JP2012194741A - Prediction device of missing value in matrix data, method for calculating missing value prediction, and missing value prediction program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To solve a problem that since a nonlinear relationship is inexpressible, it is difficult to determine a probability of a predicted value.SOLUTION: The missing value prediction device includes: input means for inputting a plurality of pieces of matrix data with different domains; parameter estimating means that learns a nonlinear relationship between lines and columns of the matrix data, models the plurality of pieces of input matrix data by a different parameter for each domain, models the parameter for each domain by a common parameter and an error term, and estimates a parameter of a model expressing the correlation among the domains by the error term; and prediction means for predicting missing values in the matrix data using the parameters estimated by the parameter estimation means and calculates a dispersion of prediction values.

Description

  The present invention relates to a matrix data missing value prediction apparatus, a missing value prediction calculation method, and a missing value prediction program, and in particular, predicts missing values of a plurality of matrix data having different domains and calculates a variance of predicted values. The present invention relates to a missing value prediction apparatus for matrix data, a missing value prediction calculation method, and a missing value prediction program.

  Matrix data missing value prediction can be applied to recommending products to customers and predicting missing values in health checkup data.

  In response to product recommendation, a plurality of scores (preference information) for the user, the product, and the user's product are input, and the score of the product that the user has not scored is predicted. If the predicted score is high, it is recommended that the user likes the product. In this case, the score of a product for which the user has not yet scored is a missing value.

  In application to health checkup data, whether or not to provide health guidance to users is determined based on the test values of multiple test items. If some test items have missing values, I can't decide whether or not to give health guidance. In this case, a plurality of inspection values of inspection items, users, and user inspection items are input to predict missing inspection values.

  In the matrix data for product recommendation, each row represents each user and each column represents each product. In the matrix data of missing value prediction of health check data, each row represents an inspection item and each column represents each user.

  Non-patent literatures 1 and 2 describe missing value prediction techniques as examples of conventional techniques for matrix value missing value prediction techniques.

  For example, in the case of application to a recommendation technique, all users and all products are expressed by a single matrix data, data is learned, and missing values are predicted.

  In recent years, a technique for improving prediction accuracy by simultaneously learning a plurality of matrix data having different domains has been developed.

  Another example of the missing value prediction technique is described in Non-Patent Document 3. The technology of Non-Patent Document 3 is different from Non-Patent Documents 1 and 2, and does not treat all data as one matrix data, but creates matrix data for each domain and learns multiple matrix data simultaneously. This is a technique for predicting missing values in consideration of the correlation between domains.

  In the case of application to product recommendation, products representing rows of matrix data are divided into domains.

  For example, when the product is a movie, the domain represents the genre of the movie, and the genre includes Thriller, Action, Comedy, Romance, and the like.

  The same applies to matrix data in which rows represent Thriller genres, columns represent users, and rows represent Action genres, columns represent users, and movies in the Comedy and Romance genres. Create matrix data and learn and predict matrix data of each genre at the same time.

  For example, as a tendency of all users, when a high score is given to a movie of Action, a high score is also given to a movie of the Thriller genre, when predicting the score of a movie of the Thriller genre Predict by considering how many points the user's Action movie has.

  For users of health checkup data, the domain represents the insurer that the user subscribes to, and creates a matrix data for each insurer and joins an insurer by learning multiple matrix data simultaneously. When predicting the inspection value of the user who performs the prediction, it is expected that the prediction accuracy is improved by making a prediction in consideration of the inspection value of the user who joins another insurer.

  Moreover, the correlation between each domain can be observed by learning simultaneously.

  For example, I want to know if the insurer has a strong or weak correlation with other insurers.

  The fact that there is a correlation means that the data trends are similar, so that insurers with a strong correlation can share data and refer to the analysis results.

  Correlation can be used as a criterion for selecting which insurer's data can be referenced.

  For example, National Health Insurance has few 40-50 generations, and Health Insurance has few 60 or more.

  When there is a strong correlation between National Health Insurance and Health Insurance, you can refer to the tendency of Health Insurance from 40 to 50 years old to know the tendency of National Health Insurance from 40 to 50s.

  Moreover, it is highly possible that the data of the same period of Kenpo is useful for prediction in predicting missing values in the 40-50s of National Health Insurance.

  Patent Document 1 has a description of a content presentation device and a content presentation method, extracts attributes associated with a user who has selected content, forms a community that is a set of users having the extracted attributes, There is a description of presenting content based on the community to which the user belongs (paragraphs 0068, 0081, 0118, etc.).

  Patent Document 2 describes a user target recommendation device, a user target recommendation method, and a program, and a plurality of users associate evaluation values obtained by evaluating each of the plurality of use targets with the users and the use targets. Based on this estimated value, the estimated value missing in the read and read evaluation value is estimated using the singular value decomposition of the matrix of evaluation values with the user and usage target as rows and columns. In addition, there is a description that a usage target to be recommended to the user is selected from among a plurality of usage targets, and that the estimated value is calculated by reduction estimation of the singular value unit of the matrix (paragraphs 0009-0012, 0017, 0034, etc.) .

  Patent Document 3 has a description of a prediction device, which configures past history data and prediction data in a matrix format so as to have unknown prediction data as a missing element of the matrix, and performs singular value decomposition on the configured data matrix. There is a description of outputting prediction data by estimating defect elements representing unknown prediction data of a matrix (paragraphs 0043 and 0075).

  Patent Document 4 has a description of a susceptibility analysis method and software. Factors that are complicated and difficult to inspect for examination items used for disease determination are estimated from items that can be measured by the subject, and the estimation results are used. In addition, there is a description of estimating the susceptibility, and the susceptibility is obtained by clustering the population distribution, tabulating by clustering node, obtaining the susceptibility in advance, and actually obtaining the distribution as a pre-established distribution. There is a description of estimating the posterior probability distribution of the subject's susceptibility on the basis of the obtained test results (paragraphs 0009 and 0013).

JP 2007-052661 A JP 2010-061513 A JP 2005-128808 A JP 2004-305664 A

Author Salakhutdinov, Ruslan and Mnih, Andriy, Title of Publication Probabilistic Matrix Factorization, NIPS Publication Date 2007 Author Title of Lawrence, Neil D. and Urtasun Publication Non-linear Matrix Factorization with Gaussian Processes, ICML Date of Publication 2009 Authors Zhang, Cao and Yeung Publication title Multi-Domain Collaborative Filtering, UAI2010 Publication date 2010

  The problem will be described using the technique disclosed in Non-Patent Document 3 as an example.

  The first problem is that it is a linear model.

  The nonlinear relationship between rows and columns of matrix data cannot be modeled, only the linear relationship is modeled.

  For example, in the case of application to product recommendation, the conventional technology can express a linear relationship between a user and a product, but cannot express a non-linear relationship.

  If complex relationships that cannot be expressed linearly can be modeled, the prediction accuracy can be improved.

  The second problem is that it is difficult for the conventional method to obtain the accuracy of the predicted value. It is practically important to quantitatively represent how reliable the predicted result is.

  For example, in the case of application to product recommendation, even if the score of a predicted product is high, if the degree of reliability is low, it is not recommended to the user, and only products with a high predicted score and high reliability are selected. Can be recommended.

In practice, since the number of products recommended to the user is limited, if the accuracy of the predicted value can be obtained, the products can be recommended in descending order of reliability.
[Object of invention]
A typical first object of the present invention is to model the non-linear relationship between rows and columns of matrix data.

  For example, in the case of application to product recommendation, improvement of prediction accuracy can be expected by expressing a complicated relationship that cannot be expressed by the linear relationship between the user and the product using a nonlinear model.

  A typical second object of the present invention is to output the reliability of the predicted value.

  It represents quantitatively how reliable the typical predicted result of the present invention is.

  The third purpose is to obtain a correlation between domains.

  Even in a model extended to a nonlinear model, correlation between domains is obtained.

An apparatus for predicting missing values of matrix data according to the present invention includes input means for inputting a plurality of matrix data having different domains,
Learn the non-linear relationship between the rows and columns of the matrix data, model the input matrix data with different parameters for each domain, and model the parameters of each domain with common parameters and error terms Parameter estimation means for estimating a parameter of a model that expresses a correlation between domains by an error term,
Prediction means for predicting a missing value of the matrix data using the estimated parameter and calculating a variance of the predicted value.

According to the present invention, there is provided a missing value predicting method for a missing value predicting apparatus for a matrix type data, learning a non-linear relationship between rows and columns of the matrix type data of a plurality of inputted matrix types having different domains. Model with different parameters for each domain, parameters for each domain are modeled by common parameters and error terms, and correlation between domains is expressed by error terms. Estimate the parameters,
Using the estimated parameters, a missing value of matrix data is predicted, and a variance of predicted values is calculated.

A program according to the present invention allows a computer to function as a matrix-shaped data missing value prediction apparatus,
Learning a non-linear relationship between rows and columns of matrix-form data of a plurality of matrix-form data having different input domains, modeling a plurality of matrix-form data having different domains with different parameters for each domain, A step of modeling parameters of a domain by a common parameter and an error term, and estimating a parameter of a model having a feature that expresses a correlation between domains by an error term;
Using estimated parameters to predict missing values in matrix data and calculate the variance of the predicted values;
Is executed.

  A typical first effect according to the present invention is an improvement in prediction accuracy. Prediction accuracy is improved by modeling not only the linear relationship between rows and columns of matrix data but also a nonlinear relationship.

  A typical second effect according to the present invention is to calculate and output the variance of the predicted value as the reliability of the predicted value. Since the applied nonlinear model determines the posterior distribution, the variance of the predicted value can be calculated.

  A typical third effect related to the present invention is a reduction in calculation amount. If the correlation between domains is simply calculated using a non-linearly expanded model, the amount of calculation becomes enormous, which is difficult to put into practical use. Multiple input matrix data is modeled with different parameters for each domain, the parameters of each domain are modeled with common parameters and error terms, and the correlation between domains is expressed with error terms to reduce the amount of computation. Can be reduced.

It is a block diagram of a 1st embodiment concerning the present invention. It is a flowchart of 1st Embodiment concerning this invention. It is an example of the input data of 2nd Embodiment concerning this invention. It is an example of the input data of 3rd Embodiment concerning this invention. It is an example of the dispersion | distribution covariance of 3rd Embodiment concerning this invention. It is a figure which shows an example of the computer which operate | moves as a missing value prediction apparatus with the program concerning this invention.

Next, typical embodiments of the present invention will be described in detail with reference to the drawings.
(First embodiment)
FIG. 1 is a configuration diagram of a missing value prediction apparatus according to an embodiment of the present invention.

  The configuration of the missing value prediction apparatus 101 of this embodiment includes an input unit 102, a parameter estimation unit 103, a missing value prediction unit 104, and an output unit 105.

  The input unit 102 inputs a plurality of matrix data having different domains. The parameter estimation unit 103 estimates model parameters. The missing value prediction unit 104 predicts missing values of the input matrix data. The output unit 105 outputs the predicted missing value. The input unit 102 includes a keyboard and a receiving unit that communicates with the network, and the output unit 105 includes a display unit such as a liquid crystal display and a transmitting unit that communicates with the network.

Next, the operation of the above configuration example will be described. FIG. 2 shows a flowchart of the operation.
(1) Step S201
A plurality of matrix data having different domains are input to the input unit 102.

Let Y_d be the matrix data of domain d. If the number of domains is D, the input data is Y_d {d = 1,2, .., D}. The matrix data Y_d is an N × M_d dimensional matrix. N representing the number of rows is common to the domains, and M_d representing the number of columns is different for each domain.
(2) Step S202
The parameter estimation unit 103 estimates model parameters. Matrix data Y_d of domain d including missing values is represented by Equation 1. “^” Indicates a power and {i,:} ^ {T} indicates {i ,:} ^{T} .
[Equation 1]
Y_d_ {i ,:} = W_d X_d_ {i,:} ^ {T} + ε

Y_d = N × M_d matrix: input data
X_d = N × q Matrix: Low-dimensional matrix data
W_d = M_d × q Matrix: Low-dimensional matrix data
N: Number of rows in Y_d
M_d: Number of columns in Y_d
q: Number of dimensions of X_d and W_d
q is common to the domains.
{i ,:} represents a matrix whose i columns are all vertical columns.
here,
ε to N (0, σ_d I_ (M_d))
I_ (M_d) = M_d × M_d matrix: The unit matrix σ_d represents the variance of the normal distribution.
Matrix data Y_d is expressed by Equation 2.
[Equation 2]
P (Y_d | X_d, σ_d) = II ^ {M_d} _ {i = 1} N (Y_d _ {:, i} | X_d X_d ^ {T}, σ_d ^ {2} I_N)

Here, N () represents a multidimensional normal distribution.
The parameters to be estimated are X_d and σ_d.
Equation 1 is the same as the model described in Non-Patent Document 2.
If X_d X_d ^ {T} in Equation 2 is the Mercer kernel K, Equation 2 becomes a nonlinear model.
As an example of Marcel kernel K,
K (i, j) = exp (-1 / 2 * γ * (x (i, j) -x (j, i)) ^ 2), i = 1,2,…, N; j = 1,2 ,…, N
And
γ is a parameter of the RBF kernel.

Next, X_d, which is a parameter estimated for each domain, is collected as a matrix X (Equation 3).
[Equation 3]
X = [X_1, X_2, .., X_D]

Here, X = N × Dq matrix.
D: Represents the number of domains Next, a vector obtained by extracting the i-th row from X is X_i :.
X_i: is a Dq × 1 vector. In the present technology, X_i: is expressed by Formula 4.
[Equation 4]
X_i: = f (X'_i) + e

here,
X ′ is a low-dimensional matrix common to all N × q ′ domains.
X′_i is a q ′ × 1 vector extracted from the i-th matrix of X ′.
q ′ represents the dimension of the X ′ matrix. Suppose that it is given in advance.
f () is a function of X'_i.
here,
e to N (0, Σ_Dq)
e is the error term, a Dq × 1 vector.
The variance-covariance matrix of e is a Dq × Dq matrix and represents a correlation between dimensions of each domain.
Equation 4 indicates that X_i: is expressed by the sum of f (X′_i) and the error term.

  This technology collects the parameters of each domain into a single matrix X, models it with a common parameter X ′ and error term e, and expresses the correlation between the domains as a variance-covariance matrix Σ_Dq of error terms. Have.

  Since Equation 4 assumes that the error term e is not independent between Dq and is correlated, X_i: is not independent between Dq.

When simply observing the correlation between Dq, as in Equation 2,
p (vec (X) | vec (X '), β) = N (vec (X) | 0, vec (X') vec (X ') ^ {T} + βI_DqN)
By
"Vec (X ') vec (X') ^ {T} + βI_DqN" gives correlation between DqN dimensions, but DqN is too difficult to put into practical use because the dimension is too large. . Here, N () represents a multidimensional normal distribution. vec (X) is a vector [X _ (:, 1) ^ {T}, X_ (:,) in which each column element of the matrix X (for example, X _ (:, i) for the i-th column) is arranged vertically. 2) ^ {T},…, X _ (:, Dq) ^ {T}] ^ {T}, a vector of size DqN × 1. T represents transposition. Vec (X ') is a vector [X' _ (:, 1) ^ {T}, X '_ (:, 2) ^ {T},…, X '_ (:, Dq) ^ {T}] ^ {T}.

  In order to express the correlation between domains while reducing the amount of calculation, an error indicating the correlation between domains is removed from X ′ by variable transformation, and X ′ is decorrelated between Dq.

First, the variance-covariance matrix Cov (e) = Σ_Dq of e is obtained by Cholesky decomposition,
cov (e) = LL ^ {T}
It becomes. L is a lower triangular matrix of Dq × Dq.

As a result, e = Le *.
here,
e * to N (0, I_Dq).
e * = Dq × 1 vector, I_Dq = Dq × Dq identity matrix.
The covariance matrix of e * is
cov (e *) = I_Dq, which is uncorrelated.
Using the above, Equation 4 can be expressed as Equation 5.
[Equation 5]
X_i: = f (X'_i :) + e
= f (X'_i :) + Le *

Next, multiplying both sides of Equation 5 by the inverse matrix L ^ {-1} of L,
[Equation 6]
L ^ {-1} X_ (i :) = L ^ {-1} f (X '_ (i :)) + e *

It becomes.

Next, X ^ {I} _ (i :) is defined by Equation 7 as a new variable.
[Equation 7]
X ^ {I} _ (i :) = L ^ {-1} f (X '_ (i :)) + e *

The error term e indicating the correlation between domains is e * with the correlation between domains eliminated, and X ^ {I} _ (i :) is uncorrelated between Dq. X ^ {I} is a matrix of the same size as X.

Next, from Equation 5 and Equation 7,
[Equation 8]
X_i: = LX ^ {I} _i:

It becomes. Equation 8 represents the relationship between X ^ {I} _i: that is not correlated between Dq and X_i that has a correlation between Dq.

[数１０]
p( X^{I} | X’ , β) = II^{Dq}_{i=0} p( X^I_(:,i) | X’ , βI_N)
= II^{Dq}_{i=0} N( X^I_(:,i) | 0, X’ X’^{T} , βI_N)

ここで、βはN()のパラメータ（分散）を表す。 When the matrix X is vec (X), a common low-dimensional vector vec (X ′) between the domains is expressed by the following equation.
[Equation 9]
p (vec (X) | vec (X ')) = (L_ {Dq} × I_ {N}) p (vec (X ^ {I}) | vec (X'))

P (vec (X_ {I}) | vec (X ′)) in Expression 9 is independent among Dq and can be expressed as Expression 10.

[Equation 10]
p (X ^ {I} | X ', β) = II ^ {Dq} _ {i = 0} p (X ^ I _ (:, i) | X', βI_N)
= II ^ {Dq} _ {i = 0} N (X ^ I _ (:, i) | 0, X 'X' ^ {T}, βI_N)

Here, β represents a parameter (dispersion) of N ().

  II ^ {N}, a simple method that does not model N independently, instead of computing the variance covariance matrix of X 'X' ^ {T} = N × N in Mathematical Formula 10, the variance covariance of DqN × DqN Since the variance matrix is calculated, the amount of calculation becomes enormous and it becomes practically difficult to calculate.

  The parameters to be estimated are [X_1, X_2,..., X_d,. q and q` are parameters input in advance.

When the estimated L is used, a variance-covariance matrix that represents the correlation between domains is obtained by Equation 11.
[Equation 11]
e = LL ^ {T} = Σ

Σ is a variance-covariance matrix and is a matrix having a size of Dq × Dq.
This matrix represents the correlation between domains.

An example in which the variance-covariance matrix Dq × Dq is compressed to D × D is shown in FIG.
(3) Step S203
In the defect prediction unit 104, a missing value is predicted.
When predicting the value of the j-th row and l-th column of domain d,
[Equation 13]
μ_d, j, l = (K_d, index_l:, index_l: + σ_d ^ {2} I) ^ {-1} K_d, index_l, j y_d, index_l, l

index_l: represents a set of indexes of row numbers having a value (not missing) in the l-th column.
[Equation 14]
ξ_d, j, l = K_d, j, j + σ_d ^ {2}-K_d, index_l, j ^ {T} (K_d, j:, j: + σ_d ^ {2} I) ^ {-1} K_d, index_l, j

Equation 13 is the predicted value, and Equation 14 represents the variance.
(4) Step S204
The output unit 105 outputs the predicted value μ of each missing value included in the plurality of input matrix data and ξ representing its reliability.
(Second Embodiment)
The second embodiment of the present invention is prediction of missing values of health check data.

  As the health check result of each subscriber {M_1, M_2, ..., M_D} of multiple insurers {d = 1, .., D}, test items {1,2, .., N}, subscribers, tests A test value in which a user's test item is missing is predicted by using, as input data, data obtained by making the matrix data composed of values into a matrix for each insurer.

FIG. 3 shows an example of input data. For example, to determine whether or not to give health guidance to subscribers based on the test values of multiple test items, if some test items have missing values, health guidance is given to subscribers with missing values. Since it is not possible to determine whether or not to perform, it is possible to determine whether or not to give health guidance to a subscriber who has a missing value by interpolating the predicted missing value.
(Third embodiment)
The third embodiment of the present invention is a product recommendation technique.

  As input information of users of multiple products, input data that is a matrix form of {d = 1,.. As for a user, the preference degree of the goods to which the score is not attached yet is estimated.

  If the predicted score is high, it is recommended that the user likes the product.

  FIG. 4 shows an example of matrix data. In FIG. 4, the genre of Thriller, Action, and Romance is taken as an example.

  An example in which the variance-covariance matrix Dq × Dq is compressed to D × D is shown in FIG. The correlation between genres can be observed.

  For example, the (1,2) element in FIG. 5 represents the correlation between Thriller and Action. The (1, 3) element represents the correlation between Thriller and Romance. FIG. 5 shows that the correlation between Thriller and Action is higher than the correlation between Thriller and Romance.

  The matrix-shaped data missing value prediction apparatus according to the present embodiment is configured by hardware, but all or part of the components illustrated in FIG. 1 may be realized by software using a computer. FIG. 6 is a diagram showing an example of a computer that operates as a missing value predicting apparatus according to a program according to the present invention.

  The computer includes a CPU 304, a disk device such as a hard disk (may be a storage means such as a ROM) 305, an input unit 301 such as a keyboard, a memory 303 such as a RAM, and a display unit 302 such as a liquid crystal display. 103, the operation of the missing value prediction unit 104 is described by a program, this program is stored in a disk device 305 such as a hard disk, information necessary for the operation is stored in a memory 303 such as a RAM, and the CPU 304 operates the program. Thus, the function of the missing value prediction apparatus of the present embodiment can be realized by a program. The program can be read into a computer by recording it on a computer-readable recording medium such as a DVD, CD-ROM, or USB memory and installing it on a hard disk.

A part or all of the above embodiment can be described as in the following supplementary notes, but is not limited to the following configuration.
(Appendix 1)
An input means for inputting a plurality of matrix data having different domains;
Learn the non-linear relationship between the rows and columns of the matrix data, model the input matrix data with different parameters for each domain, and model the parameters of each domain with common parameters and error terms Parameter estimation means for estimating a parameter of a model that expresses a correlation between domains by an error term,
A matrix data missing value prediction apparatus comprising: a predicting unit that predicts a missing value of the matrix data using an estimated parameter and calculates a variance of the predicted values.
(Appendix 2)
Missing user test items using input data that is a matrix form of insurers, consisting of test items, subscribers, and test values, which is the health check result of each insurer's health checkup The missing value prediction apparatus according to appendix 1, wherein the inspection value is predicted.
(Appendix 3)
User preference information is unregistered, using as input data data obtained by arranging the matrix data composed of users, products, and the degree of preference of the products, which are user preference information of multiple products, into a matrix for each product genre. The missing value prediction apparatus according to appendix 1, which predicts the preference level of a product.
(Appendix 4)
Learning a non-linear relationship between rows and columns of matrix-form data of a plurality of matrix-form data having different input domains, modeling a plurality of matrix-form data having different domains with different parameters for each domain, Model the parameters of the domain with common parameters and error terms, estimate the parameters of the model with the characteristics that express the correlation between domains with error terms,
A missing value prediction method for a missing value predictor for a matrix data, which predicts a missing value of matrix data using an estimated parameter and calculates a variance of the predicted values.
(Appendix 5)
Missing user test items using input data that is a matrix form of insurers, consisting of test items, subscribers, and test values, which is the health check result of each insurer's health checkup The missing value prediction method according to attachment 4, wherein the inspection value is predicted.
(Appendix 6)
User preference information is unregistered, using as input data data obtained by arranging the matrix data composed of users, products, and the degree of preference of the products, which are user preference information of multiple products, into a matrix for each product genre. The missing value prediction method according to attachment 4, wherein the preference level of the product is predicted.
(Appendix 7)
A computer that functions as a missing value prediction device for matrix data,
Learning a non-linear relationship between rows and columns of matrix-form data of a plurality of matrix-form data having different input domains, modeling a plurality of matrix-form data having different domains with different parameters for each domain, A step of modeling parameters of a domain by a common parameter and an error term, and estimating a parameter of a model having a feature that expresses a correlation between domains by an error term;
Using estimated parameters to predict missing values in matrix data and calculate the variance of the predicted values;
A computer program for executing
(Appendix 8)
Missing user test items using input data that is a matrix form of insurers, consisting of test items, subscribers, and test values, which is the health check result of each insurer's health checkup The computer program according to appendix 7, which predicts the inspection value obtained.
(Appendix 9)
User preference information is unregistered, using as input data data obtained by arranging the matrix data composed of users, products, and the degree of preference of the products, which are user preference information of multiple products, into a matrix for each product genre. The computer program according to appendix 7, which predicts the preference level of the product.

  INDUSTRIAL APPLICABILITY The present invention is used for a matrix-shaped data missing value prediction device, a missing value prediction calculation method, and a missing value prediction program that predict missing values of a plurality of matrix-shaped data having different domains and calculate a variance of predicted values. It can be applied to recommending products to customers and predicting missing values in health checkup data.

DESCRIPTION OF SYMBOLS 101 Missing value prediction apparatus 102 Input part 103 Parameter estimation part 104 Missing value prediction part 105 Output part

Claims (9)

An input means for inputting a plurality of matrix data having different domains;
Learn the non-linear relationship between the rows and columns of the matrix data, model the input matrix data with different parameters for each domain, and model the parameters of each domain with common parameters and error terms Parameter estimation means for estimating a parameter of a model that expresses a correlation between domains by an error term,
A matrix data missing value prediction apparatus comprising: a predicting unit that predicts a missing value of the matrix data using an estimated parameter and calculates a variance of the predicted values.   Missing user test items using input data that is a matrix form of insurers, consisting of test items, subscribers, and test values, which is the health check result of each insurer's health checkup The missing value prediction apparatus according to claim 1, wherein the inspection value is predicted.   User preference information is unregistered, using as input data data obtained by arranging the matrix data composed of users, products, and the degree of preference of the products, which are user preference information of multiple products, into a matrix for each product genre. The missing value prediction apparatus according to claim 1, wherein the preference level of a product is predicted. Learning a non-linear relationship between rows and columns of matrix-form data of a plurality of matrix-form data having different input domains, modeling a plurality of matrix-form data having different domains with different parameters for each domain, Model the parameters of the domain with common parameters and error terms, estimate the parameters of the model with the characteristics that express the correlation between domains with error terms,
A missing value prediction method for a missing value predictor for a matrix data, which predicts a missing value of matrix data using an estimated parameter and calculates a variance of the predicted values.   Missing user test items using input data that is a matrix form of insurers, consisting of test items, subscribers, and test values, which is the health check result of each insurer's health checkup The missing value prediction method according to claim 4, wherein the inspection value is predicted.   User preference information is unregistered, using as input data data obtained by arranging the matrix data composed of users, products, and the degree of preference of the products, which are user preference information of multiple products, into a matrix for each product genre. The missing value prediction method according to claim 4, wherein the preference level of the product is predicted. A computer that functions as a missing value prediction device for matrix data,
Learning a non-linear relationship between rows and columns of matrix-form data of a plurality of matrix-form data having different input domains, modeling a plurality of matrix-form data having different domains with different parameters for each domain, A step of modeling parameters of a domain by a common parameter and an error term, and estimating a parameter of a model having a feature that expresses a correlation between domains by an error term;
Using estimated parameters to predict missing values in matrix data and calculate the variance of the predicted values;
A computer program for executing   Missing user test items using input data that is a matrix form of insurers, consisting of test items, subscribers, and test values, which is the health check result of each insurer's health checkup The computer program according to claim 7, wherein the inspection value is predicted.   User preference information is unregistered, using as input data data obtained by arranging the matrix data composed of users, products, and the degree of preference of the products, which are user preference information of multiple products, into a matrix for each product genre. The computer program according to claim 7, wherein a preference level of a product is predicted.

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