JP2016194913A - Sectional linear model generation system and generation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a sectional linear model generation system and generation method.SOLUTION: A sectional linear model generation system includes: an acquisition module 201 that is adapted to acquire data for a plurality of tasks; a first setting module 202 that is adapted to set a relevant latent variable expressing relevancy among the plurality of tasks; a second setting module 203 that is adapted to set a model structure for a plurality of sectional linear models, and is adapted to initialize a corresponding model parameter and hierarchical latent variable; and a model optimization module 206 that is adapted to optimize the model structure and the model parameter on the basis of the data for the plurality of tasks, the task relevant latent variable and the hierarchical latent variable.SELECTED DRAWING: Figure 2

Description

  Various embodiments of the present disclosure relate to the field of machine learning, and more specifically to piecewise linear model generation systems and methods.

  In many enterprise-level machine learning applications, piecewise linear models (eg, hierarchical mixed experts, HMEs) are widely used. HME is more flexible than general linear models and has the important advantage of using probabilistic rule-based partitioning on feature space and piecewise local linear experts. The learning procedure of the HME is composed of the division structure discrimination and individual expert modeling. This becomes difficult when the training sample contains a lot of noise and the sample size is not enough. Furthermore, a flexible HME can lead to poor generalized performance due to overfitting to the training data set.

  In practical applications, there is often a set of related machine learning tasks, such as predicting energy demand for buildings in a community. A simple approach is to solve these tasks independently, ignoring the commonality between these related tasks (single task learning, STL). In multitask learning (MTL), these related tasks are learned together by utilizing appropriate shared information across the tasks. Learning multiple related tasks together has the potential to improve generalization performance because it effectively increases the sample size for each task.

  Through intertask sharing information, multitask learning processes samples together across different tasks so that the amount of samples can be increased and adaptive noise can be prevented. However, current multitask learning techniques are mainly used for fixed model structures, such as linear regression scenarios. For piecewise linear models such as HME, both model structure and model parameters must be learned. However, current multitask learning cannot.

  An object of the present disclosure is to provide a piecewise linear model generation system and generation method in order to at least partially solve the above-described problems in the prior art.

According to one aspect of the present disclosure,
An acquisition module configured to acquire data for multiple tasks;
A first setting module configured to set a task related latent variable representing the relationship between the plurality of tasks;
A second setting module configured to set a model structure for a plurality of piecewise linear models and initialize corresponding model parameters and hierarchical latent variables;
A model optimization module configured to optimize the model structure and the model parameters based on the data for the plurality of tasks, the task related latent variables and the hierarchical latent variables. ,
A piecewise linear model generation system is provided.

According to an exemplary embodiment of the present disclosure,
The task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models.

  According to an exemplary embodiment of the present disclosure, the model structure has a tree structure.

According to an exemplary embodiment of the present disclosure, the system includes:
A hierarchical latent variable optimization module configured to optimize the hierarchical latent variable based on data for the plurality of tasks, the task related latent variable, the model structure and the model parameter. Are further provided.

According to an exemplary embodiment of the present disclosure, the system includes:
A task-related potential variable optimization module configured to optimize the task-related potential variable based on the data for the plurality of tasks, the hierarchical potential variable, the model structure, and the model parameter. Are further provided.

According to an exemplary embodiment of the present disclosure, the system includes:
A determination module configured to determine whether the model structure and the model parameters are optimal;

According to an exemplary embodiment of the present disclosure,
The discrimination module discriminates whether or not the model structure and the model parameter are optimal based on the degree of matching between the model structure and the model parameter.

According to another aspect of the disclosure,
Getting data for multiple tasks,
Setting a task related latent variable representing the relationship between the plurality of tasks;
Setting up a model structure for a plurality of piecewise linear models and initializing corresponding model parameters and hierarchical latent variables;
Optimizing the model structure and the model parameters based on data for the plurality of tasks, the task-related latent variables and the hierarchical latent variables;
A piecewise linear model generation method is provided.

According to an exemplary embodiment of the present disclosure,
The task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models.

  According to an exemplary embodiment of the present disclosure, the model structure has a tree structure.

According to an exemplary embodiment of the present disclosure, the method comprises:
Further comprising optimizing the hierarchical latent variables based on the data for the plurality of tasks, the task related latent variables, the model structure and the model parameters.

According to an exemplary embodiment of the present disclosure, the method comprises:
And further optimizing the task-related potential variables based on the data for the plurality of tasks, the hierarchical potential variables, the model structure, and the model parameters.

According to an exemplary embodiment of the present disclosure, the method comprises:
Determining whether the model structure and the model parameters are optimal.

According to an exemplary embodiment of the present disclosure,
Determining whether the model structure and the model parameters are optimal,
Determining whether or not the model structure and the model parameter are optimal based on a goodness of fit between the model structure and the model parameter.

  In the technical solutions of the various embodiments of the present disclosure, new potential variables are added during the model generation process to represent relationships between tasks to facilitate the generation of piecewise linear models. Data for multiple tasks can be used for modeling, thereby improving the accuracy of model generation.

  These and other objects, features and advantages will become apparent from the following detailed description of exemplary embodiments with reference to the accompanying drawings.

FIG. 1 schematically illustrates a flowchart of a piecewise linear model generation method according to an embodiment of the present disclosure. FIG. 2 schematically illustrates a block diagram of a piecewise linear model generation system according to one embodiment of the present disclosure. FIG. 3 graphically and schematically illustrates the steps of a piecewise linear model generation method according to an embodiment of the present disclosure.

  The principles and methods of the present disclosure will now be described with reference to a plurality of exemplary embodiments in the accompanying drawings. These embodiments are described only to enable those skilled in the art to better understand and to practice the present disclosure, and are not intended to limit the scope of the present disclosure in any way. I want you to understand.

  Before describing a piecewise linear model generation method and generation system according to various embodiments of the present disclosure, some technical concepts appearing herein will be described first.

Piecewise Linear Model The pioneer of piecewise linear models is regression trees where the partition is specified by a chain of rules and the local expert is a fixed value. Although the representation of the regression tree is well interpretable, the prediction ability of individual experts is not high, and the tree height tends to increase to achieve good prediction performance.

Hierarchical Mixed Expert (HME)
The HME employs a piecewise governance method to build a piecewise model. The structure divided into trees is determined by a “gating” function, which is a probabilistic, soft-partitioning function. The HME can represent any partition structure by designing a gating function, but only a (tree) partition structure with chained rules so that the learned partition structure is practically understandable. , Employed herein.

ここで、θ及びγは、ゲーティングノードからのパラメータ、Ｅは、エキスパートの数、ε_ｊは、ルートノードからｊ番目のエキスパートノードまでの一意の経路上のゲーティングノードの全てのインデックスを含むインデックスのセットである。ｇ（ｘ，α_ｉ）は、α_ｉ＝（β_ｉ；γ_ｉ）によってパラメータ化されたゲーティング関数と呼ばれ、ψ_ｇ（ｘ，ｉ，ｊ）は、エキスパートｊ及びｉの左のサブツリーに属するｘの確率である。ｐ（ｙ｜ｘ，φ_ｊ）は、φ_ｊ＝（ω_ｊ，σ_ｊ ^２）によってパラメータ化されたガウス雑音を有するｊ番目のエキスパートの条件付き分布である。 The HME model is defined as follows.

Where θ and γ are parameters from the gating node, E is the number of experts, ε _j contains all the indices of the gating nodes on a unique path from the root node to the jth expert node A set of indexes. g (x, α _i ) is called the gating function parameterized by α _i = (β _i ; γ _i ), and ψ _g (x, i, j) is the left subtree of experts j and i Is the probability of x belonging to. p (y | x, φ _j ) is a conditional distribution of the j-th expert with Gaussian noise parameterized by φ _j = (ω _j , σ _j ² ).

があると仮定しよう。

は、ｘ^Ｎに対応する潜在的変数を表し、混合成分ｘ^（ｎ）を生成することを示す。そのような潜在的変数モデルは、因子分解情報基準（ＦＩＣ）に基づいて近時開発されたベイズ近似推論である、因子分解漸近ベイジアン（ＦＡＢ）推論によって解かれ得る。ＦＩＣは、以下のように、周辺対数尤度の漸近的近似として得られる。

ここで、ｑ（ｚ^Ｎ）は、ｚ^Ｎ上の変分分布であり、

は、モデルパラメータの最大尤度推定量である。ＦＩＣ^ｍｍにおける最も重要な項は、ｌｏｇΣ_ｎｚ_ｋ ^（ｎ）であり、そのようなＦＡＢ推論に理論的に望ましい性質を、無関係の潜在的変数の自動収縮及びパラメータの識別可能性として提供する。 FAB for mixed models (factored asymptotic Bayesian)
Now observation data

Let's assume there is.

Indicates that represents the latent variables corresponding to x ^N, to produce a mixed component x ^(n). Such a latent variable model can be solved by factored asymptotic Bayesian (FAB) reasoning, which is a Bayesian approximate reasoning recently developed based on factorized information criteria (FIC). The FIC is obtained as an asymptotic approximation of the marginal log likelihood as follows.

Where q (z ^N ) is a variational distribution on z ^N

Is the maximum likelihood estimator of the model parameter. The most important term in FIC ^mm is log Σ _n z _k ⁽ⁿ⁾ , which provides the theoretically desirable properties for such FAB inference as automatic contraction of irrelevant potential variables and parameter identifiability.

  FAB optimizes the lower bound that FIC can handle. For q and θ, maximizing the lower bound alternately ensures a monotonic increase in the lower bound of the FIC.

ここで、

は、トレーニングサンプルから推定されるパラメータであり、Ｌ（Ｗ）は、トレーニングセット上の経験的損失であり、Ω（Ｗ）は、タスク関連性を符号化する正規化項である。タスク関連性に関する異なる仮定は、異なる正規化項に至る。マルチタスク学習の分野においては、新規な正規化を用いてタスク間の関係をモデリングする多数の従来成果がある。 Multitask learning (MTL)
A common paradigm for MTL in machine learning is to minimize punishable empirical losses.

here,

Is a parameter estimated from the training sample, L (W) is the empirical loss on the training set, and Ω (W) is a normalization term that encodes the task relevance. Different assumptions about task relevance lead to different normalization terms. In the field of multitasking learning, there are a number of conventional achievements of modeling the relationship between tasks using new normalization.

  In the following, the concept of the present invention will be described with reference to an exemplary embodiment as shown in FIGS. In the following description, the principles of the present disclosure will be described with an HME model as an example of a piecewise linear model. However, the present disclosure is not limited to the HME model and can be applied to other piecewise linear models.

  The substance of the present disclosure is to address the difficult task of generating piecewise linear models using multitask learning. In this disclosure, factorized asymptotic Bayesian (FAB) and multitask learning (MTL) theories are combined. First, let's assume that a subset of tasks follows the same distribution. In the context of this disclosure, multitask learning intends to find clusters of tasks that belong to the same distribution and fit each cluster using a piecewise linear model (eg, HME model). Tasks in the same cluster can improve learning performance with each other's strength.

  FIG. 1 schematically illustrates a flowchart of a piecewise linear model generation method according to an embodiment of the present disclosure. As shown in FIG. 1, the piecewise linear model generation method generally obtains data for a plurality of tasks at 101 and a task-related latency representing an association between the tasks at 102. Setting a global variable; setting a model structure for a plurality of piecewise linear models at 103; initializing corresponding model parameters and hierarchical latent variables; and 103 for a plurality of tasks. Optimizing the model structure and model parameters based on the data, task-related latent variables and hierarchical latent variables. Hereinafter, each step will be described in detail.

  In step 101, data for N tasks may be obtained.

  In step 102, a task related latent variable representing the relationship between a plurality of tasks is set. As an example, the task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models. In other words, the relationship between tasks can be represented by the probability of each task belonging to the model. If two tasks belong to the same model, they are considered related.

  In step 103, model structures for a plurality of piecewise linear models are established and their model parameters and hierarchical latent variables are initialized. As an example, the model structure may be a tree structure and the initialization process may be performed stochastically.

  According to an exemplary embodiment, the piecewise linear model generation method includes data for a plurality of tasks, task-related potential variables, model structures, and model parameters after step 103 and before step 106. Further, step 104 may be included, which is based on optimizing hierarchical latent variables. In step 103, the hierarchical latent variables are initialized stochastically so that they can be optimized in this step 104. The hierarchical latent variable is for explaining how to divide the data, after which the feature space is divided into multiple pieces, each piece represented by a local expert. The The process of splitting pieces by hierarchical latent variables is clustered by sample, not by feature. That is, any sample is placed in one piece and any sample is placed in another piece. In a particular example, each sample is clustered according to probability. A particular optimization method may employ the process shown in Equation 9 described below.

  According to an exemplary embodiment, the piecewise linear model generation method includes data for multiple tasks, hierarchical latent variables, model structures, and model parameters after step 104 and before step 106. Based on this, the method may further include a step 105 of optimizing task-related potential variables. Since the task related latent variables set in step 102 are generated through probabilistic initialization, they need to be optimized. In this step, task-related potential variables can be optimized by using the hierarchical potential variables optimized in step 104 in conjunction with data, model structure and model parameters for multiple tasks. A particular optimization method may employ the process shown in Equation 8 described below.

  According to one exemplary embodiment, in step 106, the hierarchical latent variables optimized in step 104 and the task related latent variables optimized in step 105 optimize the model structure and model parameters. Therefore, it can be used in conjunction with data for multiple tasks. A particular optimization method may employ the process shown in Equation 10 described below.

  According to an exemplary embodiment, the piecewise linear model generation method may include a step 107 after step 106 to determine whether the model structure and model parameters are optimal, and if so, the result Step 108 is performed to output the resulting piecewise linear model, and if not optimal, return to step 104 to continue optimizing the model structure and model parameters. The evaluation index for the discrimination can be a goodness of fit between the model and the data. The fitness cannot increase without an upper limit. Instead, there is an upper limit. After increasing to some extent during the stepwise process, the increment for continued optimization is very small. When the increment is small enough, it is considered that an optimal model has been obtained, thereby aborting the optimization and in step 108 the resulting piecewise linear model is output.

  The particular embodiment described above with reference to FIG. 1 described the principle of piecewise linear model generation according to the present disclosure. However, those skilled in the art will appreciate that the piecewise linear model generation method according to the present disclosure is not limited to the specific steps described above, but instead is based on the scope limited in the claims. Based on different needs, one of ordinary skill in the art will readily envision removing or adding one or more steps.

  Next, based on a specific example, the optimization method applicable in steps 104 to 106 is described.

First, a plurality of symbols are defined as follows.
N: number of tasks L: number of samples in each task x ^NL , y ^NL : features and labels of the training dataset, respectively D: basic model for data generation M: number of HME models in mixing z: from task Assignment vector to model ζ: Assignment vector from sample to HME expert

ｍａｘ_ｑ｛ＶＬＢ（ｑ，ｘ^ＮＬ，ｙ^ＮＬ，Ｄ）｝は、ｌｏｇｐ（ｙ^ＮＬ｜ｘ^ＮＬ，Ｄ）と一致することが保証され得る。 MTL takes into account task clustering (denoted by z) and sample clustering in each task (denoted by ζ), whose main interest is the marginal likelihood p (y ^NL | x ^NL , D) is there. The lower bound of the peripheral log likelihood on q (z ^N ) and q (ζ ^NL ) derived in this way is obtained as follows.

max _q {VLB (q, x ^NL , y ^NL , D)} can be guaranteed to match logp (y ^NL | x ^NL , D).

ここで、ρ＝（α，ρ_１，…，ρ_Ｍ），αはそれぞれのクラスタに対する混合比ベクトルであり、ρ_ｃ＝（β_ｃ，γ_ｃ，φ_ｃ）は、ｃ番目のＨＭＥモデルに対するパラメータであり、ｃ＝１，…，Ｍであり、

である。 Next, factored asymptotic approximation is described. Mutual independence between the task cluster and the sample cluster in each task cluster is assumed, and a factorization information criterion (FIC) is obtained approximately in the Laplace method.

Here, ρ = (α, ρ ₁ ,..., Ρ _M ), α is a mixture ratio vector for each cluster, and ρ _c = (β _c , γ _c , φ _c ) is for the c th HME model. Parameters, c = 1,..., M,

It is.

  In the above process, the FIC is determined based only on the approximation of the marginal log likelihood.

  Next, a FAB algorithm that can be used for the piecewise linear model generation method described above is described.

ここで、Ｌ（ａ，ｂ）≡ｌｏｇｂ＋（ａ−ｂ）／ｂであり、ｑｎｇ_ｉ及びｑｎｅ_ｉは、新たなパラメータ（分布）

を有する、ｎｇ_ｉ及びｎｅ_ｉの近似である。

The FAB algorithm actually maximizes the asymptotically coincident lower bound of the FIC. The lower bound is obtained as follows.

Here, L (a, b) ≡logb + (ab) / b, and qng _i and qne _i are new parameters (distribution).

Is an approximation of ng _i and ne _i .

Thereafter, the following optimization problem arises.

The FAB algorithm repeats maximization alternately in E and M steps for q and θ. The E step optimizes the variation distribution q as follows.

である。 Where ψ _g (x _nl , i, j) is the probability of x _nl belonging to expert i of a given HME model parameterized by the remaining subtrees of expert j and (β _ci , γ _ci ) ,here,

It is.

  Equation 8 can be used in step 105 to optimize task-related potential variables, as described above. Equation 9 may achieve hierarchical potential variable optimization at step 104 as described above.

The M step optimizes the parameters as follows.

  Equation 10 can be used in step 106 to achieve optimization of model structure and model parameters, as described above.

  FIG. 2 schematically illustrates a block diagram of a piecewise linear model generation system according to one embodiment of the present disclosure. As shown in FIG. 2, a piecewise linear model generation system generally includes an acquisition module 201 configured to acquire data for multiple tasks and a task association that represents the association between the multiple tasks. A first setting module 202 configured to set potential variables, and a first configuration module configured to set model structures for a plurality of piecewise linear models and to initialize corresponding model parameters and hierarchical potential variables. A two-setting module 203 and a model optimization module 206 configured to optimize model structure and model parameters based on data for a plurality of tasks, task related latent variables and hierarchical latent variables; Prepare. Hereinafter, each module will be described in detail.

  In the acquisition module 201, data for N tasks may be acquired.

  In the first setting module 202, a task-related latent variable representing the relationship between a plurality of tasks is set. As an example, the task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models. In other words, the relationship between tasks can be represented by the probability of each task belonging to the model. If two tasks belong to the same model, the two tasks are considered related.

  In the second setting module 203, model structures for a plurality of piecewise linear models are set, and their model parameters and hierarchical latent variables are initialized. As an example, the model structure may be a tree structure and the initialization process may be performed stochastically.

  According to an exemplary embodiment, the piecewise linear model generation system is configured to optimize hierarchical latent variables based on data for multiple tasks, task related latent variables, model structure, and model parameters. A configured hierarchical latent variable optimization module 204 may further be provided. Since the hierarchical latent variables are stochastically initialized in the second setting module 203, they can be optimized by the hierarchical latent variable optimization module 204. The hierarchical latent variable is for explaining how to divide the data, after which the feature space is divided into multiple pieces, each piece represented by a local expert. The process of splitting pieces by hierarchical latent variables is clustered by sample, not by feature. That is, any sample is placed in one piece and any sample is placed in another piece. In a particular example, each sample is clustered according to probability. A particular optimization method may employ the process shown in Equation 9 above.

  According to an exemplary embodiment, a piecewise linear model generation method is configured to optimize task-related potential variables based on data for multiple tasks, hierarchical potential variables, model structure, and model parameters A task-related latent variable optimization module 205 may be further included. The task-related latent variables set in the first setting module 102 are generated through probabilistic initialization and need to be optimized. In the task-related latent variable optimization module 205, the task-related latent variable is the hierarchy optimized in the hierarchical latent variable optimization module 204, along with data, model structure and model parameters for multiple tasks. Can be optimized by using global latent variables. A particular optimization method may employ the process shown in Equation 8 above.

  According to an exemplary embodiment, the model optimization module 206 has been optimized in the hierarchical latent variable and task related latent variable optimization module 205 optimized in the hierarchical latent variable optimization module 204. Task-related latent variables can be used in conjunction with data for multiple tasks to optimize model structure and model parameters. A particular optimization method may employ the process shown in Equation 10 above.

  According to an exemplary embodiment, the piecewise linear model generation method is configured to determine whether the model structure and model parameters output by the model optimization module 206 are optimal. A discrimination module 207 may further be provided, and if optimal, the output module 208 outputs a piecewise linear model; if not optimal, the hierarchical latent variable optimization module 204, task related latent variable optimization Module 205 and model optimization module 206 continue to optimize the model structure and model parameters. The evaluation index for the discrimination can be a goodness of fit between the model and the data. The fitness cannot increase without an upper limit. Instead, there is an upper limit. After increasing to some extent during the incremental process, the incremental for continued optimization is very small. When the increment is small enough, it is considered that the optimal model has been obtained, thereby aborting the optimization and the output module 208 outputs the resulting piecewise linear model.

  The piecewise linear model generation system shown in FIG. 2 corresponds to the piecewise linear model generation method shown in FIG. Therefore, the above description of the piecewise linear model generation method with reference to FIG. 1 is equally applicable to the piecewise linear model generation system shown in FIG. 2 and will not be described in detail here.

  FIG. 3 graphically and schematically illustrates the steps of a piecewise linear model generation method according to an embodiment of the present disclosure. As shown in FIG. 3, first, the upper diagram shows obtaining data T1, T2,..., TN for a plurality of tasks, and the data for each task is a plurality of separate data. Represented by data points. Thereafter, in the middle diagram, modeling is performed using the optimization steps shown in FIG. Each task is used to model a plurality of models, and it can be understood that, for example, T1, T2, T3, and T4 may model model HME1, model HME2, and model HME3, respectively. Finally, in the lower diagram, a plurality of optimized models, such as hierarchical mixed experts HME (T1), HME (T2),..., HME (TN) are output.

  According to the present invention, new potential variables are added during the model generation process to represent the relevance between tasks to facilitate the generation of piecewise linear models, so that data for multiple tasks Can be used for modeling, thereby improving the accuracy of model generation.

  Note that embodiments of the invention may be implemented in software, hardware or a combination thereof. The hardware portion may be implemented by special logic, and the software portion may be held in memory and executed by a suitable instruction execution system such as a microprocessor or dedicated designed hardware. Those of ordinary skill in the art will be able to provide the above methods and systems in computer-executable instructions and / or control codes contained in a processor, eg, a transmission medium such as a magnetic disk, CD or DVD-ROM. It can be appreciated that such code may be implemented on a programmable memory such as read-only memory (firmware) or a data carrier such as an optical or electronic signal carrier. The apparatus and its components in this embodiment are implemented by, for example, a very large scale integrated circuit or gate array, a semiconductor such as a logic chip or transistor, or a field programmable gate array or programmable logic device, or various types of processors. It is realized by software or a combination of the above hardware circuit and software circuit, for example, firmware.

  Although the operations of the method according to the present invention have been described in a particular order in the drawings, this is desirable only when these operations are performed in that particular order, or all of the operations shown are performed. It does not require or mean that the result is achieved. Instead, the steps described in the flowchart may be performed in a different order. In addition or alternatively, some steps may be excluded and performed, multiple steps may be combined into one step and / or performed to perform May be broken down into multiple steps.

  Although the invention has been described with reference to the presently contemplated embodiments, it is to be understood that the invention is not limited to the disclosed embodiments. On the contrary, the invention is intended to cover various modifications and equivalent changes within the spirit and scope of the appended claims. The scope of the appended claims is consistent with the broadest description and covers all such modifications and equivalent structures and functions.

(Appendix 1)
An acquisition module configured to acquire data for multiple tasks;
A first setting module configured to set a task related latent variable representing the relationship between the plurality of tasks;
A second setting module configured to set a model structure for a plurality of piecewise linear models and initialize corresponding model parameters and hierarchical latent variables;
A model optimization module configured to optimize the model structure and the model parameters based on the data for the plurality of tasks, the task related latent variables and the hierarchical latent variables. ,
Piecewise linear model generation system.

(Appendix 2)
The task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models;
The piecewise linear model generation system according to attachment 1.

(Appendix 3)
The model structure has a tree structure,
The piecewise linear model generation system according to attachment 1.

(Appendix 4)
A hierarchical latent variable optimization module configured to optimize the hierarchical latent variable based on data for the plurality of tasks, the task related latent variable, the model structure and the model parameter. Further comprising
The piecewise linear model generation system according to attachment 1.

(Appendix 5)
A task-related potential variable optimization module configured to optimize the task-related potential variable based on the data for the plurality of tasks, the hierarchical potential variable, the model structure, and the model parameter. Further comprising
The piecewise linear model generation system according to attachment 1.

(Appendix 6)
A determination module configured to determine whether the model structure and the model parameters are optimal;
The piecewise linear model generation system according to attachment 1.

(Appendix 7)
The determination module determines whether or not the model structure and the model parameter are optimal based on a goodness of fit between the model structure and the model parameter.
The piecewise linear model generation system according to attachment 6.

(Appendix 8)
Getting data for multiple tasks,
Setting a task related latent variable representing the relationship between the plurality of tasks;
Setting up a model structure for a plurality of piecewise linear models and initializing corresponding model parameters and hierarchical latent variables;
Optimizing the model structure and the model parameters based on data for the plurality of tasks, the task-related latent variables and the hierarchical latent variables;
Piecewise linear model generation method.

(Appendix 9)
The task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models;
The piecewise linear model generation method according to attachment 8.

(Appendix 10)
The model structure has a tree structure,
The piecewise linear model generation method according to attachment 8.

(Appendix 11)
Further comprising optimizing the hierarchical latent variables based on data for the plurality of tasks, the task related latent variables, the model structure and the model parameters;
The piecewise linear model generation method according to attachment 8.

(Appendix 12)
Further comprising optimizing the task-related potential variables based on data for the plurality of tasks, the hierarchical potential variables, the model structure, and the model parameters;
The piecewise linear model generation method according to attachment 8.

(Appendix 13)
Further determining whether the model structure and the model parameters are optimal,
The piecewise linear model generation method according to attachment 8.

(Appendix 14)
Determining whether the model structure and the model parameters are optimal,
Determining whether the model structure and the model parameter are optimal based on a degree of fit between the model structure and the model parameter,
The piecewise linear model generation method according to attachment 13.

Claims (10)

An acquisition module configured to acquire data for multiple tasks;
A first setting module configured to set a task related latent variable representing the relationship between the plurality of tasks;
A second setting module configured to set a model structure for a plurality of piecewise linear models and initialize corresponding model parameters and hierarchical latent variables;
A model optimization module configured to optimize the model structure and the model parameters based on the data for the plurality of tasks, the task related latent variables and the hierarchical latent variables. ,
Piecewise linear model generation system. The task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models;
The piecewise linear model generation system according to claim 1. The model structure has a tree structure,
The piecewise linear model generation system according to claim 1. A hierarchical latent variable optimization module configured to optimize the hierarchical latent variable based on data for the plurality of tasks, the task related latent variable, the model structure and the model parameter. Further comprising
The piecewise linear model generation system according to claim 1. A task-related potential variable optimization module configured to optimize the task-related potential variable based on the data for the plurality of tasks, the hierarchical potential variable, the model structure, and the model parameter. Further comprising
The piecewise linear model generation system according to claim 1. A determination module configured to determine whether the model structure and the model parameters are optimal;
The piecewise linear model generation system according to claim 1. The determination module determines whether or not the model structure and the model parameter are optimal based on a goodness of fit between the model structure and the model parameter.
The piecewise linear model generation system according to claim 6. Getting data for multiple tasks,
Setting a task related latent variable representing the relationship between the plurality of tasks;
Setting up a model structure for a plurality of piecewise linear models and initializing corresponding model parameters and hierarchical latent variables;
Optimizing the model structure and the model parameters based on data for the plurality of tasks, the task-related latent variables and the hierarchical latent variables;
Piecewise linear model generation method. The task-related latent variable is configured to represent a correspondence relationship between each task in the plurality of tasks and each piecewise linear model in the plurality of piecewise linear models;
The method of generating a piecewise linear model according to claim 8. The model structure has a tree structure,
The method of generating a piecewise linear model according to claim 8.

Images