JP2011154554A - Deficit value prediction device, deficit value prediction method, and deficit value prediction program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a deficit value prediction device for improving accuracy in predicting a deficit value in matrix shape data. <P>SOLUTION: A parameter estimating means 82 estimates a parameter which maximizes likelihood that data when a function converts a factor matrix is matrix shape data, among the parameters of the function for converting the factor matrix being the matrix which is defined by each factor element of one factor in the matrix shape data having two factors and also which expresses the features of the respective factor elements of the other factor in the matrix shape data. A deficit value predicting means 83 predicts the deficit value of the matrix element in the matrix shape data through the use of the parameter estimated by the parameter estimating means 82 and the value of the known matrix element in the matrix shape data. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a missing value prediction system, a missing value prediction method, and a missing value prediction program, and in particular, a missing value prediction system and a missing value prediction method for predicting an unknown matrix element value in matrix data including two factors. And a missing value prediction program.

  When handling matrix data including unknown matrix elements, it is required to accurately predict the value of an unknown matrix element (hereinafter sometimes referred to as a missing value) from the observed known part. For example, in a collaborative filtering system that recommends products based on matrix data that collects product ratings from multiple users, it predicts unknown scores of products not evaluated by users and recommends products with high predicted scores to users. To do.

  In such a system, as a general method for predicting missing values of matrix data, matrix data including missing values as matrix elements is decomposed into a plurality of small matrix data using a probabilistic model, and the decomposition is performed. A method of predicting missing values of original matrix data from matrix data is used. A method for predicting a missing value in this way is described in Non-Patent Document 1 and Non-Patent Document 2.

  In the method described in Non-Patent Document 1, a linear structure of matrix data including missing values in matrix elements is extracted by a probability model, and is decomposed into small matrix data for each factor constituting the matrix. Then, matrix data that approximates the original matrix data is predicted using a linear combination of the decomposed matrix data.

  Further, according to the method described in Non-Patent Document 2, a nonlinear structure of matrix data including missing values in matrix elements is extracted by a probability model, and is decomposed into small matrix data for each factor constituting the matrix. Then, matrix data that approximates the original matrix data is predicted using the decomposed matrix data. That is, it can be said that the method described in Non-Patent Document 2 is an extended method of the method described in Non-Patent Document 1.

Ruslan Salakhutdinov and Andriy Mnih, "Probabilistic Matrix Factorization" In Neural Information Processing Systems (NIPS), 2007. Neil D. Lawrence and Raquel Urtasun, "Non-linear Matrix Factorization with Gaussian Processes", Proceedings of the 26th International Conference on Machine Learning (ICML), pp.601-608, Montreal, Canada, 2009.

  In the methods described in Non-Patent Document 1 and Non-Patent Document 2, when a factor matrix is given, the original matrix data is conditionally independent, so there is no conditionally independent constraint on the original matrix data. Compared to the case, there is a problem that the prediction accuracy is low.

  For example, in the method described in Non-Patent Document 1, when a factor matrix of each factor included in the original matrix data is given, each matrix element of the original matrix data is conditionally independent. Further, since the method described in Non-Patent Document 1 is a method for extracting a linear structure, there is a problem that a nonlinear and complicated structure cannot be extracted.

  On the other hand, in the method described in Non-Patent Document 2, since a nonlinear structure can be extracted, the prediction accuracy is higher than the missing value prediction system of Non-Patent Document 1. Specifically, in the method described in Non-Patent Document 2, it is assumed that a prior distribution is assumed for one factor and integration is eliminated (marginalized), and the influence of the factor on the original data is eliminated to make nonlinearity. Extract structure. However, even in the method described in Non-Patent Document 2, when the factor matrix of the factor that was not deleted is given among the two factors included in the original matrix data, the original matrix data is deleted. The other factor element is conditionally independent.

  As described above, the methods described in Non-Patent Document 1 and Non-Patent Document 2 have the property that, when a factor matrix is given, the original matrix data is conditionally independent. For this reason, there is no conditionally independent constraint on the original matrix data, and the accuracy is reduced compared to the prediction accuracy of the model incorporating the correlation between each matrix element of the original matrix data. There is a problem.

  Therefore, an object of the present invention is to provide a missing value prediction apparatus, a missing value prediction method, and a missing value prediction program that can improve the accuracy of predicting missing values in matrix data.

  The missing value predicting apparatus according to the present invention is a matrix defined for each factor element of one factor in matrix data including two factors, and the characteristics of each factor element of the other factor in the matrix data are obtained. Parameter estimating means for estimating a parameter that maximizes the likelihood that the data when the function transforms the factor matrix is matrix data among the parameters of the function that converts the factor matrix that is a matrix to represent, and the parameter estimating means And a missing value predicting means for predicting a missing value of the matrix element in the matrix data using the estimated parameter and the value of the known matrix element in the matrix data.

  The missing value prediction method according to the present invention is a matrix defined for each factor element of one factor in matrix data including two factors, and the characteristics of each factor element of the other factor in the matrix data are determined. Among the functions that convert the factor matrix that is the matrix to represent, the function that maximizes the likelihood that the data when the factor matrix is converted is matrix data is estimated, and the parameters used in estimating the function and It is characterized in that a missing value of a matrix element in the matrix data is predicted using a value of a known matrix element in the matrix data.

  The missing value prediction program according to the present invention is a matrix defined for each factor element of one factor in matrix data including two factors, and each factor element of the other factor in the matrix data is stored in a computer. A parameter estimation process for estimating a parameter that maximizes the likelihood that the data obtained when the function transforms the factor matrix is matrix data, among the parameters of the function that transforms the factor matrix that is a matrix representing the characteristics of Using the parameters estimated by the parameter estimation process and the values of known matrix elements in the matrix data, a missing value prediction process for predicting the missing values of the matrix elements in the matrix data is executed.

  According to the present invention, it is possible to improve the accuracy of predicting missing values in matrix data.

It is a block diagram which shows one Embodiment of the missing value prediction apparatus by this invention. It is a flowchart which shows the example of the operation | movement in embodiment of this invention. It is explanatory drawing which shows the example of matrix form data. It is explanatory drawing which shows the example of the malfunction prediction system in the Example of this invention. It is a sequence diagram which shows the example of operation | movement in the Example of this invention. It is explanatory drawing which shows the example of the matrix form data transmitted. It is explanatory drawing which shows the example of the prediction result which filled the missing value with the predicted value. It is a block diagram which shows the example of the minimum structure of the missing value prediction apparatus by this invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 1 is a block diagram showing an embodiment of a missing value prediction apparatus according to the present invention. The missing value prediction apparatus 101 according to the present embodiment includes an input unit 102, an approximation unit 103, a prediction unit 104, and an output unit 105.

  For example, the input unit 102 notifies the approximation unit 103 of matrix data input by the user. Here, the matrix-type data is a matrix having a factor number of 2, for example, data in which the vertical axis and the horizontal axis of the matrix are factors. In the following description, matrix data input to the input means 102 is denoted as Y.

  For each factor element of one factor in the input matrix data Y, the approximating means 103 performs matrix data (hereinafter referred to as factor matrix) representing the characteristics of each factor element of the other factor in the input matrix data Y. Defined as data). Then, the approximating means 103 estimates a parameter that maximizes the likelihood of the matrix-like data Y to which data is inputted when the function transforms the factor matrix data among the parameters of the function that transforms the factor matrix data. . In the following description, factor matrix data representing the characteristics of each factor element in one factor is denoted as X, and a function for converting the factor matrix data X is denoted as F.

  Specifically, the approximation means 103 is input for each factor element of one factor included in the input matrix data Y for the purpose of approximating the matrix data Y input to the input means 102. The parameter of the function having the matrix data representing the feature of each factor element of the other factor included in the matrix data Y as an argument is estimated.

  The prediction unit 104 predicts the value of an unknown matrix element (that is, a missing value) from the result estimated by the approximation unit 103 and the value of the known matrix element of the matrix data. For example, the predicting unit 104 predicts a missing value using the parameter estimated by the approximating unit 103 and the values of known matrix elements.

  The output unit 105 outputs the prediction result of the missing value predicted by the prediction unit 104. For example, the output unit 105 may display the prediction result on a display device (not shown) such as a display. Alternatively, the output unit 105 may store the prediction result in a storage device (not shown) provided in the missing value prediction apparatus 101 or connected to the missing value prediction apparatus 101. Further, the output unit 105 may notify the prediction result to another system (not shown).

  The approximation means 103 and the prediction means 104 are realized by a CPU of a computer that operates according to a program (missing value prediction program). For example, the program may be stored in a storage unit (not shown) of the missing value prediction apparatus 101, and the CPU may read the program and operate as the approximation unit 103 and the prediction unit 104 according to the program. Further, each of the approximating unit 103 and the predicting unit 104 may be realized by dedicated hardware.

  Next, the operation will be described. FIG. 2 is a flowchart showing an example of the operation in this embodiment. FIG. 3 is an explanatory diagram showing an example of matrix data. In the matrix data illustrated in FIG. 3, each axis represents a factor of the matrix data, the vertical axis represents the factor “movie”, and the horizontal axis represents the factor “user”. That is, the matrix data Y is data in which the vertical axis and the horizontal axis mean factors, and the number of factors is two. In addition, the matrix elements of the matrix data illustrated in FIG. 3 are scores obtained by the user evaluating each movie in the range of 1 to 5, and blank portions (blank matrix elements) indicate missing values of the matrix data. To express.

  In the following description, it is assumed that matrix data of bivariate and single sequence data is input. The input matrix data is Y, and the matrix data Y is M × N-dimensional matrix data. The matrix data illustrated in FIG. 3 includes M types of movies (that is, factor elements of the factor “movie”) (specifically, five factors A to E), and the number of users (that is, the factor “user”). "Is a matrix data of N elements (specifically, 30 persons from 1 to 30).

  First, when the matrix data Y is input, the input unit 102 notifies the approximated unit 103 of the input matrix data Y (step S201). For the purpose of approximating the input matrix data Y, the approximating means 103 for each factor element of one factor included in the input matrix data Y, the other factor included in the matrix data. A parameter of a function having a matrix data representing the characteristics of each factor element as an argument is estimated (step S202).

  Specifically, first, the approximating means 103 converts the matrix data Y including missing values into matrix elements into the following (M × N) × one-dimensional vector data (hereinafter referred to as vector Y). Deform. M and N are the number of factor elements.

Y = [Y ₁ Y ₂ ... Y _N ]
= [Y ₁₁ , y ₁₂ , ..., y _1M , y ₂₁ , y ₂₂ , ..., y _2M , ..., y _N1 , y _N2 , ..., y _NM ] ^T

Here, Y _N represents a row vector of the vector Y, and y _NM represents a matrix element of the vector Y. Next, the approximating means 103 defines the vector Y as shown in Equation 1 below.

  Y = F (X) + ε (Formula 1)

  X is a factor matrix, and the function F is a (M × N) × 1-dimensional vector. Specifically, the function F is defined as follows.

F = [F ₁ F ₂ ... F _N ]
_{= [F 11, f 12,} ···, f 1M, f 21, f 22, ···, f 2M, ···, f N1, f N2, ···, f NM] T

Here, F _N represents a row vector of the function F. Further, ε in Equation 1 is defined as follows.

ε = N (0, σ ² I)

Here, N () represents a Gaussian distribution. Also, σ ² represents the variance, and I represents the unit matrix. Next, a factor matrix X ′ exemplified below is defined as a factor matrix representing the characteristics of each factor element.

  As described above, X ′ is a MN × q matrix representing the characteristics of the factors on the horizontal axis of the original matrix data Y. MN represents the number of features of the factor matrix X ′. Here, the feature of each factor element on the vertical axis of the matrix data Y is represented by each factor element on the horizontal axis, and the dimension of the feature is M. That is, the characteristics of the first row of the matrix data Y (that is, the first factor element of the factor on the vertical axis) are the matrix element (first row, first column), (first row, second column name). ,... (First row, Mth column). That is, since the number of factor elements on the vertical axis is N, the factor matrix X ′ is matrix data representing the characteristics of each factor element on the horizontal axis for each factor element on the vertical axis. Can be said.

  Q is a parameter representing the dimension of the feature of the factor matrix X ′. The value of q is given in advance by a user or the like.

Here, X ₁ ′ represents the first row vector of the factor matrix X ′. Therefore, for example, the row vector Y ₁ of the first row of the matrix data Y can be expressed as follows. Here, ε is the same as ε in Equation 1.

Y ₁ = F ₁ (X ₁ ') + ε

  Next, the approximating means 103 defines the probability distribution of the vector Y as shown in Equation 2 exemplified below.

P (Y | F (X ′)) = N (Y | F (X ′), σ ² I) (Formula 2)

  Here, a case will be described in which the probability distribution of the function F is defined as in Expression 3 exemplified below using a Gaussian process.

P (F | X) = GP (F | 0, K ^WX ) = N (F | 0, K ^WX ) (Formula 3)

The Gaussian process is a stochastic process that captures a nonlinear input / output relationship as being obtained from a normal stochastic process, and is characterized in that a stochastic process can be described only by matrix operation. K ^WX represents a Gaussian distribution covariance matrix. Each element k ^WX _ij of the covariance matrix can be expressed as follows.

k ^WX _ij = <X _i ′, X _j ′>

Note that <> represents an inner product. That is, k ^WX _ij can be expressed as an inner product of X _i ′ and X _j ′.

The covariance matrix K ^WX is a parameter that needs to be estimated, but is NM × NM matrix data having a large size. Therefore, when trying to estimate the covariance matrix K ^WX , it is necessary to estimate all NM × NM matrix elements, which increases the calculation cost. Therefore, the approximating means 103 changes Equation 3 and defines the probability distribution of the function F as shown in Equation 4 exemplified below.

Here, X is M × q matrix data, and W is matrix data representing an N × r function. Note that r is a parameter representing the dimension of the feature of the function W, and the value of r is given in advance by a user or the like. That is, Expression 4 is obtained by replacing the covariance matrix K ^WX in Expression 3 with the following contents (hereinafter referred to as estimation target parameters).

  Here, the following symbols represent Kronecker products.

K ^W is N × N matrix data called a kernel that satisfies the Marcel theorem. Similarly, K ^X is M × M matrix data that satisfies Mercer's theorem (ie, called a kernel).

Here, the matrix element k ^W _ij of the matrix K ^W and the matrix element k ^X _ij of the matrix K ^X can be expressed as follows, respectively.

k ^W _ij = k ^W (W _i , W _j ) = <W _i , W _j >
_{^{k X ij = k X (X}} i, X j) = <X i, X j>

Note that <> represents an inner product. That is, k ^W _ij can be expressed as an inner product of W _i and W _j , and k ^X _ij can be expressed as an inner product of X _i and X _j . Specifically, the matrix element ^k W of the matrix _{^{K W (W i, W j}} ) represents the distance between the _{W i} and _{W j} on the high-dimensional vector space by mapping the _{W i} and _{W j} nonlinearly. The same applies to the matrix element k ^X (X _i , X _j ) of the matrix K ^X.

The estimation target parameter described above is a parameter that needs to be estimated, like the covariance matrix ^KWX . When estimating the content of the estimation target parameter, the approximating means 103 estimates N × N + M × M matrix elements. That is, when estimating the covariance matrix K ^WX , it is necessary to estimate all NM × NM matrix elements, but when estimating the estimation target parameter, N × N + M × M matrix elements are estimated. That's fine. Therefore, the calculation cost can be reduced as compared with the case where the covariance matrix K ^WX is estimated.

  Next, a method for reducing the calculation order when estimating the parameters will be described. As described above, by using the model illustrated in Expression 4, it is possible to reduce the parameter to be estimated as compared with the model illustrated in Expression 3. Furthermore, in order to reduce the calculation order as compared with the model illustrated in Expression 3, first, Expression 4 is transformed into Expression 5 below.

Note that F ^X is a function having X as an argument. ^FW is a function having W as an argument. Here, the calculation order in the models illustrated in Expression 4 and Expression 5 is O (M ³ N ³ ). Therefore, Formula 5 illustrated below is defined by approximating Formula 5. The calculation order in the model illustrated in Equation 6 is O (MNN ² ).

F _n ^X is a function defined under the assumption that each n is independent. That is, it can be said that defining F _n ^X assumes independence of each factor element having the number N of factor elements in Equation 4. However, the independence assumed here is different from the independence used in the method described in Non-Patent Document 2, for example. For example, in Equation 6, the part that can be said to have assumed independence is the following part.

  On the other hand, in the method described in Non-Patent Document 2, the part assuming independence is a part represented by Equation 7 below.

When both are compared, the part which can be said to have assumed the independence in Formula 6 is different from Formula 7 in that ^FW is included. Thus, unlike the independence assumption in Equation 7, in Equation 6, the missing information in the independence assumption is supplemented with ^FW .

  In an actual problem, data representing characteristics for each factor may be newly given. For example, as a feature of the factor “movie”, information on actors who appeared in the movie, information on the date of movie announcement, movie production company, movie distribution company, and the like are given. Further, for example, information such as gender, age, and region is given as a feature of the factor “user”. Data given in this way is called metadata. Using these metadata, the model illustrated in Expression 6 may be defined as Expression 8 illustrated below, and further defined as Expression 9 using Expression 8.

  Here, R represents metadata of a factor representing the vertical axis of the matrix data Y (that is, a factor having M factor elements). S represents metadata of a factor representing the horizontal axis of the matrix data Y (that is, a factor having N factor elements). Note that Expression 9 expanded by introducing metadata is called a hierarchical model of Expression 6.

Next, a specific method for estimating parameters will be described. The parameters that need to be estimated are K ^W, K ^X and σ. Therefore, the approximating means 103 estimates a parameter that maximizes the likelihood that the matrix when the function F transforms the factor matrix X is matrix data Y. For example, the approximating means 103 may estimate parameters K ^W, K ^X and σ that maximize the marginal likelihood logP (Y | X) exemplified in the following Expression 10 using a gradient method.

  The model thus derived (model for predicting missing values) has the following characteristics. That is, the matrix data Y including missing values as matrix elements is modeled by the function F and the factor matrix X by the probability model, and the prior probability of the function F (for example, Equation 3 above) is defined by the Gaussian process. Therefore, the model can take into account the nonlinear correlation structure.

  Furthermore, since the original matrix data Y is expressed using the function F and the factor matrix X in this model, there is no conditionally independent constraint on the original matrix data Y. Specifically, the present model incorporates the correlation between the matrix elements of the original matrix data Y. Therefore, it can suppress that prediction accuracy falls.

  Further, in this model, paying attention to the structure of the covariance matrix of the function F, a large covariance matrix is represented by a Kronecker product of two small matrices representing covariance. Therefore, it is possible to reduce the amount of calculation by reducing the number of parameters that need to be estimated. Specifically, with respect to matrix-shaped data (that is, factor matrix) X representing the characteristics of each element of one factor included in the original matrix-shaped data Y, the total number of matrix elements (feature dimension × number of elements) A parameter is estimated, and for the other factor, a parameter of approximately the square of the number of elements of matrix data may be estimated.

Next, the prediction unit 104 predicts the value of the unknown matrix element from the result estimated by the approximation unit 103 and the value of the known matrix element of the matrix data (step S203). The prediction unit 104 uses, for example, K ^W and K ^X (that is, W and X), which are parameters estimated by the approximation unit 103, and the values of known matrix elements of the matrix data, and the following Expression 11 To predict unknown matrix elements (missing values).

Here, D is NM × NM matrix data whose diagonal component is the square of σ. Y is vector data obtained by modifying the original matrix data Y. Further, k ^W _i: represents an N-dimensional vector in which the i-th row of K ^W is a column vector, and k ^X _i: represents a column vector in the i-th row of K ^X. For example, when the value of the element y _1M of the vector Y is missing, the prediction unit 104 may predict an unknown matrix element (missing value) using Equation 12 illustrated below using Equation 11.

  Hereinafter, Y ′ represents data in which all missing portions of the matrix data Y are predicted (that is, data in which missing values of the matrix data are filled with predicted values). Finally, the output unit 105 outputs matrix data Y ′ in which missing values are filled with predicted values (step S <b> 204).

As described above, according to the present embodiment, first, for each factor element of the factor in the vertical axis direction of the matrix data Y including two factors, each factor element of the factor in the horizontal axis direction of the matrix data Y A factor matrix X representing the characteristics of is defined. Next, the approximation means 103 maximizes the likelihood (peripheral likelihood) that the data when the function transforms the factor matrix X among the parameters of the function F that transforms the factor matrix X is matrix data Y. Parameters to be estimated. Then, the prediction unit 104 predicts a missing value of the matrix element of the matrix data using the estimated parameters K ^W and K ^X (that is, W and X) and the values of the known matrix elements in the matrix data Y. To do. In this way, it is possible to improve the accuracy of predicting missing values in matrix data.

  For example, in the method described in Non-Patent Document 1, it is necessary to decompose the original matrix data into small matrix data for every factor and estimate the total number of elements of the decomposed factor matrix data. Therefore, the calculation cost is high. Further, in the method described in Non-Patent Document 2, it is only necessary to estimate the total number of elements of one factor matrix data, but it is still half the calculation cost of Non-Patent Document 1, and the original matrix data is conditional. The property of being independent remains.

  However, according to the present embodiment, the number of parameters that need to be estimated is reduced by expressing the large covariance matrix by the Kronecker product of the two small matrices representing the covariance. It can be suppressed.

  Hereinafter, the present invention will be described with reference to specific examples, but the scope of the present invention is not limited to the contents described below. In the following embodiment, a case where the present invention is applied to a system that receives product defect information from a company or factory and predicts future defects from the defect information in advance (hereinafter referred to as a defect prediction system) will be described. explain.

  FIG. 4 is an explanatory diagram illustrating an example of a failure prediction system according to the present embodiment. In addition, about the structure similar to the said embodiment, the code | symbol same as FIG. 1 is attached | subjected and description is abbreviate | omitted. The defect prediction system in this embodiment includes a client system 401 and a server system 403. The client system 401 and the server system 403 are connected to each other via the communication network 402.

  First, the outline of the present embodiment will be described. First, product defect information from client systems operated at each company that manufactures home appliances such as televisions and refrigerators, and parts products such as semiconductors, or from client systems operated at each factory that manufactures products. Is sent to the server system. The server system predicts in advance the defects that have not occurred at the present time but will occur in the future based on the transmitted defect information of the past product (known defect information). Send to client system. On the client system side, by using the prediction information transmitted in this way, it is possible to prevent the occurrence of defects. Also, the client system can be prepared for the trouble before the trouble occurs.

  Hereinafter, each component will be described. The client system 401 manages product failure information and the like. Specifically, the client system 401 stores product failure information that has occurred in the past, and transmits the failure information to the server system 403 via the communication network 402.

  The server system 403 includes a missing value prediction apparatus 101 and a prediction result storage unit 404. The server system 403 manages information of the client system 401. Specifically, when the server system 403 receives product failure information from the client system 401, the server system 403 predicts a future failure based on the failure information and transmits the prediction information to the client system 401.

  The missing value prediction apparatus 101 is the same as the missing value prediction apparatus 101 described in the above embodiment. Here, the missing value predicting apparatus 101 predicts information on a defective part that has not occurred in the product from the input matrix data. In addition, the prediction result storage unit 404 stores the matrix data with missing value prediction output from the missing value prediction apparatus 101.

  Next, the operation will be described. FIG. 5 is a sequence diagram showing an example of operation in the present embodiment.

  First, each client system 401 transmits defect information of each product to the server system 403 via the communication network 402 (step S501). FIG. 6 is an explanatory diagram illustrating an example of matrix data transmitted from each client system 401 in the present embodiment. Each axis of the matrix data illustrated in FIG. 6 represents a factor of the matrix data. Since matrix data is data having a vertical axis and a horizontal axis, the number of factors is two. In the matrix data illustrated in FIG. 6, the vertical axis represents the content of “failure”, and the horizontal axis represents “product” in which the failure may occur.

  Further, in the following description, a case will be described in which the matrix element of the matrix data is the number of product defects. That is, the matrix elements illustrated in FIG. 6 indicate the number of product defects, and the blank matrix elements indicate missing values (that is, no defects have occurred). However, the matrix element is not limited to the number of defects. The matrix element may be, for example, a probability of occurrence of a failure, or may be a binary value indicating whether or not a failure has occurred. When the matrix element is the number of product defects, the predicted value of the missing part can be said to be the number of defects that may occur in the future.

  For example, each client system 401 transmits the matrix data illustrated in FIG. 6 to the server system 403. Note that when the missing portion in the matrix data is expressed in the form of “(product, defect)”, the missing portions of the matrix data illustrated in FIG. 6 are (1, D), (1, E), (2, D), (3, E), (4, A), (4, C), (5, E), (30, A) and (30, B).

  Upon receiving the product defect information, the server system 403 inputs the product defect information to the missing value prediction apparatus 101 as matrix data (step S502). Hereinafter, this input data is assumed to be Y. The missing value predicting apparatus 101 (more specifically, the approximating means 103 and the predicting means 104 in FIG. 1) predicts missing values based on the input matrix data Y (step S503).

  Specifically, as shown in the above embodiment, first, for each piece of information indicating a product, a factor matrix that represents a feature of information indicating a product defect is defined. The approximating means 103 estimates a parameter that maximizes the likelihood that the data of the function that transforms the factor matrix is the matrix data to which the data when the function transforms the factor matrix is input. Then, the predicting unit 104 predicts information on a defective part that has not occurred in the product using the estimated parameters and information on known defective parts in the matrix data.

  Thereafter, the missing value prediction apparatus 101 (more specifically, the output unit 105 in FIG. 1) outputs matrix data (hereinafter referred to as Y ′) in which missing values are filled with predicted values. Specifically, the missing value prediction apparatus 101 stores the prediction result in the prediction result storage unit 404 (step S504).

  FIG. 7 is an explanatory diagram illustrating an example of a prediction result (that is, matrix data Y ′) in which missing values are filled with values predicted in the present embodiment. When the missing part in the matrix data Y is expressed in the form of “(product, defect, predicted value)”, the missing part of the matrix data Y ′ illustrated in FIG. 7 is (1, D, 1.01). ), (1, E, 0.3), (2, D, 2), (3, E, 2.0), (4, A, 0.5), (4, C, 2.5), (5, E, 5), (30, A, 2.0) and (30, B, 2.0).

  Next, the missing value prediction apparatus 101 (more specifically, the output unit 105 in FIG. 1) transmits a prediction result (that is, matrix data Y ′) to the client system 401 (step S505), and the client system 401. Receives the prediction result (that is, matrix data Y ′) (step S506).

  From the above, for example, problems that may occur in the future on the client system 401 side operated in each company that manufactures home appliances such as televisions and refrigerators and parts products such as semiconductors, and in each factory that manufactures products. By using the prediction information, it is possible to prevent the occurrence of defects. Moreover, in each said company and each factory, it can prepare for a malfunction before malfunction occurs.

Next, an example of the minimum configuration of the missing value prediction apparatus according to the present invention will be described. FIG. 8 is a block diagram showing an example of the minimum configuration of the missing value prediction apparatus according to the present invention. The missing value predicting apparatus 81 according to the present invention includes a factor element (for example, vertical axis) of one factor in matrix data (for example, matrix data Y) including two factors (for example, vertical axis and horizontal axis factors). Factor matrix that is defined for each factor element of the other factor in the matrix data (for example, each factor element of the factor on the horizontal axis) For example, among parameters of a function (for example, function F) that transforms the factor matrix X), a parameter that maximizes the likelihood that the data when the function transforms the factor matrix is matrix data is estimated (for example, Parameter estimation means 82 (estimated using Equation 5), parameters estimated by the parameter estimation means 82 (for example, W, X) and values of known matrix elements in the matrix data, Matrix elements in the row form data (e.g., y _ij in equation ₁₁₎ to predict the missing values (e.g., to predict the missing value by Equation 11) and a missing value predicting means 83.

  With such a configuration, the accuracy of predicting missing values in matrix data can be improved. Specifically, since the original matrix data is expressed using a function and a factor matrix, there is no condition-independent constraint on the original matrix data, so that the prediction accuracy can be improved.

  Note that at least a missing value prediction apparatus as described below is also disclosed in any of the embodiments described above.

(1) For each factor element of one factor (for example, factor element of the vertical axis) in matrix data (for example, matrix data Y) including two factors (for example, vertical and horizontal axes) A factor matrix (for example, factor matrix X) that is a matrix that is defined and that represents the characteristics of each factor element of the other factor (for example, each factor element of the factor on the horizontal axis) in the matrix data Of the parameters of the function to be converted (for example, function F), the parameter that maximizes the likelihood that the data when the function converts the factor matrix is matrix data is estimated (for example, estimated using Equation 10). Parameter estimation means, the parameters estimated by the parameter estimation means (for example, W, X), and the values of known matrix elements in the matrix data, , To predict the missing values of y _ij) in the equation 11 (e.g., to predict the missing value by Equation 11) missing values prediction apparatus and a missing value predicting means.

(2) The parameter estimation means converts the factor matrix based on the probability distribution (for example, Equation 3) in the factor matrix of the function defined using the Gaussian distribution covariance matrix (for example, K ^WX ). A missing value prediction device that estimates the parameters of a function that maximizes the likelihood that the data is matrix data.

(3) Based on a probability distribution (for example, Equation 4) in which the parameter estimation means represents a Gaussian distribution covariance matrix as a Kronecker product (for example, an estimation target parameter) of two matrices representing covariance, A missing value prediction apparatus that estimates a parameter of a function that maximizes the likelihood that data obtained by transforming a factor matrix is matrix data.

(4) A parameter estimation unit estimates a parameter of a function that maximizes a marginal likelihood value determined by the probability distribution of the function in the factor matrix and the probability distribution of the matrix data in the function and factor matrix. Prediction device.

(5) When the parameter estimation means includes information indicating a product and a defect of the product as two factors, the matrix defined for each information indicating a product which is one factor in the matrix data Among the parameters of the function that converts the factor matrix that represents the characteristics of the information indicating the malfunction of the product, which is the other factor in the matrix data, the data when the factor matrix is converted is matrix data. A deficiency in which a parameter that maximizes a certain likelihood is estimated, and the missing value predicting means predicts information on a defect location that has not occurred in the product using the estimated parameter and information on a known failure location in the matrix data. Value prediction device.

  The present invention is suitably applied to a missing value prediction system that predicts the value of an unknown matrix element in matrix data including two factors.

DESCRIPTION OF SYMBOLS 101 Missing value prediction apparatus 102 Input means 103 Approximation means 104 Prediction means 105 Output means 401 Client system 402 Communication network 403 Server system 404 Prediction result storage part

Claims (9)

Transforms a factor matrix that is defined for each factor element of one factor in matrix data including two factors and that represents the characteristics of each factor element of the other factor in the matrix data Parameter estimation means for estimating a parameter that maximizes the likelihood that the data when the function transforms a factor matrix among the parameters of the function is the matrix data;
And a missing value predicting means for predicting a missing value of a matrix element in the matrix data using the parameter estimated by the parameter estimating means and a value of a known matrix element in the matrix data. Missing value prediction device. Based on the probability distribution in the factor matrix of the function defined using the Gaussian covariance matrix, the parameter estimation means maximizes the likelihood that the data when the function transforms the factor matrix is matrix data. The missing value prediction apparatus according to claim 1, wherein a parameter of a function to be estimated is estimated. The parameter estimation means is the likelihood that the data when the function transforms the factor matrix based on the probability distribution that expresses the Gaussian distribution covariance matrix as the Kronecker product of the two matrices representing the covariance. The missing value predicting apparatus according to claim 2, wherein a parameter of a function that maximizes is estimated. The parameter estimation means estimates a parameter of a function that maximizes a marginal likelihood value determined by the probability distribution of the function in the factor matrix and the probability distribution of the matrix data in the function and the factor matrix. The missing value prediction apparatus according to claim 3. The parameter estimation means is a matrix defined for each piece of information indicating a product which is one factor in the matrix data when the matrix data includes information indicating a product and a defect of the product as two factors. Among the parameters of the function that converts the factor matrix that represents the characteristic of the information indicating the malfunction of the product that is the other factor in the matrix data, the data when the function converts the factor matrix is the matrix data Estimate the parameters that maximize the likelihood that
The missing value predicting means predicts information on a non-occurring defect location of the product using the estimated parameter and information on a known defect location in the matrix data. The missing value prediction apparatus according to claim 1. Transforms a factor matrix that is defined for each factor element of one factor in matrix data including two factors and that represents the characteristics of each factor element of the other factor in the matrix data Among the parameters of the function, the parameter that maximizes the likelihood that the data when the function transforms the factor matrix is the matrix data is estimated,
A missing value prediction method, wherein a missing value of a matrix element in the matrix data is predicted using an estimated parameter and a value of a known matrix element in the matrix data. Based on the probability distribution in the factor matrix of a function defined using a Gaussian distribution covariance matrix, the parameter of the function that maximizes the likelihood that the data when the function transforms the factor matrix is matrix data. The missing value prediction method according to claim 6. On the computer,
Transforms a factor matrix that is defined for each factor element of one factor in matrix data including two factors and that represents the characteristics of each factor element of the other factor in the matrix data A parameter estimation process for estimating a parameter that maximizes the likelihood that data when the function transforms a factor matrix is the matrix data among the parameters of the function; and
Missing value prediction for executing missing value prediction processing for predicting missing values of matrix elements in the matrix data using the parameters estimated by the parameter estimation processing and the values of known matrix elements in the matrix data program. On the computer,
In the parameter estimation process, based on the probability distribution in the factor matrix of the function defined using the Gaussian distribution covariance matrix, maximize the likelihood that the data when the function transforms the factor matrix is matrix data The missing value prediction program according to claim 8, wherein a parameter of a function to be estimated is estimated.

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