustering and feature selection. Furthermore, unsupervised learning is often used as a preprocessing step for machine learning. Examples of this include pre-training and feature selection.

[0010] Thus, it is important to develop technology that ensures the fairness of unsupervised learning.

[0011] The data used in feature selection (original data) is manually created and often contains bias against the protected group. Therefore, when feature selection is applied to the original data, the data after feature selection may also contain bias. This bias is known to affect machine learning models and cause unfair results for the protected group.

[0012] Therefore, fair feature selection that takes fairness into account is important. Fair feature selection is defined as a problem of trade-off evaluation between the approximation rate with the original data and the fairness of the approximated data for the number of selected features. In other words, it is required to achieve both accuracy and fairness.

[0013] For example, a convex optimization framework is known for unbiased unsupervised feature selection, in which a kernel function is used to estimate the nonlinear correlations of high-dimensional features X.

[0014] Specifically, the loss function L shown in the following equation (1) is minimized.

[0015]

number

[0016] ρ is a function that calculates something like a covariance. For example, ρ(K,K S )=Tr(HKHHK S H) = Tr(HKHK S ) It is.

[0017] Tr represents the trace of a matrix. For example, A∈R n×n For Tr(A)=Σ n i=1 a ii It is.

[0018] α and β are hyperparameters.

[0019] In high-dimensional spaces, we assume that there are nonlinear relationships that are generally difficult to estimate using linear functions, and we use a vector u∈{0,1} to select the "features not to be selected." d has been introduced. [Prior art documents] [Patent documents]

[0020] [Patent Document 1] Japanese Patent Application Publication No. 10-63635 [Patent Document 2] Special Publication No. 2021-501384 [Patent Document 3] US Patent Application Publication No. 2017 / 0213153 [Patent Document 4] U.S. Pat. No. 1,104,8727 [Non-patent literature]

[0021] [Non-Patent Document 1] Xiaoying Xing, Hongfu Liu, Chen Chen, Jundong Li, “Fairness-Aware Unsupervised Feature Selection”, [online], June 4, 2021, [Retrieved January 25, 2022], Internet<URL:https: / / arxiv.org / abs / 2106.02216> Summary of the Invention [Problem to be solved by the invention]

[0022] However, in such conventional fairness techniques for unsupervised learning, the nonlinear correlation constraints cannot always guarantee fairness.

[0023] In the above formula (1), in particular, the kernel matrix K S ,K Z Since the selection features and the protected attributes on which the model is based are both low-dimensional (z≪d′≪d), a linear correlation may be assumed. Nonlinear correlations assume high dimensions, resulting in overfitting. In addition, there is a high possibility that spurious constraints will be imposed due to spurious correlations that do not take causation into account.

[0024] Therefore, in conventional fairness techniques for unsupervised learning, regularization does not work well, and the selection feature matrix X s There is also the problem that the four types of kernel matrices each require a large amount of calculation.

[0025] In one aspect, the present invention aims to enable the generation of training data that takes fairness into consideration. [Means for solving the problem]

[0026] For this reason, this training data generation program causes a computer to execute the following process: for each of a first value and a second value of a first attribute among multiple attributes included in data, calculate the occurrence probability of a value of a second attribute other than the first attribute among the multiple attributes, select one or more of the second attributes from the multiple attributes based on a loss function including a parameter representing the difference between the occurrence probabilities for each of the first value and the second value, and generate training data based on the one or more attributes. Effect of the Invention

[0027] According to one embodiment, training data can be generated with fairness in mind. [Brief description of the drawings]

[0028] [Figure 1] FIG. 1 is a diagram illustrating a configuration of an information processing apparatus as an example of an embodiment. [Diagram 2] 1 is a flowchart illustrating a feature function learning process in an information processing device as an example of an embodiment. [Diagram 3] 11 is a diagram illustrating the occurrence probability of each of two groups classified based on approximate data generated by feature selection performed by an information processing device as one example of an embodiment, in comparison with a conventional method. FIG. [Figure 4] 11 is a diagram illustrating the probability density of each selected feature of two groups classified based on approximate data generated by feature selection performed by an information processing device as one example of an embodiment, in comparison with a conventional method. FIG. [Diagram 5] FIG. 1 is a diagram illustrating a hardware configuration of an information processing apparatus according to an embodiment; DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0029] Below, we refer to the drawing to generate the training data. ProductionThe following describes an embodiment of the program, training data generation method, and information processing device. However, the embodiment described below is merely an example, and there is no intention to exclude the application of various modified examples and techniques not explicitly stated in the embodiment. In other words, the present embodiment can be implemented with various modifications without departing from the spirit of the invention. Furthermore, each figure does not intend to include only the components shown in the figure, but can include other functions, etc.

[0030] (A) Configuration FIG. 1 is a diagram illustrating a schematic configuration of an information processing device 1 as an example of an embodiment. As shown in FIG. 1, the information processing device 1 has functions as a feature selection unit 110, a loss calculation unit 120, a gradient calculation unit 130, a parameter update unit 140, and a training data generation unit 101.

[0031] Training data D is input to the feature selection unit 110. The training data D is training data for training a machine learning model. The training data D may be called input data D. The training data D may be expressed as D={X, Z}.

[0032] X is the feature matrix, X∈R n×d X corresponds to the first attribute among a plurality of attributes included in the data (input data).

[0033] Z is the guard attribute matrix, Z∈R n×d Z corresponds to a second attribute other than the first attribute among a plurality of attributes included in the data (input data).

[0034] For n data sets, each data i is a d-dimensional feature vector Xi ∈ R 1×d and the z-dimensional protected attribute vector Zi∈R 1×z It is expressed as:

[0035] The feature selection unit 110 uses the feature selection vector f to select the feature matrix X from the feature matrix X included in the training data D. s Select the selected feature matrix X s Select feature matrix X sIt can be said that.

[0036] The feature selection unit 110 has the functions of a diagonal matrix generation unit 111 and a product calculation unit 112 .

[0037] The diagonal matrix generation unit 111 generates a diagonal matrix F of the feature selection vector f.

[0038] F = diag(f), where diag represents the diagonalization of a vector.

[0039] The product calculation unit 112 calculates the product XF of the feature matrix X and the diagonal matrix F.

[0040] Selection feature matrix X s =XF.

[0041] The loss calculation unit 120, the gradient calculation unit 130, and the parameter update unit 140 realize the function of the feature selection vector update unit 100. The feature selection vector update unit 100 updates the feature function f used by the feature selection unit 110 while taking fairness into consideration.

[0042] The loss calculation unit 120 calculates the selected feature matrix X s For the loss function L ours Calculate.

[0043] Loss function L ours is expressed by the following equation (2).

[0044]

number

[0045] As shown in FIG. 1, the loss calculation unit 120 calculation The sparseness constraint calculation unit 123 has functions as a smoothing unit 121, a fairness constraint calculation unit 122, and a sparsity constraint calculation unit 123.

[0046] Uncorrelated calculation The unit 121 calculates the loss function L shown in the above formula (2). ours The formula of ρ(K,K s ) is calculated.

[0047] ρ(K,K s )=Tr(HKHHK s H) = Tr(HKHK s ) Uncorrelated calculation The unit 121 calculates the original feature matrix X and the selected feature matrix X s Calculate the nonlinear correlation of

[0048] Tr is the trace of the matrix.

[0049] For example, A∈R (n×n) For Tr(A)=Σ n i=1 a ii It is. In addition, the following H n is defined.

[0050]

number

number

[0051] AB is the product of matrices A and B. K is a matrix obtained by applying kernel function k to matrix X.

[0052] K ij =k(X i ,X j ), K∈R n×n k is a kernel function, and may be, for example, a polynomial kernel or a radial basis function kernel as shown below.

[0053]

number

[0054] The fairness constraint calculation unit 122 calculates the loss function L ours a in the formula u |(μ + -μ - )F| 2 + a s |(Σ + -Σ - )F| 2 Calculate. The fairness constraint calculation unit 122 calculates the loss function L ours We directly incorporate the fairness metric Δ into the above equation as a constraint. The fairness metric Δ is expressed as the following equation (3). Δ=sup t |P(h(X i s )≦t|Z i =1)-P(h(X i s )≦t|Z i =0) | (3) h:R d′ →{0,1}: Can be a simple linear classifier such as a Support Vector Machine (SVM).

[0055] Let the classifier h have parameters w, for example, h(X s )=w T X s The following is output.

[0056] P(h(X i s )≦t|Z i =1) is the first value of the protection attribute (G + ) is the probability of occurrence of P(h(X i s )≦t|Z i =0) is the second value of the protection attribute (G - ) is the probability of occurrence.

[0057] This setting can easily be used with other machine learning models, such as kernel SVM.

[0058] t: The threshold used in the classifier.

[0059] In the fairness metric, the selected feature matrix X s We use this to evaluate how well the protected attributes are differentiated. The fairness metric represents the total variation distance of probability accuracy, called the Kolmogorov distance, which measures the distance between two probability distributions.

[0060] The loss function L expressed by the following formula (4) ours For the minimization problem minL ours applies.

[0061]

number

[0062] In addition, there is no need to consider the function u, and the kernel matrix K u ,K p is also similar, the amount of calculation can be reduced.

[0063] However, the fairness metric constraint Δ is difficult to optimize because it uses a non-differentiable function (unit step).

[0064] Therefore, we obtain an upper bound on the fairness metric Δ and approximate the minimization problem of Δ as shown in the following equation (5). Δ≦|(μ + -μ - )F| 2 +|F(Σ + -Σ - )F T | 2 (5) However, G + ={i|Z i =1}, G - ={i|Z i For two groups, μ+ and μ - are the respective mean vectors, and Σ + and Σ - are the respective variance-covariance matrices.

[0065] Mean vector μ + ,μ - can be expressed, for example, by the following formula:

[0066]

number

[0067]

number

[0068] The right-hand side of the above formula (6) is the total variation distance. Therefore, by applying Pinsker's inequality, it can be expressed as the following formula (7).

[0069]

number

[0070]

number

[0071]

number

[0072] Note that w is a parameter of the classifier h, and is therefore outside the scope of minimization.

[0073] In the above embodiment, the equation is expanded using the Gaussian distribution, but the present invention is not limited to this, and the equation may be expanded using a method other than the Gaussian distribution.

[0074] min (s + -s - )=min(w T FΣ + F T ww T FΣ - F T w) =min (FΣ + F T -FΣ - F T ) =min F(Σ + F T -Σ - )F T =min |F(Σ + F T -Σ - )F T | 2 |F(Σ + F T -Σ - )F T | is the selected feature matrix X s This can be interpreted as a constraint (first constraint) that brings the variances of the characteristics of the two groups closer together.

[0075] min (m + -m - )=min (w T μ + Fw T μ - F) =min (μ + F-μ - F) =min F(μ + -μ - )F =min |(μ + -μ - )F| 2 |(μ + -μ - )F| is the selected feature matrix X s This can be interpreted as a constraint (the second constraint) that brings the average characteristics of the two groups closer together.

[0076] The fairness constraint calculation unit 122 calculates the first constraint ((Σ + -Σ - )F T |) and the second constraint (|(μ + -μ - )F|) and the first value (G + ) and the second value (G - ) for each of the occurrence probabilities (distribution distance: Δ=sup t |P(h(X i s )≦t|Z i =1)-P(h(X i s )≦t|Z i=0)|) minimization problem.

[0077] The sparsity constraint calculation unit 123 calculates the loss function L ours Calculate β||f|| of the expression. The sparse constraint is that the feature selection vector f is in {0,1} d This is a constraint to become

[0078] The sparsity constraint calculation unit 123 can calculate β∥f∥ using a known method, and a detailed description thereof will be omitted.

[0079] The gradient calculation unit 130 calculates the gradient ∂L based on the above formula (4). our Calculate / ∂f.

[0080] The parameter update unit 140 updates the parameters of the feature selection vector f by using the gradient calculated by the gradient calculation unit 130. The parameter update unit 140 updates the parameters by using a gradient method.

[0081] The parameter update unit 140 uses, for example, the gradient descent method to calculate the loss function L ours In this case, the parameters are optimized so that the loss is small.

[0082] The loss function L shown in equation (4) ours The first value G + and the second value G - The difference between the occurrence probability for each of the distributions (distribution distance: Δ=sup t |P(h(X i s )≦t|Z i =1)-P(h(X i s )≦t|Z i =0)|) is included. That is, the loss function L ours is G + (first value) and G - (second value) and the difference between the occurrence probability for each (distribution distance: Δ=sup t |P(h(X i s )≦t|Zi =1)-P(h(X i s )≦t|Z i Includes a parameter representing =0)|).

[0083] The parameter update unit 140 updates the loss function L ours In order to reduce the loss, we use the loss function L ours Optimize the parameters of the loss function L ours In the first value G + and the second value G - This includes the condition that the difference between the occurrence probabilities for each of the above (the distribution distance) must be small.

[0084] Then, the parameter update unit 140 updates the parameters of the feature selection vector f.

[0085] The update process of the parameters of the feature selection vector f by the parameter update unit 140 can be expressed by the following equation.

[0086]

number

[0087] The feature selection vector f is given by the loss function L ours is reflected, and this loss function L ours The first value G + and the second value G - The difference between the occurrence probabilities for each of the above (distribution distance: Δ=sup t |P(h(X i s )≦t|Z i =1)-P(h(X i s )≦t|Z i =0)|) is reflected.

[0088] The feature selection vector update unit 100 updates the selected feature matrix X by the feature selection unit 110 until the feature selection vector f converges.s The loss function L ours Calculation of the gradient ∂L by the gradient calculation unit 130 our The calculation of / ∂f and parameter update of the feature selection vector f are repeated.

[0089] Whether the feature selection vector f has converged can be confirmed by a known method, and the description thereof will be omitted.

[0090] The feature selection unit 110 executes fair feature selection using the trained feature selection vector f, thereby realizing fair feature selection for high-dimensional data.

[0091] The training data generator 101 generates one or more features selected by the feature selector 110 (selected feature matrix X s ) to generate training data.

[0092] The feature selection unit 110 outputs one or more selected feature matrices X by using the learned feature selection vector f for the input data. s The fairness of the data is guaranteed. This ensures that the selected feature matrix X s A machine learning model trained using training data generated using the training data will also achieve fairness. raw The training data generated by the generation unit 101 is low-dimensional, has a high approximation rate to the original data (input data), and simultaneously achieves the fairness of the data after approximation.

[0093] (B) Operation The learning process of the feature selection vector f in the information processing device 1 as one example of the embodiment configured as described above will be described with reference to the flowchart (steps S1 to S6) shown in FIG.

[0094] In step S1, a feature selection vector f is initialized. The parameters of the feature selection vector f may be initialized using any values.

[0095] In step S2, input data (observation data D) is input to the feature selection unit 110, and the feature selection unit 110 selects a feature matrix X from the feature matrix X included in the observation data D using a feature selection vector f. s Select .

[0096] In step S3, the loss calculation unit 120 calculates the loss function L using the above formula (2). ours Calculate.

[0097] In step S4, the gradient calculation unit 130 calculates the loss function L ours Based on the gradient ∂L our Calculate / ∂f.

[0098] In step S5, the parameter update unit 140 updates the parameters of the feature selection vector f based on the gradient calculated by the gradient calculation unit 130.

[0099] In step S6, the feature selection vector update unit 100 (see FIG. 1) checks whether the feature selection vector f has converged.

[0100] If the result of the check is that the feature selection vector f has not converged (see the NO route in step S6), the process returns to step S2, and the feature selection unit 110 generates a new selected feature matrix X s Select .

[0101] On the other hand, if the feature selection vector f has converged (see the YES route in step S6), the process ends.

[0102] Then, the feature selection unit 110 inputs the training data into the trained feature selection vector f to perform fair feature selection. The training data generation unit 101 generates training data based on one or more features selected in this way.

[0103] (C) Effects In this way, according to the information processing device 1 as an example of the embodiment, the fairness Δ can be improved regardless of the type of correlation by using the fairness metric as a direct constraint.

[0104] FIG. 3 shows two groups G classified based on approximate data generated by feature selection performed by an information processing device 1 according to an embodiment. + ,G - 13 is a diagram showing the occurrence probability of each of the above in comparison with the conventional method.

[0105] In Fig. 3, symbol A represents group G in the conventional method. + The probability of occurrence of P(h(X i s )≦t|Z i =1) and G - The probability of occurrence of P(h(X i s )≦t|Z i =0). Also, the symbol B indicates the group G + The probability of occurrence of P(h(X i s )≦t|Z i =1) and G - The probability of occurrence of P(h(X i s )≦t|Z i =0).

[0106] In the method of the information processing device 1, a fairness constraint based on a fairness metric is used to + ,G - We can evaluate the actual difference in the probability of occurrence of and minimize that difference. This allows us to optimize fairness. + ,G - The difference in the occurrence probability of each of the above can be taken into consideration, and the difference in the occurrence probability is small, resulting in an unfair state. In other words, fairness can be improved.

[0107] In contrast, the conventional method uses a fairness constraint based on non-correlation. + ,G -We cannot evaluate the actual difference in the probability of occurrence of . This makes it difficult to optimize fairness by using spurious correlation. + ,G - This makes it difficult to take into account the difference in the probability of occurrence, resulting in an unfair situation.

[0108] FIG. 4 shows two groups G classified based on approximate data generated by feature selection performed by an information processing device 1 according to an embodiment. + ,G - FIG. 13 is a diagram showing the probability density of each selected feature in comparison with the conventional method.

[0109] In Fig. 4, symbol A represents group G in the conventional method. + Selection of feature matrix X s The probability density distribution of G - Selection of feature matrix X s The symbol B indicates the distribution of the probability density of the group G by the information processing device 1. + Selection of feature matrix X s The probability density distribution of G - Selection of feature matrix X s and the probability density distribution of

[0110] In the method of the information processing device 1, the selection feature matrix X s We directly constrain the shape of the distribution of the probability density of . This allows any classifier to distinguish between two groups G + ,G - In other words, regardless of the type of correlation, the selected feature matrix X s This makes it difficult to distinguish between the protected attributes, thereby achieving fairness.

[0111] In contrast, the conventional method uses a fairness constraint based on non-correlation. s We do not impose any constraint on the shape of the distribution of the probability density of . This allows any classifier to distinguish between two groups G + ,G - This leads to a distinction and creates unfairness.

[0112] (D) Other FIG. 5 is a diagram illustrating a hardware configuration of an information processing device 1 as an example of an embodiment.

[0113] The information processing device 1 is a computer and includes, as components, a processor 11, a memory 12, a storage device 13, a graphics processing device 14, an input interface 15, an optical drive device 16, a device connection interface 17, and a network interface 18. These components 11 to 18 are configured to be able to communicate with each other via a bus 19.

[0114] The processor (control unit) 11 controls the entire information processing device 1. The processor 11 may be a multiprocessor. The processor 11 may be, for example, any one of a CPU, a Micro Processing Unit (MPU), a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Programmable Logic Device (PLD), a Field Programmable Gate Array (FPGA), and a Graphics Processing Unit (GPU). The processor 11 may also be a combination of two or more types of elements from the CPU, MPU, DSP, ASIC, PLD, FPGA, and GPU.

[0115] Then, the processor 11 executes a control program (training data generation program: not shown) for the information processing device 1, thereby realizing the functions of the feature selection unit 110, the loss calculation unit 120, the gradient calculation unit 130, the parameter update unit 140, and the training data generation unit 101 illustrated in FIG. 1.

[0116] The information processing device 1 realizes the functions of the feature selection unit 110, the loss calculation unit 120, the gradient calculation unit 130, the parameter update unit 140, and the training data generation unit 101 described above, for example, by executing a program (training data generation program, OS program) recorded on a computer-readable non-transitory recording medium.

[0117] The programs describing the processing contents to be executed by the information processing device 1 can be recorded on various recording media. For example, the programs to be executed by the information processing device 1 can be stored in the storage device 13. The processor 11 loads at least a part of the programs in the storage device 13 into the memory 12 and executes the loaded programs.

[0118] The programs to be executed by the information processing device 1 (processor 11) may also be recorded in a non-transitory portable recording medium such as the optical disk 16a, the memory device 17a, or the memory card 17c. The programs stored in the portable recording medium are executable after being installed in the storage device 13, for example, under the control of the processor 11. The processor 11 may also read and execute the programs directly from the portable recording medium.

[0119] The memory 12 is a storage memory including a ROM (Read Only Memory) and a RAM (Random Access Memory). The RAM of the memory 12 is used as a main storage device of the information processing device 1. The RAM temporarily stores at least a part of the program to be executed by the processor 11. The memory 12 also stores various data necessary for processing by the processor 11.

[0120] The storage device 13 is a storage device such as a hard disk drive (HDD), a solid state drive (SSD), or a storage class memory (SCM), and stores various data.

[0121] An OS program, a control program, and various data are stored in the storage device 13. The control program includes a training data generation program.

[0122] As the auxiliary storage device, a semiconductor storage device such as an SCM or a flash memory can also be used. Furthermore, a plurality of storage devices 13 may be used to configure a RAID (Redundant Arrays of Inexpensive Disks).

[0123] The storage device 13 may store data generated during processing by at least one of the feature selection unit 110, the loss calculation unit 120, the gradient calculation unit 130, the parameter update unit 140, and the training data generation unit 101.

[0124] A monitor 14a is connected to the graphics processing device 14. The graphics processing device 14 displays an image on the screen of the monitor 14a in accordance with an instruction from the processor 11. Examples of the monitor 14a include a display device using a CRT (Cathode Ray Tube) and a liquid crystal display device.

[0125] A keyboard 15a and a mouse 15b are connected to the input interface 15. The input interface 15 transmits signals sent from the keyboard 15a and the mouse 15b to the processor 11. The mouse 15b is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

[0126] The optical drive device 16 uses a laser beam or the like to read data recorded on an optical disk 16a. The optical disk 16a is a portable, non-transient recording medium on which data is recorded so that it can be read by the reflection of light. Examples of the optical disk 16a include a DVD (Digital Versatile Disk), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), and a CD-R (Recordable) / RW (ReWritable).

[0127] The device connection interface 17 is a communication interface for connecting peripheral devices to the information processing device 1. For example, a memory device 17a or a memory reader / writer 17b can be connected to the device connection interface 17. The memory device 17a is a non-transitory recording medium equipped with a communication function with the device connection interface 17, such as a Universal Serial Bus (USB) memory. The memory reader / writer 17b writes data to a memory card 17c or reads data from the memory card 17c. The memory card 17c is a card-type non-transitory recording medium.

[0128] The network interface 18 is connected to a network. The network interface 18 transmits and receives data via the network. Other information processing devices, communication devices, etc. may be connected to the network.

[0129] The disclosed technology is not limited to the above-described embodiment, and may be modified in various ways without departing from the spirit of the present embodiment. Each configuration and each process of the present embodiment may be selected as necessary, or may be combined as appropriate.

[0130] For example, in the above embodiment, a method based on Pinsker's inequality exemplified in the above formula (4) is used as a method for approximating the minimization problem of the fairness metric Δ, but the method is not limited to this and can be modified as appropriate. For example, an approximation method using a function such as a sigmoid function or a hinge function may be used. Also, an approximation method using sampling such as Monte Carlo sampling may be used.

[0131] Furthermore, the above disclosure enables a person skilled in the art to implement and manufacture the present embodiment. [Explanation of symbols]

[0132] 1. Information processing device 11 Processor (control unit) 12. Memory 13 Storage device 14 Graphics Processing Unit 14a Monitor 15 Input Interface 15a Keyboard 15b Mouse 16 Optical drive device 16a Optical disc 17 Device connection interface 17a Memory Device 17b Memory Reader / Writer 17c Memory Card 18 Network Interface 19 Bus 100 Feature selection vector update section 101 Training Data Generation Unit 110 Feature Selection Unit 111 Diagonal matrix generator 112 Product calculation section 120 Loss calculation section 121 Decorrelation Calculation Unit 122 Fairness constraint calculation section 123 Sparsity constraint calculation part 130 Gradient Calculation Unit 140 Parameter Update Section

Claims

1. calculating, for each of a first value and a second value of a first attribute among a plurality of attributes included in the data, a probability of occurrence of a value of a second attribute other than the first attribute among the plurality of attributes; selecting one or more of the second attributes from the plurality of attributes based on a loss function including a parameter representing a difference between the occurrence probability for each of the first value and the second value; generating training data based on the one or more attributes; A training data generation program that causes a computer to execute a process.

2. a first constraint for the selected second attribute such that the variance of the second attribute in two groups, a group of values ​​of the first attribute and a group of values ​​of the second attribute, is approximated; a second constraint for approximating the average of the second attributes of the two groups to the selected second attribute; approximating a minimization problem of the difference between the occurrence probabilities for the first value and the second value based on 2. The training data generating program according to claim 1, wherein the program causes the computer to execute a process.

3. calculating, for each of a first value and a second value of a first attribute among a plurality of attributes included in the data, a probability of occurrence of a value of a second attribute other than the first attribute among the plurality of attributes; selecting one or more of the second attributes from the plurality of attributes based on a loss function including a parameter representing a difference between the occurrence probability for each of the first value and the second value; generating training data based on the one or more attributes; A training data generation method, characterized in that the processing is executed by a computer.

4. calculating, for each of a first value and a second value of a first attribute among a plurality of attributes included in the data, a probability of occurrence of a value of a second attribute other than the first attribute among the plurality of attributes; selecting one or more of the second attributes from the plurality of attributes based on a loss function including a parameter representing a difference between the occurrence probability for each of the first value and the second value; generating training data based on the one or more attributes; 1. An information processing device comprising: a control unit that executes processing.

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