JP7563575B2 - Information processing device, information processing method, and program - Google Patents

Description

The present invention relates to an information processing device, an information processing method, and a program for estimating a generalized linear regression model.

Conventionally, devices that perform regression analysis such as linear regression or generalized linear regression have been proposed. In recent years, in order to avoid overlearning that can occur when applying to big data, estimation of regression models with sparseness constraints has been proposed.

For example, Patent Document 1 discloses a generalized linear regression model subject to sparseness constraints (hereinafter also referred to as a "sparse generalized linear regression model").

Japanese Patent Application Publication No. 2020-062369

In linear regression or generalized linear regression techniques, there may be non-negligible variation in the quality of the obtained data. However, the technique described in Patent Document 1 has a problem in that it is not possible to estimate a suitable sparse generalized linear regression model when the quality of the data varies.

One aspect of the present invention has been made in consideration of the above problems, and one example of its objective is to realize an information processing device capable of estimating a suitable sparse generalized linear regression model even when the data quality varies.

An information processing device according to one aspect of the present invention comprises an acquisition means for acquiring input data including a plurality of datasets consisting of explanatory variables and objective variables, information regarding the quality of each dataset, and information regarding the shape of the residual distribution, a preprocessing means for initializing regression coefficients of a generalized linear regression model subject to a sparseness constraint by referring to at least any of the data or information included in the input data acquired by the acquisition means, and an update means for executing an update process for updating the regression coefficients by referring to the input data.

An information processing method according to one aspect of the present invention includes an information processing device acquiring input data including a plurality of datasets consisting of explanatory variables and objective variables, information regarding the quality of each dataset, and information regarding the shape of the residual distribution, initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed by referring to at least any of the data or information included in the acquired input data, and performing an update process that updates the regression coefficients by referring to the input data.

A program according to one aspect of the present invention is a program that causes a computer to function as an information processing device, and is characterized in that the program causes the computer to function as: an acquisition means that acquires input data including a plurality of data sets consisting of explanatory variables and objective variables, information regarding the quality of each data set, and information regarding the shape of the residual distribution; a preprocessing means that refers to at least any of the data or information included in the input data acquired by the acquisition means and initializes regression coefficients of a generalized linear regression model that is subject to a sparseness constraint; and an update means that performs an update process that updates the regression coefficients by referring to the input data.

According to one aspect of the present invention, an information processing device can be realized that is capable of estimating a suitable sparse generalized linear regression model even when data quality varies.

1 is a block diagram showing a configuration of an information processing device according to a first exemplary embodiment of the present invention. FIG. 2 is a flow chart showing the flow of an information processing method according to the first exemplary embodiment of the present invention. FIG. 11 is a block diagram showing a configuration of an information processing device according to a second exemplary embodiment of the present invention. FIG. 11 is a diagram showing a specific example of a dataset according to the second exemplary embodiment of the present invention. FIG. 11 is a flow chart showing the flow of an information processing method according to an exemplary embodiment 2 of the present invention. FIG. 11 is a flow chart showing a flow of pre-processing according to the second exemplary embodiment of the present invention. FIG. 11 is a flow chart showing the flow of an optimization process according to the second exemplary embodiment of the present invention. FIG. 11 is a flow diagram showing the flow of an update preparation process according to the second exemplary embodiment of the present invention. FIG. 11 is a block diagram showing a configuration of an information processing device according to an exemplary embodiment 3 of the present invention. FIG. 1 is a block diagram showing a configuration of a computer that functions as an information processing device according to first to third exemplary embodiments of the present invention.

[Example embodiment 1]
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A first exemplary embodiment of the present invention will be described with reference to the drawings. This exemplary embodiment is a basic form of the exemplary embodiments described below.

<Configuration of information processing device>
The configuration of an information processing device 10 according to this exemplary embodiment will be described with reference to FIG. 1. FIG. 1 is a block diagram showing the configuration of the information processing device 10. The information processing device 10 is a device that generates a generalized linear regression model (sparse generalized linear regression model) with a sparseness constraint. More specifically, the information processing device 10 is a device that estimates regression coefficients of a sparse generalized linear regression model. Note that in this exemplary embodiment, estimating the regression coefficients of a sparse generalized linear regression model may be expressed as generating the model, or as determining the model.

As shown in FIG. 1, the information processing device 10 includes an acquisition unit 11, a preprocessing unit 12, and an update unit 13. The acquisition unit 11 is a component that realizes an acquisition means in this exemplary embodiment. The preprocessing unit 12 is a component that realizes a preprocessing means in this exemplary embodiment. The update unit 13 is a component that realizes an update means in this exemplary embodiment.

The acquisition unit 11 acquires input data including multiple datasets consisting of explanatory variables and objective variables, information regarding the quality of each dataset, and information regarding the shape of the residual distribution.

Here, an example of information regarding the quality of each dataset is the reliability of each dataset expressed as a numerical value. As an example, the numerical value may be larger when the reliability of the dataset is high and may be smaller when the reliability of the dataset is low.

The information on the shape of the residual distribution is, for example, a function that expresses the shape of the residual distribution. In this exemplary embodiment, the function that expresses the shape of the residual distribution is sometimes simply referred to as a distribution function. Specific examples of distribution functions include, but are not limited to, the present exemplary embodiment, normal distribution, Bernoulli distribution, Poisson distribution, binomial distribution, Gaussian distribution, etc. As described above, the target of the information processing device 10 according to this exemplary embodiment is a generalized linear regression model, and the processing described in this exemplary embodiment is generally applicable to various distribution functions.

The data and information contained in the input data are not limited to those described above. The input data may include other data and information. As an example, the input data may include a regularization parameter. Here, the regularization parameter is, as an example, a parameter that specifies a regularization term (also called a penalty term, etc.) included in an evaluation function that is referenced when the update unit 13 described later updates the regression coefficient.

The acquisition unit 11 may acquire all or a part of the input data by reading it from a storage device built into the information processing device 10, or by reading it from an external storage device. The acquisition unit 11 may also acquire all or a part of the input data by receiving it from another device via a communication unit.

The preprocessing unit 12 initializes the regression coefficients of the sparse generalized linear regression model by referring to at least any of the data or information included in the input data acquired by the acquisition unit 11. As an example, the preprocessing unit 12 may initialize the regression coefficients using random numbers generated by a random function, or may initialize the regression coefficients to have predetermined initial values. In addition to the initialization process of the regression coefficients, the preprocessing unit 12 may also perform a process of initializing various parameters referenced in the update process of the regression coefficients.

The update unit 13 refers to the input data and executes an update process to update the regression coefficients initialized by the preprocessing unit 12. As an example, the update unit 13 refers to an evaluation function of a sparse generalized linear regression model and updates the regression coefficients so as to reduce the value of the evaluation function.

As an example, the update unit 13 repeatedly executes the update process by referring to the input data until the regression coefficients satisfy a predetermined convergence condition. An example of the predetermined convergence condition is that the amount of change in the regression coefficients due to the update process is equal to or less than a threshold value. However, the update process of the regression coefficients is not limited to the process described above.

<Flow of information processing method>
The flow of the information processing method S10 executed by the information processing device 10 configured as above will be described with reference to Fig. 2. Fig. 2 is a flow diagram showing the flow of the information processing method S10.

Information processing method S1 is a method for generating a sparse generalized linear regression model, and includes steps S11 to S13 as shown in FIG. 2.

(Step S11)
In step S11 (acquisition process), the acquisition unit 11 acquires input data including a plurality of data sets each consisting of an explanatory variable and a target variable, information on the quality of each data set, and information on the shape of the residual distribution. A specific example of the process performed by the acquisition unit 11 has been described above, and therefore will not be described here.

(Step S12)
In step S12 (preprocessing), the preprocessing unit 12 initializes the regression coefficients of the generalized linear regression model with the sparseness constraint by referring to at least any data or information included in the input data acquired in the acquisition process S11. A specific example of the processing by the preprocessing unit 12 has been described above, and therefore will not be described here.

(Step S13)
In step S13 (update process), the update unit 13 executes the update process of updating the regression coefficients by referring to the input data acquired in the acquisition process S11. A specific example of the process performed by the update unit 13 has been described above, and therefore a description thereof will be omitted here.

<Advantages of this exemplary embodiment>
As described above, the information processing device 10 according to the present exemplary embodiment initializes and updates the regression coefficients by referring to input data including information on the quality of each data set. Therefore, according to the information processing device 10 according to the present exemplary embodiment, even if the quality of the data sets varies, a suitable sparse generalized linear regression model can be generated.

Exemplary embodiment 2
A second exemplary embodiment of the present invention will be described in detail with reference to the drawings. Note that components having the same functions as those described in the first exemplary embodiment are given the same reference numerals, and the description thereof will not be repeated.

<Configuration of information processing device>
The configuration of the information processing device 10A according to this exemplary embodiment will be described with reference to FIG. 3. FIG. 3 is a block diagram showing the configuration of the information processing device 10A. The information processing device 10A is a device that generates a sparse generalized linear regression model. More specifically, it is a device that determines the regression coefficients of the sparse generalized linear regression model. As shown in FIG. 3, the information processing device 10A includes an acquisition unit 11A, a preprocessing unit 12A, an update unit 13A, and an output unit 14A. Note that the arrows in the figure simply indicate the direction of data flow and do not exclude bidirectionality.

(Acquisition Department)
The acquisition unit 11 acquires input data including a plurality of data sets each consisting of an explanatory variable and a target variable, information on the quality of each data set, and information on the shape of the residual distribution.

The input data acquired by the acquisition unit 11A is data used to generate a sparse generalized linear regression model (hereinafter also simply referred to as a "regression model"). The input data acquired by the acquisition unit 11A includes a plurality of data sets dn each consisting of explanatory variables _xn (1≦n≦N; N is a natural number representing the number of data sets ₎ and objective variables _yn , quality information _wn , a function form of a distribution function A, and a regularization parameter λ.

Although the mathematical notation does not limit the present exemplary embodiment, as an example, the explanatory variable x _n is expressed as an M-dimensional vector having as many components as the number M of explanatory variables in each data set. In other words, when n is fixed, the explanatory variable x _n can be expressed as a vector having M components, where the value of M is the number of explanatory variables. For this reason, the explanatory variable x _n may be expressed as an explanatory variable vector. In addition, a matrix in which the explanatory variable vector x _n is arranged in the number N of data sets may be expressed as an explanatory variable matrix X.
Note that the above content does not limit the present embodiment, and the explanatory variable x _n may be expressed as a scalar having one component in each data set.

(Dataset)
A data set d _n is a set of explanatory variables x _n and objective variables y _n . The explanatory variables are variables that can be considered to represent the cause of a target event, for example. The explanatory variables are also referred to as independent variables and predictor variables, for example. The objective variables are variables that can be considered to represent the result of a target event, for example. The objective variables are also referred to as dependent variables and response variables, for example.

(Quality Information)
The quality information w _n is information about the quality of each data set d _n . As an example, the quality information w _n may be a numerical representation of the reliability of each data set d _n . As an example, the quality information w _n may be a larger value as the reliability of the data set d _n is higher, and a smaller value as the reliability of the data set d _n is lower.

In addition, the quality information w _n is expressed as an M-dimensional vector having components equal to the number M of explanatory variables in each data set, as an example. In other words, when n is fixed, the quality information w _n can be expressed as a vector having M components, and the value of M is the number of quality information. For this reason, the quality information w _n may be expressed as a quality information vector. In addition, a matrix in which the quality information vector w _n is arranged in the number N of data sets may be expressed as a quality information matrix W. In addition, the above content does not limit the present embodiment, and the quality information w _n may be expressed as a scalar having one component in each data set.

(Distribution function)
The distribution function A is information relating to the shape of the residual distribution, and is, for example, a function that expresses the shape of the residual distribution.

As in the first exemplary embodiment, in this exemplary embodiment, a function expressing the shape of the residual distribution may be simply referred to as a distribution function. Specific examples of distribution functions include, but are not limited to, a normal distribution, a Bernoulli distribution, a Poisson distribution, a binomial distribution, and a Gaussian distribution. As described above, the target of the information processing device 10 according to this exemplary embodiment is a generalized linear regression model, and the processing described in this exemplary embodiment is generally applicable to various distribution functions.

(Regularization parameter)
The normalization parameter is, for example, a parameter that specifies a normalization term (also called a penalty term) included in an evaluation function that is referred to when an update unit 13A described later updates a regression coefficient. For example, the normalization parameter is introduced as a coefficient that indicates the magnitude of the contribution of the normalization term.

Here, the specific normalization term is generally determined appropriately according to the required constraint conditions. In this exemplary embodiment, a normalization term expressing a sparseness constraint is adopted. There are various ways to express a sparseness constraint, but in this exemplary embodiment, as an example, L0 sparseness using an L0 normalization term and L1 sparseness using an L1 regularization term are given. The normalization parameter in this exemplary embodiment is the coefficient of the L0 normalization term included in the evaluation function E of the sparseness generalized linear regression model generated by the information processing device 10A.

In the information processing device 10A according to this exemplary embodiment, a configuration is adopted in which the input data includes a regularization parameter. Therefore, according to the information processing device 10A, a more suitable sparse generalized linear regression model can be generated compared to a case in which the input data does not include a regularization parameter.

(Pretreatment section)
The preprocessing unit 12A refers to the data and information included in the input data acquired by the acquisition unit 11A, and executes a process of initializing the regression coefficient φ of the sparse generalized linear regression model. As an example, the preprocessing unit 12A refers to the explanatory variables x _n , the function form of the distribution function A, and the quality information w _n , and generates an initial solution (initial value) of the regression coefficient φ, a first derivative A'(θ) which is the first-order differential of the function A(θ), a second derivative A''(θ) which is the second-order differential of the function A(θ), a unit matrix I _M (M×M), a unit matrix I _N (N×N), and a weight matrix W. Here, the unit matrix I _M (M×M) is a unit matrix of M rows×M columns, and the unit matrix I _N (N×N) is a unit matrix of N rows×N columns. Details of the preprocessing executed by the preprocessing unit 12A will be described later. Note that θ, which is introduced for convenience in the above description, represents the functions A, A', and A'', and does not limit the present exemplary embodiment in any way.

(Update Department)
The update unit 13A refers to the input data and executes an update process for updating the regression coefficient φ initialized by the preprocessing unit 12. As an example, the update unit 13A includes an update preparation unit 131, a regression coefficient update unit 132, and a convergence determination unit 133, as shown in FIG.

The update preparation unit 131 performs a preparation process for updating the regression coefficient φ. As an example, the update preparation unit 131 generates a matrix D, a vector ^Y, a vector Z, and a matrix V by referring to the regression coefficient φ, a function A'(θ), and a function A''(θ). Details of the preparation process performed by the update preparation unit 131 will be described later. Here, the notation "^Y" is a representation of the notation normally expressed as "Y with a tilde" using characters that can be used in the specification. The specific notation does not limit this embodiment.

The regression coefficient update unit 132 updates the regression coefficient φ by referring to a portion of the input data, various matrices generated by the preprocessing unit 12A, and data generated by the update preparation unit 131. Specifically, the regression coefficient update unit 132 updates the regression coefficient φ by referring to the matrix D, vector ^Y, vector Z, matrix V, unit matrix I (M×M), unit matrix I (N×N), and weight matrix W. The regression coefficient update process executed by the regression coefficient update unit 132 will be described later.

The convergence determination unit 133 determines whether the regression coefficient φ has converged to a point where it satisfies a predetermined convergence condition. Details of the determination process performed by the convergence determination unit 133 will be described later.

(Output section)
The output unit 14A outputs the regression coefficient φ that is determined to have converged by the convergence determination unit 133. The output unit 14A may be equipped with a display panel, for example, and configured to display the value of the regression coefficient φ that is determined to have converged by the convergence determination unit 133, or may be configured to store the value of the regression coefficient φ that is determined to have converged by the convergence determination unit 133 in a recording medium (not shown). The value of the regression coefficient φ output by the output unit 14A is referred to in various analyses.

(Example of a data set)
FIG. 4 is a diagram showing a specific example of a data set d _n according to the exemplary embodiment 2. In the example of FIG. 4, a plurality of dots d11 and a plurality of dots d12 are shown in a coordinate space represented by a horizontal axis indicating an explanatory variable x _n and a vertical axis indicating a response variable y _n . The plurality of dots d11 and the plurality of dots d12 represent a data set according to the exemplary embodiment 2. In other words, each of the plurality of dots d11 and the plurality of dots d12 shown in FIG. 4 represents a pair of an explanatory variable x _n and a response variable y _n included in the data set d _n corresponding to each n. A more specific example of the explanatory variable x _n will be described in the exemplary embodiment described later, but an example of the explanatory variable x n is the number of factories in a city, and an example of the response variable y _n is the amount of chemical exposure in the air of the city measured by a surveyor. However, this example does not limit the present exemplary embodiment in any way.

As shown in Fig. 4, the data sets include a data set with relatively high reliability and a data set with relatively low reliability. A dot d11 represents a highly reliable data set d _n , and a dot d12 represents a low reliability data set d _n . The highly reliable data set d _n is, for example, a data set showing a measurement result of a measurement engineer with a lot of experience. On the other hand, the low reliability data set d _n is, for example, a data set showing a measurement result of a measurement engineer with little experience. However, this example does not limit the present exemplary embodiment in any way.

As described above, the quality of the data set d _n used for the generation process of the regression model generally varies. For example, when an inexperienced measurement engineer performs a measurement, the measurement result may contain a large error. In the example of FIG. 4, two dots d12 located in area a11 may be of lower quality than the other dots d11 and d12.

The information processing device 10A according to the present exemplary embodiment can generate a suitable sparse generalized linear regression model by taking into account such variations in the quality of the data set using the quality information w _n .

<Flow of information processing method>
The flow of the information processing method S10A executed by the information processing device 10A configured as above will be described with reference to Fig. 5. Fig. 5 is a flow diagram showing the flow of the information processing method S10A. As shown in Fig. 5, the information processing method S10A includes steps S11A to S14A.

(Step S11A)
In step S11A, the acquiring unit 11A acquires input data, which includes a plurality of data sets d _n each consisting of an explanatory variable x _n and a target variable y _n , quality information w _n , a functional form of the distribution function A, and a regularization parameter λ, as described above.

(Step S12A)
In step S12A, the preprocessing unit 12A refers to at least any data or information included in the input data acquired in the acquisition process S11A, and initializes the regression coefficients φ of the generalized linear regression model with the sparseness constraint imposed. Details of step S12A will be described later.

(Step S13A)
In the update process S13A, the update unit 13A executes the update process of updating the regression coefficient φ by referring to the input data acquired in the acquisition process S11A. As an example, the update unit 13A executes the update process by referring to an evaluation function E of a generalized linear regression model. As an example, the evaluation function E includes an L0 regularization term whose coefficient is a regularization parameter. As an example, the update unit 13A updates the regression coefficient φ so that the evaluation function E becomes smaller.

More specifically, the update unit 13A executes the update process by referring to an evaluation function E given by the following formula (1), for example.

In formula (1), the number of data N is the total number of data sets _dn . The quality information _wn , the distribution function A, the explanatory variable _xn , the objective variable _yn , and the regularization parameter λ are information or data contained in the input data. T is a symbol representing transposition. |φ| ₀ is the L0 norm of the regression coefficient φ.

In step S13A, the update unit 13A converges the regression coefficient φ according to the procedure of the Newton-Raphson method, for example. When the Newton-Raphson method is used, the gradient ∇E and the Hessian matrix H(φ) are given by the following formulas (2) and (3), for example.

In the information processing device 10A according to this exemplary embodiment, an update process is performed by referring to an evaluation function E of a generalized linear regression model, the evaluation function E including an L0 regularization term having a regularization parameter as a coefficient. Therefore, according to the information processing device 10A, a more suitable sparse generalized linear regression model can be generated compared to a case where an evaluation function including an L0 regularization term having a regularization parameter as a coefficient is not referred to.

Moreover, in the information processing device 10A according to this exemplary embodiment, the update process is performed by referring to the evaluation function E given by the above formula (1). Therefore, according to the information processing device 10A according to this exemplary embodiment, even when the quality of the data varies, a suitable sparse generalized linear regression model can be generated.

(Step S14A)
In step S14A, the output unit 14A outputs the regression coefficient φ.

(Pretreatment)
6 is a flow diagram showing the flow of the pre-processing performed by the pre-processing unit 12A (the processing of step S12A in FIG. 5). As shown in FIG. 6, the pre-processing performed by the pre-processing unit 12A includes steps S121 to S125. Note that some steps may be executed in parallel or in a different order.

(Step S121)
In step S121, the preprocessing unit 12A counts the number of features M and the number of data N. Here, the number of features M is the number of dimensions of the variable _xn , which is a vector.

(Step S122)
In step S122, the pre-processing unit 12A reads out the first derivative A'(θ) and the second derivative A''(θ). As an example, the pre-processing unit 12A derives the first derivative A'(θ) and the second derivative A''(θ) from the distribution function A acquired by the acquisition unit 11A. The pre-processing unit 12A may be configured to perform the derivation process by a numerical calculation, an analytical calculation, or a combination of these.

(Step S123)
In step S123, the preprocessing unit 12A refers to the quality information wn to generate a weighting matrix _W. As an example, the weighting matrix W is expressed by the following formula (4).

(Step S124)
In step S124, the pre-processing unit 12A initializes the regression coefficient φ. As an example, the pre-processing unit 12A initializes the regression coefficient φ by using a random number generated by a random function.

(Step S125)
In step S125, the preprocessing unit 12A generates unit matrices I _M and I _N. As described above, the unit matrix I _M is a unit matrix of M rows by M columns, and the unit matrix I _N is a unit matrix of N rows by N columns.

(Update process)
7 is a flow diagram showing the flow of the update process (the process of step S13A in FIG. 5) performed by the update unit 13A. As shown in FIG. 7, the update process performed by the update unit 13A includes steps S131 to S133. Note that some steps may be performed in parallel or in a different order.

(Step S131)
In steps S131 to S133, the update unit 13A repeatedly executes the update process (the process of steps S131 to S132) by referring to the input data until the regression coefficient φ satisfies a predetermined convergence condition. First, in step S131, the update preparation unit 131 executes the update preparation process. The update preparation process will be described later.

(Step S132)
In step S132, the regression coefficient update unit 132 updates the regression coefficient φ. For example, the regression coefficient update unit 132 updates the regression coefficient φ by the following equation (5).

More specifically, the regression coefficient update unit 132 can be configured to update the regression coefficient φ according to, for example, the following equation (6a) or (6b).

In formulas (6a) and (6b), the regularization parameter λ is a parameter included in the input data acquired by the acquisition unit 11A. The unit matrix I and the weight matrix W are matrices generated by the preprocessing unit 12A. The matrix D, the matrix V, and the vector Z are matrices and vectors calculated by the update preparation unit 131 in step S131. The matrix X is a matrix representation of the explanatory variables x _n (1≦n≦N).

As an example, the regression coefficient update unit 132 may update the regression coefficient φ using different algorithms depending on whether the number of data N is greater than the number of features M. As an example, when the number of data N is equal to or greater than the number of features M, the regression coefficient update unit 132 may update the regression coefficient φ using formula (6a), and when the number of data N is less than the number of features M, the regression coefficient φ may be updated using formula (6b).

(Step S133)
In step S133, the convergence determination unit 133 determines whether the regression coefficient φ satisfies a predetermined convergence condition. The convergence condition may be, for example, a condition that the amount of change in the regression coefficient φ due to one update process is equal to or less than a threshold. Specifically, for example, the convergence condition may be the following formula (7). In formula (7), η is the regression coefficient before the update, φ _new is the regression coefficient after the update, and ε is a predetermined threshold.

If the regression coefficient φ satisfies the convergence condition (step S133; YES), the update unit 13A ends the update process. On the other hand, if the regression coefficient φ does not satisfy the convergence condition (step S133; NO), the update unit 13A returns to the process of step S131.

(Update preparation process)
Fig. 8 is a flow diagram showing the flow of the update preparation process (step S131 in Fig. 7) performed by the update preparation unit 131. As shown in Fig. 8, the update preparation process performed by the update preparation unit 131 includes steps S311 to S314. Note that some steps may be performed in parallel or in a different order.

(Step S311)
In step S311, the update preparation unit 131 calculates a vector Θ by the following equation (8). The vector Θ is used in the calculation process of the vector ^Y. In equation (8), φ _old is the regression coefficient before the update.
Θ = Xφ _old ... (8)

(Step S312)
In step S312, the update preparation unit 131 generates matrices D and V. The matrices D and V are used in the subsequent process of updating the regression coefficient φ. As an example, the matrices D and V are expressed by the following formula (9). In formula (9), η _m (1≦m≦M) is the regression coefficient φ _old before the update. V _n (1≦n≦N) is a function A″(x _n φ).

ここで、A’の引数は、ステップＳ３１１において算出したベクトルΘの各成分である。 (Step S313)
In step S313, the update preparation unit 131 calculates a vector ^Y. As an example, the vector ^Y is expressed by the following formula (10).

Here, the arguments of A' are the components of the vector Θ calculated in step S311.

(Step S314)
In step S314, the update preparation unit 131 calculates a vector Z. The vector Z is used in the update process of the regression coefficient φ in a later stage. The update preparation unit 131 calculates the vector Z by the following formula (11), for example. In formula (11), φ ^old is the regression coefficient before the update, and the vector ^Y is the vector calculated by the update preparation unit 131 in step S313.

The update preparation unit 131 calculates the matrix D, the vector ^Y, the vector Z, and the matrix V by the above-mentioned processing, and provides the calculated matrix D, the vector ^Y, the vector Z, and the matrix V to the regression coefficient update unit 132. Then, the regression coefficient update unit 132 updates the regression coefficients by the above-mentioned processing.

(Effects of the information processing device 10A)
In the generation of a conventional regression model, if the total number of datasets is sufficiently large, it is possible to generate a regression model without using a low-reliability dataset. On the other hand, if the total number of datasets is small, it may be necessary to use a low-reliability dataset to generate a regression model. However, if a low-reliability dataset is treated in the same way as a high-reliability dataset, the error of the low-reliability dataset may strongly affect the regression model, and an appropriate regression model may not be generated.

In contrast, the information processing device 10A according to the present exemplary embodiment initializes and updates the regression coefficients φ by referring to the quality information w _n related to the quality of each data set d _n . Therefore, even if the quality of the data sets d _n varies, it is easy to generate a suitable sparse generalized linear regression model.

In addition, the information processing device 10A according to this exemplary embodiment is configured to repeatedly execute the update process by referring to the input data until the regression coefficient φ satisfies a predetermined convergence condition. Therefore, according to the information processing device 10A according to this exemplary embodiment, in addition to the effect of the information processing device 10 according to the first exemplary embodiment, the effect of being able to generate a more suitable sparse generalized linear regression model can be obtained.

Exemplary embodiment 3
A third exemplary embodiment of the present invention will be described in detail with reference to the drawings. Note that components having the same functions as those described in the first and second exemplary embodiments are denoted by the same reference numerals, and the description thereof will not be repeated.

The configuration of the information processing device 10B according to this exemplary embodiment will be described with reference to FIG. 9. FIG. 9 is a block diagram showing the configuration of the information processing device 10B. In addition to an acquisition unit 11A, a preprocessing unit 12A, and an update unit 13A, the information processing device 10B includes a quality information generation unit 15. Note that the arrows in the figure simply indicate the direction of data flow and do not exclude bidirectionality.

The quality information generating unit 15 acquires information on the reliability of each data set d _n , and generates quality information w _n that is information on quality by referring to the acquired information on reliability. Here, the information on reliability may use information indicating the accuracy of the device that acquires each data set d _n , the proficiency of the worker, and the like. Although specific examples of the information on reliability are not limited to this exemplary embodiment, the information on reliability may be, for example, information on the proficiency of the measurement engineer. Furthermore, the information on reliability may be, for example, information indicating the length of measurement experience of the measurement engineer. In this case, for example, the information on reliability may be a larger value the longer the experience of the measurement engineer.

As an example, the quality information generating unit 15 refers to information regarding the reliability of each data set d _n , and generates quality information w _n for each data set d _n such that the value of the quality information w _n increases as the reliability increases.

According to this embodiment, the information processing device 10B can generate a sparse generalized linear regression model that appropriately takes into account the reliability of each dataset.

[Software implementation example]
Some or all of the functions of the information processing devices 10, 10A, and 10B may be realized by hardware such as an integrated circuit (IC chip), or may be realized by software.

In the latter case, the information processing devices 10, 10A, and 10B are realized, for example, by a computer that executes instructions of a program, which is software that realizes each function. An example of such a computer (hereinafter referred to as computer C) is shown in FIG. 10. Computer C has at least one processor C1 and at least one memory C2. Memory C2 stores program P for operating computer C as information processing devices 10, 10A, and 10B. In computer C, processor C1 reads and executes program P from memory C2, thereby realizing each function of information processing devices 10, 10A, and 10B.

The processor C1 may be, for example, a central processing unit (CPU), a graphic processing unit (GPU), a digital signal processor (DSP), a micro processing unit (MPU), a floating point number processing unit (FPU), a physics processing unit (PPU), a microcontroller, or a combination of these. The memory C2 may be, for example, a flash memory, a hard disk drive (HDD), a solid state drive (SSD), or a combination of these.

The computer C may further include a RAM (Random Access Memory) for expanding the program P during execution and for temporarily storing various data. The computer C may further include a communications interface for transmitting and receiving data to and from other devices. The computer C may further include an input/output interface for connecting input/output devices such as a keyboard, mouse, display, and printer.

The program P can also be recorded on a non-transitory, tangible recording medium M that can be read by the computer C. Such a recording medium M can be, for example, a tape, a disk, a card, a semiconductor memory, or a programmable logic circuit. The computer C can acquire the program P via such a recording medium M. The program P can also be transmitted via a transmission medium. Such a transmission medium can be, for example, a communications network or broadcast waves. The computer C can also acquire the program P via such a transmission medium.

[Application example]
The above-described information processing devices 10, 10A, and 10B (hereinafter, referred to as "information processing devices 10, etc.") can be applied to various problems. As an example, the information processing device 10, etc. can be applied as a device for generating a regression model in which the number of factories in a city is the explanatory variable x _n and the amount of chemical exposure in the air in the city is the objective variable y _n . As illustrated in FIG. 4, the reliability of a data set may vary depending on whether an experienced or inexperienced measurement technician performed the measurement, or on conditions such as the performance of the measurement device. The reliability of a data set that is the measurement result of an inexperienced measurement technician may be low. In the generation of a conventional regression model, if the total number of data is sufficiently large, it is possible to generate a regression model without using low-reliability data. On the other hand, if the total number of data is small, there are cases where low-reliability data must be used to generate a regression model. However, if low-reliability data is treated in the same way as high-reliability data, errors in the low-reliability data may strongly affect the regression model, and an appropriate regression model may not be generated.

In contrast, the information processing device 10 according to the present exemplary embodiment initializes and updates the regression coefficient φ by referring to the quality information w _n related to the quality of each data set d _n . Therefore, even if the quality of the data set d _n varies, it is easy to generate a suitable sparse generalized linear regression model.

In addition, the information processing device 10, etc., can be used as an apparatus for generating a regression model in which the measurement value of a seismic intensity meter is the explanatory variable x _n and the information representing the damage situation caused by an earthquake is the objective variable yn. Depending on the performance of the seismic intensity meter and the installation location of the seismic intensity meter, the data set d _n , which is the measurement result, may include data of low quality. For example, depending on the installation location of the seismic intensity meter, the measurement result may include noise due to cars traveling nearby. Even in such a case, the information processing device 10, etc. can generate a suitable regression model by setting quality information w _n for each data d _n according to conditions such as the installation location of the seismic intensity meter.

[Additional Note 1]
The present invention is not limited to the above-described embodiment, and various modifications are possible within the scope of the claims. For example, embodiments obtained by appropriately combining the technical means disclosed in the above-described embodiment are also included in the technical scope of the present invention.

[Additional Note 2]
Some or all of the above-described embodiments can be described as follows. However, the present invention is not limited to the aspects described below.

(Appendix 1)
An acquisition means for acquiring input data including a plurality of data sets each consisting of an explanatory variable and a target variable, information regarding the quality of each data set, and information regarding the shape of the residual distribution;
A pre-processing means for initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed thereon by referring to at least any data or information included in the input data acquired by the acquisition means;
and an update means for executing an update process for updating the regression coefficients by referring to the input data.
23. An information processing apparatus comprising:

(Appendix 2)
the updating means repeatedly executes the updating process by referring to the input data until the regression coefficients satisfy a predetermined convergence condition.
2. The information processing device according to claim 1 .

(Appendix 3)
The input data includes a regularization parameter.
3. The information processing device according to claim 1 or 2.

(Appendix 4)
the update means executes the update process by referring to an evaluation function of a generalized linear regression model, the evaluation function including an L0 regularization term having the regularization parameter as a coefficient.
4. The information processing device according to claim 3.

ここで、Ｎは前記データセットの個数を表す自然数、ｘ_ｎは前記説明変数、φは回帰係数、ｙ_ｎは前記目的変数、ｗ_ｎは前記品質に応じた重み係数、Ａは前記残差分布の形状を表現する関数、Ｔは転置を表す記号、λは正則化パラメータ、｜φ｜_０は、回帰係数φのＬ０ノルム、である。 (Appendix 5)
The update means executes the update process by referring to the evaluation function given by the following formula (12):
5. The information processing device according to claim 3 or 4.

Here, N is a natural number representing the number of the data sets, _xn is the explanatory variable, φ is a regression coefficient, _yn is the objective variable, _wn is a weighting coefficient according to the quality, A is a function expressing the shape of the residual distribution, T is a symbol representing transposition, λ is a regularization parameter, and |φ| ₀ is the L0 norm of the regression coefficient φ.

(Appendix 6)
The method further includes a quality information generating means for acquiring information on the reliability of each data set, and generating information on the quality by referring to the acquired information on the reliability.
6. The information processing device according to claim 1,

(Appendix 7)
An information processing device,
obtaining input data including a plurality of data sets of explanatory variables and a response variable, information about the quality of each data set, and information about the shape of the residual distribution;
Initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed thereon by referring to at least any data or information included in the acquired input data;
executing an update process for updating the regression coefficients by referring to the input data;
An information processing method comprising:

(Appendix 8)
the information processing device repeatedly executes the update process by referring to the input data until the regression coefficients satisfy a predetermined convergence condition.
8. The information processing method according to claim 7,

(Appendix 9)
The input data includes a regularization parameter.
9. The information processing method according to claim 7 or 8.

(Appendix 10)
the information processing device executes the update process by referring to an evaluation function of a generalized linear regression model, the evaluation function including an L0 regularization term having the regularization parameter as a coefficient.
10. The information processing method according to claim 9,

ここで、Ｎは前記データセットの個数を表す自然数、ｘ_ｎは前記説明変数、φは回帰係数、ｙ_ｎは前記目的変数、ｗ_ｎは前記品質に応じた重み係数、Ａは前記残差分布の形状を表現する関数、Ｔは転置を表す記号、λは正則化パラメータ、｜φ｜_０は、回帰係数φのＬ０ノルム、である。 (Appendix 11)
The information processing device executes the update process by referring to an evaluation function given by the following formula (13):
11. The information processing method according to claim 9 or 10.

Here, N is a natural number representing the number of the data sets, _xn is the explanatory variable, φ is a regression coefficient, _yn is the objective variable, _wn is a weighting coefficient according to the quality, A is a function expressing the shape of the residual distribution, T is a symbol representing transposition, λ is a regularization parameter, and |φ| ₀ is the L0 norm of the regression coefficient φ.

(Appendix 12)
The information processing device further includes acquiring information regarding reliability of each data set, and generating information regarding the quality by referring to the acquired information regarding the reliability.
12. The information processing method according to any one of claims 7 to 11.

(Appendix 13)
A program for causing a computer to function as an information processing device,
The program causes the computer to
an acquisition means for acquiring input data including a plurality of data sets each consisting of an explanatory variable and a target variable, information on the quality of each data set, and information on the shape of the residual distribution;
A pre-processing means for initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed thereon by referring to at least any data or information included in the input data acquired by the acquisition means;
and an update unit that executes an update process to update the regression coefficients by referring to the input data.
A program characterized by:

(Appendix 14)
the updating means repeatedly executes the updating process by referring to the input data until the regression coefficients satisfy a predetermined convergence condition.
14. The program according to claim 13.

(Appendix 15)
The input data includes a regularization parameter.
15. The program according to claim 13 or 14.

(Appendix 16)
the update means executes the update process by referring to an evaluation function of a generalized linear regression model, the evaluation function including an L0 regularization term having the regularization parameter as a coefficient.
17. The program according to claim 16,

ここで、Ｎは前記データセットの個数を表す自然数、ｘ_ｎは前記説明変数、φは回帰係数、ｙ_ｎは前記目的変数、ｗ_ｎは前記品質に応じた重み係数、Ａは前記残差分布の形状を表現する関数、Ｔは転置を表す記号、λは正則化パラメータ、｜φ｜_０は、回帰係数φのＬ０ノルム、である。 (Appendix 17)
The update means executes the update process by referring to an evaluation function given by the following formula (14):
17. The program according to claim 15 or 16.

Here, N is a natural number representing the number of the data sets, _xn is the explanatory variable, φ is a regression coefficient, _yn is the objective variable, _wn is a weighting coefficient according to the quality, A is a function expressing the shape of the residual distribution, T is a symbol representing transposition, λ is a regularization parameter, and |φ| ₀ is the L0 norm of the regression coefficient φ.

(Appendix 18)
The method further includes a quality information generating means for acquiring information on the reliability of each data set, and generating information on the quality by referring to the acquired information on the reliability.
18. The program according to any one of claims 13 to 17.

(Appendix 19)
A computer-readable recording medium having the program according to claim 13 recorded thereon.

[Additional Note 3]
A part or all of the above-described embodiments can be further expressed as follows.

At least one processor, the processor comprising:
an acquisition process for acquiring input data including a number of data sets of explanatory variables and response variables, information about the quality of each data set, and information about the shape of the residual distribution;
A pre-processing step of initializing regression coefficients of a generalized linear regression model having a sparseness constraint by referring to at least any data or information included in the input data acquired by the acquisition means;
and updating the regression coefficients by referring to the input data.

The information processing device may further include a memory, and the memory may store a program for causing the processor to execute the acquisition process, the pre-processing, and the update process. The program may also be recorded on a computer-readable, non-transitory, tangible recording medium.

1, 10, 10A, 10B Information processing device 11, 11A Acquisition unit (acquisition means)
12, 12A Pretreatment section (pretreatment means)
13, 13A Update unit (update means)
14A Output unit 15 Quality information generating unit 131 Update preparation unit 132 Regression coefficient updating unit 133 Convergence determination unit S1, S10, S10A Information processing method

Claims (9)

an acquisition means for acquiring input data including a plurality of data sets each consisting of an explanatory variable and a target variable, information on the quality of each data set, and information on the shape of the residual distribution;
A pre-processing means for initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed thereon by referring to at least any data or information included in the input data acquired by the acquisition means;
and an update means for executing an update process for updating the regression coefficients by referring to the input data ,
The update means executes the update process by referring to an evaluation function given by the following formula (a):
Here, N is a natural number representing the number of the data sets, x _n is the explanatory variable, φ is a regression coefficient, y _n is the objective variable, w _n is a weighting coefficient according to the quality, A is a function expressing the shape of the residual distribution, T is a symbol representing transposition, λ is a regularization parameter, and |φ| ₀ is the L0 norm of the regression coefficient φ.
23. An information processing apparatus comprising: the updating means repeatedly executes the updating process by referring to the input data until the regression coefficients satisfy a predetermined convergence condition.
2. The information processing apparatus according to claim 1, The input data includes the regularization parameters.
3. The information processing apparatus according to claim 1, wherein the information processing apparatus is a computer. the updating means performs the updating process by referring to the evaluation function of a generalized linear regression model, the evaluation function including an L0 regularization term having the regularization parameter as a coefficient.
4. The information processing apparatus according to claim 3. The method further includes a quality information generating means for acquiring information on the reliability of each data set, and generating information on the quality by referring to the acquired information on the reliability.
5. The information processing apparatus according to claim 1, wherein the information processing apparatus further comprises: a first input section; An information processing device,
obtaining input data including a plurality of data sets of explanatory variables and a response variable, information about the quality of each data set, and information about the shape of the residual distribution;
Initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed thereon by referring to at least any data or information included in the acquired input data;
executing an update process for updating the regression coefficients by referring to the input data;
Including,
The update process is performed by referring to an evaluation function given by the following formula (a):
Here, N is a natural number representing the number of the data sets, x _n is the explanatory variable, φ is a regression coefficient, y _n is the objective variable, w _n is a weighting coefficient according to the quality, A is a function expressing the shape of the residual distribution, T is a symbol representing transposition, λ is a regularization parameter, and |φ| ₀ is the L0 norm of the regression coefficient φ.
Information processing methods. the information processing device repeatedly executes the update process by referring to the input data until the regression coefficients satisfy a predetermined convergence condition.
7. The information processing method according to claim 6 , The input data includes the regularization parameters.
8. The information processing method according to claim 6, wherein the first and second inputs are input to the information processing apparatus. A program for causing a computer to function as an information processing device,
The program causes the computer to
an acquisition means for acquiring input data including a plurality of data sets each consisting of an explanatory variable and a target variable, information on the quality of each data set, and information on the shape of the residual distribution;
A pre-processing means for initializing regression coefficients of a generalized linear regression model with a sparseness constraint imposed thereon by referring to at least any data or information included in the input data acquired by the acquisition means;
an updating means for executing an updating process for updating the regression coefficients by referring to the input data ;
The update means executes the update process by referring to an evaluation function given by the following formula (a):
Here, N is a natural number representing the number of the data sets, x _n is the explanatory variable, φ is a regression coefficient, y _n is the objective variable, w _n is a weighting coefficient according to the quality, A is a function expressing the shape of the residual distribution, T is a symbol representing transposition, λ is a regularization parameter, and |φ| ₀ is the L0 norm of the regression coefficient φ.
A program characterized by:

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