Model learning device, model learning method, and model learning program

Abstract

A model learning device according to an embodiment of the present invention comprises: an input data acquisition unit that acquires input data including shuffled training data following a training distribution, unlabeled test data following a test distribution having a probability distribution different from the training distribution, a probability model, an importance model, and a hyperparameter; an importance model parameter estimation unit that estimates a parameter of the importance model by minimizing an objective function using the shuffled training data, the unlabeled test data, the importance model, and the hyperparameter included in the input data; a probability model parameter estimation unit that calculates relative importance using the shuffled training data, the probability model, the importance model, and the hyperparameter included in the input data, and estimates a parameter of the probability model by maximizing an objective function using the relative importance; and a probability model parameter processing unit that outputs the parameter of the probability model.

Description

Model learning device, model learning method, and model learning program

[0001] The embodiments relate to a model learning device, a model learning method, and a model learning program.

[0002] Shuffled regression (SR) is a problem in which a regression model is trained from data (shuffled data) where the correspondence between input features and target output values ​​is unknown. Data collected independently by different organizations or devices, and data collected without linking to personal information to protect privacy, such as annual income or test scores, are often known to be represented as shuffled data. Standard supervised regression (hereinafter referred to as Coupled Regression (CR)) requires data with a one-to-one correspondence between input and output. Therefore, it cannot handle shuffled data. SR is often used, for example, in the analysis of cell measurement records (see, for example, Non-Patent Document 1), health records, and in the field of computer vision.

[0003] While various studies have been conducted on shuffled data (see, for example, Non-Patent Documents 1, 2, 3, and 4), all of these studies implicitly assume that the training and test data are derived from the same probability distribution. Therefore, if this assumption does not hold, for example, an income prediction model trained using shuffled data collected in a region with biases in user attributes such as nationality, age, and occupation may exhibit poor prediction performance when predicting income in a region with different biases. In fact, such performance degradation has been reported in cross-reported data (CR), and the setting where the input distributions during training and testing are different has been formulated as covariate shift (see, for example, Non-Patent Document 5).

[0004] Abubakar Abid and James Zou. A stochastic expectation-maximization approach to shuffled linear regression. In Annual Allerton Conference on Communication, Control, and Computing, pp. 470-477, 2018. Martin Slawski, Mostafa Rahmani, and Ping Li. A sparse representation-based approach to linear regression with partially shuffled labels. Incertainty in Artificial Intelligence, pp. 38-48, 2020.Guanhua Fang and Ping Li. Regression with label permutation in generalized linear model. In International Conference on Machine Learning, pp. 9716-9760, 2023.Masahiro Kohjima. Shuffled deep regression. In AAAI Conference on Artificial Intelligence, Vol.38, pp. 13238-13245, 2024 Sugiyama, Masaru, Supervised learning under covariate shift, Journal of the Japanese Neural Network Society, Vol.13, No.3, pp. 111-118, 2006.

[0005] However, unlike standard supervised regression (CR), existing shuffle regression (SR) methods do not yet exist that can handle covariate shifts. Therefore, existing SR methods have the problem of not being able to accurately estimate the regression function when the input distribution changes between training and testing, such as when there is a bias in data collection or when the probability distribution changes over time.

[0006] Therefore, the present invention has been made in view of the above circumstances, and its objective is to provide a model learning device, a model learning method, and a model learning program that can estimate a regression model even when the probability distributions followed by the input features of the training distribution and the test distribution change.

[0007] The model learning device of the embodiment includes: an input data acquisition unit that acquires input data including shuffled training data following a training distribution, unlabeled test data following a test distribution having a probability distribution different from the training distribution, a probability model, an importance model, and hyperparameters; an importance model parameter estimation unit that estimates the parameters of the importance model by minimizing an objective function using the shuffled training data, unlabeled test data, importance model, and hyperparameters included in the input data; a probability model parameter estimation unit that calculates relative importance using a quantity defined by the ratio of the test distribution and a mixed distribution obtained by mixing the training distribution and the test distribution, based on the shuffled training data, probability model, importance model, and hyperparameters included in the input data and the parameters of the importance model, and estimates the parameters of the probability model by maximizing an objective function using the relative importance; and a probability model parameter processing unit that outputs the parameters of the probability model.

[0008] According to the embodiment, a model learning device, a model learning method, and a model learning program can be provided that enable estimation of a regression model from shuffled data when the training distribution and test distribution are different.

[0009] Figure 1 shows an example of the probability distribution of input features according to one embodiment. Figure 2 shows an example of coupled data under covariate shift according to one embodiment. Figure 3 shows an example of shuffled data under covariate shift according to one embodiment. Figure 4 is a block diagram showing an example of the hardware configuration of a model learning device according to one embodiment. Figure 5 is a block diagram showing the software configuration of a model learning device according to one embodiment in relation to the hardware configuration shown in Figure 4. Figure 6 is a flowchart showing an example of the operation in which a model learning device according to one embodiment estimates and outputs the parameters of a probabilistic model.

[0010] Each embodiment is described below with reference to the drawings. Each embodiment illustrates an apparatus or method for realizing the technical idea of ​​the invention. The drawings are schematic or conceptual. Hereafter, components having substantially the same function and configuration are denoted by the same reference numerals. The numbers following the letters that constitute the reference numerals are used to distinguish elements that are referenced by reference numerals containing the same letters and that have similar configurations.

[0011] [Embodiment] (1) Preparation First, we define regular supervised data (hereinafter referred to as couple data) and the shuffle data used in this study, and describe the formulation and method in existing CR for covariate shift adaptation. (1.1) Couple data and shuffle data The space of input features is represented as follows.

[0012]

[0013] Furthermore, the space for target output values ​​is represented as follows:

[0014]

[0015] In CR, n ｃｔｒ Consider a setup where couple training data defined as a set of individual training samples, expressed as follows, is available.

[0016]

[0017] However, x ｃｔｒ ｉ ∈X and yｃｔｒ ｉ ∈Y represents the input feature amount and the target output value of the i-th sample respectively. In this coupled training data, the input and output correspond one-to-one. In contrast, in the case of shuffle regression (SR), only the shuffled training data D ｓｔｒ is given. Consider the setting where only the shuffled training data D ｓｔｒ is defined as follows by a three-tuple of the size of the set

[0018]

[0019] , the set x of input feature amounts ｓｔｒ , and the set y of target output values ｓｔｒ .

[0020]

[0021] Here, n represents the total number of the three-tuples (the size of the data). When the size of the set of the i-th sample is m ｓｔｒ ｉ =K, x ｓｔｒ ｉ and y ｓｔｒ ｉ are respectively sets of K input feature amounts and target output values, and are represented as follows.

[0022]

[0023]

[0024] However, x ｓｔｒ ｉｋ ∈X, y ｓｔｒ ｉｋ ∈Y. The output corresponding to the k-th element x ｓｔｒ ｉｋ of the i-th input set is one of the elements of the i-th output set

[0025]

[0026] , but it is not known which one.

[0027] When the size of each sample of the shuffled data is all 1 (m ｓｔｒ ｉ=1), since shuffled data becomes couple data, it can be said that shuffled data is a more general representation of data that includes couple data. Also, the sample size of the couple data during testing will be (x ｃｔｅ , y ｃｔｅ We will represent it as ) and from now on, we will represent the sample of shuffled data as follows.

[0028]

[0029] In this covariate shift adaptation, in addition to the training data, unlabeled data following a test distribution (data that does not include the target output value) is used. Details will be described later.

[0030] Unlabeled couple data is represented as follows:

[0031]

[0032] Furthermore, unlabeled shuffled data can be represented as follows:

[0033]

[0034] In early shuffle regression studies, the assumption that the data size is n=1 has been used. However, in practice, data is often collected multiple times by repeating measurements or changing the target user group. In this case, even if the correspondence between input and output is hidden for privacy reasons, it is possible to know from which measurement / user group the data was collected, and it will be represented as shuffled data with n>1.

[0035] (1.2) Covariate Shift in CR Here, we describe existing methods that adapt to covariate shift in the setting of CR. Each sample of the training data (x ｃｔｒ , y ｃｔｒ ) is a certain probability density q ｔｒ Assume that the data is generated independently from a training distribution with (x, y). This training distribution is the input distribution q. ｔｒ (x) and conditional distribution q ｔｒ It can be decomposed into a product of (y|x), and q ｔｒ (x, y) = q ｔｒ (x)qｔｒ It can be written as (y | x). Similarly, the test sample (x ｃｔｅ , y ｃｔｅ ) is the test distribution q ｔｅ (x, y) = q ｔｅ (x)q ｔｅ Assume that (y | x) is generated independently.

[0036] In covariate shift settings, the input distribution differs between training and testing (i.e., q ｔｒ (x) ≠ q ｔｅ (x)) Consider the settings.

[0037] Figure 1 shows an example of the probability distribution of input features according to one embodiment. As shown in Figure 1, in one embodiment, the probability distributions of the training distribution qtr and the test distribution qte are different. Here, the support of these two distributions is equal (support(q)) such that the importance / density ratio, which will be defined later, is bounded. ｔｒ (x))=supp(q ｔｅ (x)))) Let's assume that the conditional distribution remains constant during training and testing (therefore, q from now on) ｃ (y | x) : = q ｔｒ (y | x) = q ｔｅ (represented as (y|x)). Therefore, under covariate shift, the joint probability distributions during training and testing will be different from each other (i.e., q ｔｒ (x, y) ≠ q ｔｅ (x, y)).

[0038] Figure 2 shows an example of coupled data under a covariate shift according to one embodiment. As shown in Figure 2, a covariate shift is also considered one of the special cases of a setting called a dataset or distribution shift.

[0039] The objective of CR is to create a probabilistic model f with parameter θ∈Θ. θ Using (y | x), the test loss R is defined below. ＣＲ The goal is to obtain the parameter that minimizes [the specified value].

[0040]

[0041] Here, the most standard probabilistic model is the regression function model h θ (x): X → Y and Gaussian distribution N(y | μ, σ) ２ f is defined using ) θ (y|x)=N(y|h θ (x), 1.0 ２ ) are examples. Using this model, the squared error loss function can be derived.

[0042] In CR methods adapted to covariate shifts (for example, the method described in Non-Patent Document 5), the expected value of the test loss (Equation (1)) is taken in a different way and expressed as follows.

[0043]

[0044] However, r(x) := q ｔｅ (x) / q ｔｒ (x) is a quantity called importance or density ratio. Using this quantity, the test distribution q in equation (1) can be expressed as follows: ｔｅ The expected value with respect to the training distribution q is given by equation (2). ｔｒ It is replaced with the expected value related to D. IWR (Importance Weighted Regression) is the expected value of equation (2) with the couple training data D ｃｔｒ The quantity approximated by the sample

[0045]

[0046] We will use this. And the quantity in question is expressed as follows.

[0047]

[0048] If the importance r(x) is known, then use the training data

[0049]

[0050] Since this can be calculated, the parameter θ can be estimated by minimizing it.

[0051]

[0052] is an unbiased estimator of the test loss (equation (1)), but it has been pointed out that the parameters estimated by IWR have problems with robustness and stability. This is because r(x) is unbounded, and the denominator q ｔｒ This is because when (x) is small, it can take on extremely large values. Therefore, instead of importance, we use exponentially-flatten adaptive importance {r(x)}. γ (0 ≤ γ ≤ 1) (see, for example, Non-Patent Document 5), or relative importance r α (x) (See, for example, Reference 1 (Makoto Yamada, Taiji Suzuki, Takafumi Kanamori, Hirotaka Hachiya, and Masashi Sugiyama. Relative density-ratio estimation for robust distribution comparison. Neural computation, Vol.25, No.5, pp. 1324-1370, 2013)) an input distribution called q ｔｅ (x) and α mixture distribution q α (x) = αq ｔｅ (x) + (1 - α)q ｔｒ A quantity r defined as the ratio of (x) (0 ≤ α < 1) α (x) := q ｔｅ (x) / q α (x) is often used.

[0053] To summarize the above, the objective function of a CR method adapted to covariate shifts can be expressed by the following equation.

[0054]

[0055] The method of estimating the parameters by minimizing equation (3) is called EIWR (Exponentially-flatten Importance Weighted Regression) when α > 0 and γ = 1, and RIWR (Relative Importance Weighted Regression) when α > 0 and γ = 1. Furthermore, when α = 0 and γ = 1, the loss function of IWR is

[0056]

[0057] This matches. Note that the relative importance r α (x) is different from the usual importance, if α > 0, then if the support does not match (supp(q ｔｅ (x))≠supp(q ｔｒ (x))) is bounded, and therefore is a quantity that can be defined without assuming the agreement of supports. The objective function of equation (3) has a regularization term with respect to the parameter θ (for example, L １ Regularization and L ２ In some cases, we consider objective functions that incorporate regularization or other modifications. To apply the methods described in this section, the importance or relative importance values ​​used in equation (3) must be known. Next, we will explain how to estimate these.

[0058] (1.3) Estimation of Importance (Density Ratio) The importance r(x) can be estimated using any density ratio estimation method (for example, the method described in Reference 2 (Masaru Sugiyama, A New Approach to Machine Learning Based on Density Ratios. Statistical Mathematics, Vol. 58, No. 2, pp. 141-155, 2010) and its advanced methods). Here, we will describe a method called RuLSIF (Relative unconstrained Least-Squares Importance Fitting) (see, for example, Reference 1), which can be used to estimate both importance and relative importance. RuLSIF uses an importance model g with parameter η. η This method uses (x) to estimate the parameter η in a way that minimizes the squared error of the relative importance with respect to the model defined by the following equation.

[0059]

[0060] Input features of the couple training data

[0061]

[0062] and (test distribution q ｔｅ (Obtained from x) Unlabeled test data

[0063]

[0064] When taking the sample average using [ ], the squared error \(J\) can be approximated by the following formula.

[0065]

[0066] The approximated squared error

[0067]

[0068] The model obtained by substituting the parameter \(\hat{\eta}\) obtained by minimizing [ ]

[0069]

[0070] can be used as the importance \(r(x)\) and relative importance \(r\) α \((x)\) in the previous section. When estimating the (usual) importance with RuLSIF, the parameter \(\alpha = 0\) can be set.

[0071] (2) Definition of Covariate Shift in Shuffled Regression In shuffled regression (SR), the training samples \((m\) ｓｔｒ , \(x\) ｓｔｒ , \(y\) ｓｔｒ ) and test samples \((m\) ｓｔｅ , \(x\) ｓｔｅ , \(y\) ｓｔｅ ) are generated independently according to the training distribution \(q\) ｓｔｒ \((m, x, y)=q\) ｓｔｒ \((m, x)q\) ｓｔｒ \((y|x)\) and the test distribution \(q\) ｓｔｅ \((m, x, y)=q\) ｓｔｅ \((m, x)q\) ｓｔｅ \((y|x)\) respectively. The joint probability distribution of the set size \(m\) and the input set \(x\) can be decomposed as \(q\) ｓｔｒ \((m, x)=q\) ｓｔｒ \((m)q\) ｓｔｒ \((x|m)\). From now on, similar to the covariate shift in CR in the previous section, in the covariate shift in SR, the following assumption (Assumption 1 (A1)) is assumed to hold.

[0072] A1: Identical Conditional Distributions The conditional probability is constant and does not change between training and testing. That is, the following equation holds.

[0073] \(q\) ｓｔｒ(y|x) = q ｓｔｅ (y|x) (=: q ｓ (y|x))

[0074] For the algorithm and theoretical construction of the proposed method, it is also assumed that one or both of two assumptions (Assumption 2 (A2) and Assumption 3 (A3)) hold as necessary.

[0075] Assumption A2: Decomposition of Input Distributions Each element of the input set during training and testing is independently generated according to the training distribution q ｔｒ (x) and the test distribution q ｔｅ (x). That is, the training distribution q ｔｒ (x) and the test distribution can be decomposed as follows.

[0076]

[0077] Assumption A3: Identical Support The size m of the set and the support of the joint probability distribution of the input set x are constant during training and testing. That is, the following equation holds.

[0078] supp(q ｓｔｒ (m, x)) = supp(q ｓｔｅ (m, x))

[0079] In ordinary SR, the probability distribution for generating data is assumed to be constant during training and testing. In contrast, in SR under covariate shift, the probability distribution followed by the set size and input values is not constant (i.e., q ｓｔｒ (m, x) ≠ q ｓｔｅ (m, x)), and a more general setting is considered. Under this general setting, the joint probability distribution of the input and output also becomes non-constant (i.e., q ｓｔｒ (m, x, y) ≠ q ｓｔｅ (m, x, y)).

[0080] FIG. 3 is a diagram showing an example of shuffled data under covariance according to an embodiment. Regarding Assumption A2 (Remark on A2): To adapt to the differences in the set size and the probability distribution followed by the input feature amounts, the shuffled training data D ｓｔｒIn addition, probability distribution q ｓｔｅ Assume that unlabeled test data obtained from (m, x), represented by the following formula, is available.

[0081]

[0082] This input set

[0083]

[0084] Under assumption A2, the test distribution q ｔｅ (x)

[0085]

[0086] It can be considered as individual data points.

[0087] Regarding assumption A3 (Remark on A3): In SR, the size of the set in the training data is often always greater than 1 (q ｓｔｒ (m=1)=0), the size in the test data is always assumed to be 1 (q ｓｔｒ (m=1)=1). This does not satisfy the assumption that the support of assumption (A3) is constant. Therefore, similar to the CR shown in the previous section, we derive the theory using this assumption, and then derive an algorithm that does not depend on this assumption using relative importance.

[0088] (3) Conditional probability model: shuffle regression (SR) conditional probability q ｓ (y | x) is a probability model f (with the same definition as CR). θ It is defined using a latent variable, a permutation matrix P (see, for example, Non-Patent Document 1). The permutation matrix is ​​used to rearrange the order of each element in the input set. A permutation matrix P of size K × K has elements [P] ｋｌ It is a double probability matrix where is either 0 or 1, and satisfies the following conditions:

[0089]

[0090] Hereafter, we will denote the set of all permutation matrices of size K×K as Π(K). The number of elements in this set is |Π(K)| = K!. Given a set size m and an input set x, the process of generating the output set y consists of the following two steps: For each sample i=1, ..., n, set size m ｉ and input set x ｉ Suppose the following is given. Under these conditions, (Step 1) Permutation matrix P ｉ is a uniform distribution uni(P ｉ It is generated according to ) however all P∈Π(m ｉ ) and uni(P) = 1 / m ｉ ! (Step-2) Output set y ｉ The following probability distribution is used to generate them.

[0091]

[0092]

[0093] is the input set x ｉ Matrix representation of (matrix X) ｉ The kth row is x ｉｋ (corresponding to) and [P ｉ X ｉ ] ｋ This is matrix P ｉ X ｉ This represents the k-th row vector. This probability distribution is determined by the order of the elements of the input set (matrix X) by the permutation matrix. ｉ (Row) swapped, and the probability model f θ Output set y ｉ This shows that each element is determined. Note that the order of operations on this probability model and the permutation matrix can be changed.

[0094] Here, this generation process is common to both training and testing because the conditional probabilities are invariant. Therefore, the superscripts x and y (str and ste) are omitted.

[0095] Based on the above generation process, and given the input set x, the permutation matrix P is generated. ｉ and output set y ｉ The joint probability is given by the following formula:

[0096]

[0097] Permutation matrix P ｉ By marginalizing and eliminating it, the output set y is obtained given the input set x. ｉ The probability distribution can also be obtained.

[0098]

[0099] In shuffle regression (SR), the goal is to estimate the parameter θ∈Θ that minimizes the following test loss.

[0100]

[0101] Note that this test loss (equation (5)) is given when the size m of the set is always 1 (q ｓｔｅ (m=1)=1) is a more general loss function that matches the test loss in normal supervised regression (Equation (1)).

[0102] (4) Due to the difference between the training and test distributions for covariate shift adaptation in shuffle regression, it is easy to imagine that the standard method of SR will fail under covariate shift. Therefore, in one embodiment, an approach using importance is adopted, similar to variable shift adaptation in normal supervised regression (CR). This uses the following equation for the loss function (equation (5)).

[0103] Theorem 1.1 Under assumption A1 and assumption A3, the following equation holds:

[0104]

[0105] However, u(m, x) := q ｓｔｅ (m, x) / q ｓｔｒ (m, x) represents the importance in SR.

[0106] Proof hypothesis A3 implies that u(m,x) is bounded. By hypothesis A1, the following equation holds.

[0107]

[0108] Furthermore, when hypothesis A2 holds, the importance u(m,x) can be decomposed as follows.

[0109]

[0110] From the above theorem, a method can be considered to minimize the following equation, which is a sample approximation of equation (6).

[0111]

[0112] However, as stated in "Regarding Assumption A3," the support for the probability distribution of the input set and set size may not coincide between training and testing. In such cases, to avoid the importance values ​​diverging, it is considered promising to use an approach that utilizes relative importance (and exponential flattening such as adaptive importance), similar to the objective function of a normal supervised regression (CR) (Equation (3)). Therefore, as a covariate shift adaptation method in SR, the following objective function is used (under Assumption A2).

[0113]

[0114] However, the United Nations α (m, x) is the relative importance in SR as defined below, based on the importance in equation (7).

[0115]

[0116] Purpose

[0117]

[0118] This is the loss function when γ = 1.0 and α = 0.0.

[0119]

[0120] It matches.

[0121] Equation (8) is defined even if the supports do not match, but in the case of a disjoint where there is no overlap at all in the supports.

[0122]

[0123] Therefore, it cannot be said to be effective. Thus, in such cases, the term relating to the distribution with respect to the set size m is not used, and the relative importance is calculated using the term relating to the distribution of the input set as follows.

[0124]

[0125] We will use an objective function that utilizes [this method].

[0126]

[0127] However, relative importance is expressed as follows:

[0128]

[0129] Note the above loss function

[0130]

[0131] This does not include a regularization term with respect to the parameter θ, but L １ Regularization, L ２ You can also consider the objective function as a result of adding any regularization terms, such as regularization terms.

[0132] (5) Overview of the parameter estimation algorithm The overall estimation of the proposed method consists of (Step-1) estimation of relative importance (Equation (9) or Equation (11)) and (Step-2) weighted shuffle regression that minimizes the objective function (Equation (8) or Equation (10)).

[0133] (6) Estimation of Importance (Density Ratio) in Shuffle Regression - The method of one embodiment requires the use of (relative) importance, similar to the method of covariate shift adaptation in CR. (Relative) importance is estimated using the density ratio estimation method, similar to the case of CR, on the shuffle training data D ｓｔｒ Shuffled data without labels

[0134]

[0135] It can be estimated from the relative importance r of the input features. For example, the relative importance r of the input features. α Importance model that approximates

[0136]

[0137] This uses RuLSIF (see, for example, reference 1) to determine the objective function

[0138]

[0139] It can be estimated by minimizing the distribution q related to the size of the set. ｓｔｒ (m) and q ｓｔｅSince (m) are both discrete probability distributions, the relative importance of these distributions can also be calculated by taking the ratio of the individual estimation results. Therefore, the relative importance can be calculated using equations (9) and (11).

[0140]

[0141] An estimated value is obtained.

[0142] (6) A weighted shuffle regression algorithm that minimizes the weighted shuffle regression objective function (equation (8) or equation (10)) can be constructed by modifying any existing algorithm used in SR, such as the expectation-maximization (EM) algorithm (see, for example, Non-Patent Documents 1 and 4). When using a sparse EM algorithm (see, for example, Non-Patent Document 4), the probability distribution q with respect to the permutation matrix is ​​as shown below. ｐｅｒｍ An algorithm can be constructed that repeatedly performs an E-step to update the parameter and an M-step to update the parameter θ.

[0143]

[0144] Here, this is the algorithm when equation (8) is used as the objective function. The algorithm is almost the same when equation (10) is used.

[0145] In step E described above, the permutation matrix is ​​a candidate set consisting of L permutation matrices.

[0146]

[0147] A sparse constraint is introduced so that the probability of being anything other than the given set is 0. Candidate set

[0148]

[0149] This can be created by sorting the output of the model and is updated at regular intervals (for details, see, for example, Non-Patent Document 4). The objective function F in M-step can be interpreted as the objective function of weighted regression in normal CR. Specifically, the objective function F is such that each sample is an input feature

[0150]

[0151] , output y ｉｋ , weight z ｉｌ {u α (m ｉ , x ｉ )} γ This matches the objective function of weighted regression given the following. Therefore, if the probabilistic model f is a model defined by a Gaussian distribution and a linear regression function, this sparse EM algorithm can also be interpreted as Iterative Reweighted Least Squares (IRLS). When the parameter γ used for exponential flattening is 0, this algorithm matches the existing algorithm in Non-Patent Document 4. Note that the above EM algorithm is just one example, and other algorithms (e.g., Non-Patent Document 2, Non-Patent Document 3) can also be used, and similar algorithms can be constructed by modifying them to handle (relative) importance weights. Any probability distribution and regression function can be used in the probabilistic model.

[0152] (Configuration) Next, the hardware and software configurations of the model learning device for carrying out the method described above will be explained. Figure 4 is a block diagram showing an example of the hardware configuration of the model learning device 1 according to one embodiment. The model learning device 1 is a computer that analyzes input data and generates and outputs output data. For example, the model learning device 1 is installed in any location set by the user who manages the model learning device 1.

[0153] As shown in Figure 4, the model learning device 1 comprises a control unit 10, a program storage unit 20, a data storage unit 30, a communication interface 40, and an input / output interface 50. The control unit 10, program storage unit 20, data storage unit 30, communication interface 40, and input / output interface 50 are connected to each other via a bus so as to be able to communicate with each other. Furthermore, the communication interface 40 may be connected to an external device so as to be able to communicate with it via a network. In addition, the input / output interface 50 is connected to an input device 2 and an output device 3 so as to be able to communicate with them.

[0154] The control unit 10 controls the model learning device 1. The control unit 10 includes a hardware processor such as a central processing unit (CPU). For example, the control unit 10 may be an integrated circuit capable of executing various programs.

[0155] The program storage unit 20 can use a combination of non-volatile memory that can be written to and read at any time, such as EPROM (Erasable Programmable Read Only Memory), HDD (Hard Disk Drive), and SSD (Solid State Drive), as a storage medium, and non-volatile memory such as ROM (Read Only Memory). The program storage unit 20 stores programs necessary to execute various processes. In other words, the control unit 10 can realize various controls and operations by reading and executing programs stored in the program storage unit 20.

[0156] The data storage unit 30 is a storage device that uses a combination of non-volatile memory, such as an HDD or memory card, which allows for writing and reading at any time, and volatile memory, such as RAM (Random Access Memory), as storage media. The data storage unit 30 is used to store data acquired and generated during the process in which the control unit 10 executes a program and performs various processing.

[0157] The communication interface 40 includes one or more wired or wireless communication modules. For example, the communication interface 40 includes a communication module that connects to an external device via a network, either wired or wirelessly. The communication interface 40 may also include a wireless communication module that connects to an external device wirelessly, such as a Wi-Fi access point and a base station. Furthermore, the communication interface 40 may include a wireless communication module that connects to an external device wirelessly using short-range wireless technology. In other words, the communication interface 40 can be any general communication interface that can communicate with an external device and send and receive various types of information under the control of the control unit 10.

[0158] The input / output interface 50 is connected to the input device 2, output device 3, etc. The input / output interface 50 is an interface that enables the transmission and reception of information between the input device 2, output device 3, etc. The input / output interface 50 may be integrated with the communication interface 40. For example, the model learning device 1 and at least one of the input device 2 or output device 3 may be wirelessly connected using short-range wireless technology, and information may be transmitted and received using said short-range wireless technology.

[0159] The input device 2 may include, for example, a keyboard or pointing device for the user to input various information to the model learning device 1. The input device 2 may also include a reader for reading data to be stored in the program storage unit 20 or data storage unit 30 from a memory medium such as a USB memory, or a disk device for reading such data from a disk medium.

[0160] The output device 3 includes a display, etc., that shows the results calculated by the control unit 10, such as a virtual space. The output device 3 also includes a printer, etc., that prints the information displayed on the display.

[0161] Figure 5 is a block diagram showing the software configuration of a model learning device 1 according to one embodiment, in relation to the hardware configuration shown in Figure 4. The control unit 10 includes an input data acquisition unit 101, an importance model parameter estimation unit 102, a probability model parameter estimation unit 103, and a probability model parameter processing unit 104.

[0162] The input data acquisition unit 101 is an acquisition unit that acquires input data. For example, the input data is shuffle training data D. ｓｔｒ , probability model f θ Importance model g η , unlabeled shuffled data D (following the test distribution) ｓｕｔｅ This includes hyperparameters (such as the relative importance parameter α, the regularization term added to the objective function, and the maximum number of iterations of the algorithm). The input data acquisition unit 101 stores the acquired input data in the input data storage unit 301.

[0163] The importance model parameter estimation unit 102 is an estimation unit that estimates the parameters η of the importance model. For example, the importance model parameter estimation unit 102 estimates the parameters of the importance model by minimizing an objective function using the shuffled training data, unlabeled test data, importance model, and hyperparameters included in the input data. For example, the importance model parameter estimation unit 102 estimates the parameters η of the importance model using a density ratio estimation method such as RuLSIF (see, for example, Reference 1). The importance model parameter estimation unit 102 stores the estimated parameters η of the importance model in the importance model parameter storage unit 302.

[0164] The probability model parameter estimation unit 103 is an estimation unit that estimates the parameters θ of the probability model. For example, the probability model parameter processing unit 104 calculates relative importance using a quantity defined by the ratio of the test distribution and a mixture distribution obtained by mixing the training distribution and the test distribution, based on the shuffled training data, probability model, importance model, and hyperparameters included in the input data, and the parameters of the importance model. Furthermore, the probability model parameter processing unit 104 estimates the parameters of the probability model by maximizing an objective function using the relative importance. For example, the probability model parameter processing unit 104 calculates relative importance (equation (9) or equation (11)). Then, the probability model parameter processing unit 104 maximizes the log-likelihood function of equation (8) or equation (10) using an EM algorithm or the like to find the parameters θ. The probability model parameter estimation unit 103 stores the calculated parameters θ in the probability model parameter storage unit 303.

[0165] The probability model parameter processing unit 104 is an output unit that outputs the parameter θ to the output device 3 or an external device. For example, the probability model parameter processing unit 104 outputs the parameter θ stored in the probability model parameter storage unit 303 to the output device 3 or an external device.

[0166] The data storage unit 30 includes an input data storage unit 301, an importance model parameter storage unit 302, and a probability model parameter storage unit 303. The input data storage unit 301 is used to store input data acquired by the input data acquisition unit 101. The importance model parameter storage unit 302 is used to store the importance model parameters estimated by the importance model parameter estimation unit 102. The probability model parameter storage unit 303 is used to store the probability model parameters estimated by the probability model parameter estimation unit 103.

[0167] [Operation] Figure 6 is a flowchart showing an example of the operation in which a model learning device 1 according to one embodiment estimates and outputs the parameters of a probabilistic model. The operation shown in this flowchart is realized when the control unit 10 of the model learning device 1 reads and executes a program stored in the program storage unit 20.

[0168] This operation is initiated when instructed by the user managing the model learning device 1.

[0169] In step ST101, the input data acquisition unit 101 acquires the training shuffle data D ｓｔｒ , probability model f θ Importance model g η , unlabeled shuffled data D (following the test distribution) ｓｕｔｅ The system acquires input data including unlabeled test data (i.e., unlabeled test data) and hyperparameters (such as the relative importance parameter α, the regularization term added to the objective function, and the maximum number of iterations of the algorithm). For example, when a user inputs input data into an input device 2, the input data acquisition unit 101 acquires the input data. The input data acquisition unit 101 stores the input data in the input data storage unit 301.

[0170] In step ST102, the importance model parameter estimation unit 102 estimates the parameters η of the importance model. The importance model parameter estimation unit 102 estimates the shuffled training data D included in the input data. ｓｔｒ、 Unlabeled test data, importance model g ηThe importance model parameter η^ is determined by taking the hyperparameters as input and using a density ratio estimation method such as RuLSIF (see, for example, Reference 1). After that, the importance model parameter estimation unit 102 stores the parameter η^ in the importance model parameter storage unit 302. In step ST103, the probability model parameter estimation unit 103 estimates the parameter θ of the probability model. The probability model parameter estimation unit 103 shuffles the training data D in the input data storage unit 301. ｓｔｒ , probability model f θ、 Importance Model g η、 The importance model parameter storage unit 302 takes the parameter η^ and hyperparameters as input, calculates the relative importance (equation (9) or equation (11)), and maximizes the log-likelihood function of equation (8) or equation (10) using the aforementioned EM algorithm or the like to find the parameter θ. Subsequently, the probability model parameter estimation unit 103 stores the calculated parameter θ in the probability model parameter storage unit 303.

[0171] In step ST104, the probability model parameter processing unit 104 outputs the parameter θ stored in the probability model parameter storage unit 303 to the output device 3 or an external device.

[0172] (Effects of the Embodiment) As described above, in one embodiment, the relationship between the loss function during training and testing in SR is theoretically analyzed using a ratio of two probability density functions called Importance (density ratio), and a new method based on this theoretical analysis is proposed. The theoretical analysis and formulation can be used regardless of the choice of model or parameter estimation algorithm, and it is possible to greatly expand the scope of application of SR.

[0173] Furthermore, in the model learning device 1 according to one embodiment, even when the probability distribution of the input features changes between training and testing, the regression function can be accurately estimated from shuffled data.

[0174] [Other Embodiments] In the above embodiment, we consider an objective function that does not include a regularization term for the parameters, but we may also consider an objective function with an arbitrary regularization term added, such as L1 regularization or L2 regularization. Furthermore, for optimizing the objective function, methods used for parameter optimization of any probabilistic model other than the EM algorithm, such as (stochastic) gradient methods, Newton's method, or Markov chain Monte Carlo methods, can be used. In addition, any model other than a linear model, such as a neural network, can be used as the regression function of the probabilistic model. Regarding the probability distribution of the model, in addition to the Gaussian distribution, distributions belonging to the exponential family of distributions such as the Bernoulli distribution and the Poisson distribution, or any probability distribution such as the Laplace distribution can be used.

[0175] Furthermore, in the above embodiment, the model learning device 1 can also construct the operation of each component as a program, install it on a computer used as a user device, or on a computer used as an external device, and run it.

[0176] Furthermore, the method described in the above embodiment can be distributed by storing the program (software means) that can be executed by a computer in a storage medium such as a magnetic disk (floppy disk, hard disk, etc.), an optical disk (CD-ROM, DVD, MO, etc.), or a semiconductor memory (ROM, RAM, flash memory, etc.), and by transmitting it via a communication medium. The program stored on the medium also includes a configuration program that configures the software means (including not only the execution program but also tables and data structures) to be executed by the computer. The computer realizing this device reads the program stored in the storage medium and, if necessary, constructs the software means using the configuration program, and executes the above-described process by controlling its operation with this software means. The storage medium referred to in this specification is not limited to distribution mediums, but also includes storage mediums such as magnetic disks and semiconductor memories provided inside the computer or in devices connected via a network.

[0177] In short, this invention is not limited to the embodiments described above, and can be modified in various ways during implementation without departing from its essence. Furthermore, each embodiment may be combined as appropriately as possible, in which case the combined effects can be obtained. Moreover, the embodiments described above include inventions at various stages, and various inventions can be extracted by appropriate combinations of the multiple constituent elements disclosed.

[0178] 1...Model learning device 10...Control unit 101...Input data acquisition unit 102...Importance model parameter estimation unit 103...Probability model parameter estimation unit 104...Probability model parameter processing unit 20...Program storage unit 30...Data storage unit 301...Input data storage unit 302...Importance model parameter storage unit 303...Probability model parameter storage unit 40...Communication interface 50...Input / output interface 2...Input device 3...Output device

Claims

1. A model learning device comprising: an input data acquisition unit that acquires input data including shuffled training data following a training distribution, unlabeled test data following a test distribution having a probability distribution different from the training distribution, a probability model, an importance model, and hyperparameters; an importance model parameter estimation unit that estimates the parameters of the importance model by minimizing an objective function using the shuffled training data, unlabeled test data, importance model, and hyperparameters included in the input data; a probability model parameter estimation unit that calculates relative importance using a quantity defined by the ratio of the test distribution and a mixed distribution obtained by mixing the training distribution and the test distribution, based on the shuffled training data, probability model, importance model, and hyperparameters included in the input data and the parameters of the importance model, and estimates the parameters of the probability model by maximizing an objective function using the relative importance; and a probability model parameter processing unit that outputs the parameters of the probability model.

2. The support for the training distribution and the test distribution are equal, the model learning apparatus according to claim 1.

3. A model learning method executed by the processor of a model learning device, comprising: acquiring input data including shuffled training data following a training distribution, unlabeled test data following a test distribution having a probability distribution different from the training distribution, a probability model, an importance model, and hyperparameters; estimating the parameters of the importance model by minimizing an objective function using the shuffled training data, unlabeled test data, importance model, and hyperparameters included in the input data; calculating relative importance using a quantity defined by the ratio of the test distribution and a mixed distribution obtained by mixing the training distribution and the test distribution, based on the shuffled training data, probability model, importance model, and hyperparameters included in the input data and the parameters of the importance model; estimating the parameters of the probability model by maximizing an objective function using the relative importance; and outputting the parameters of the probability model.

4. A model learning program comprising instructions to be executed by the processor of a model learning device, wherein the instructions include: acquiring input data including shuffled training data following a training distribution, unlabeled test data following a test distribution having a probability distribution different from the training distribution, a probability model, an importance model, and hyperparameters; estimating the parameters of the importance model by minimizing an objective function using the shuffled training data, unlabeled test data, importance model, and hyperparameters included in the input data; calculating relative importance using a quantity defined by the ratio of the test distribution and a mixed distribution obtained by mixing the training distribution and the test distribution, based on the shuffled training data, probability model, importance model, and hyperparameters included in the input data and the parameters of the importance model; estimating the parameters of the probability model by maximizing an objective function using the relative importance; and outputting the parameters of the probability model.

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