JP6569497B2 - Prediction device, method and program - Google Patents

Description

  The present invention relates to a prediction apparatus, method, and program for calculating a predicted value of an objective variable with respect to an explanatory variable to be predicted using actual data.

When the prediction target is predicted using the actual data, the variable to be predicted is called an objective variable, and the input data when calculating the predicted value of the objective variable is called an explanatory variable, and is often represented by symbols y and x, respectively. .
When predicting a certain target variable y, it is common to construct a prediction model that covers the entire space of the target variable and the explanatory variable, as in equation (1). y ′ is a predicted value of the objective variable y, x is an explanatory variable, and θ is a parameter that defines a prediction model.
y ′ = f (x, θ) (1)
When the input / output characteristics of the prediction model gradually change, the prediction model is periodically learned again, or the parameter θ is sequentially updated every time new performance data is obtained.

When the input / output characteristics are nonlinear, such as steel and chemical plants, and when the input / output characteristics change drastically, a so-called database type prediction method may be used.
In the database type prediction method, the explanatory variable x _q (request point) of the current prediction target is selected from the actual data {x _n , y _n } (combination of the actual values of the explanatory variable x and the objective variable y) stored in the database. K pieces of neighborhood data {x _k , y _k } similar to the above are selected. Then, using these neighborhood data {x _k , y _k }, the parameter θ of the local prediction model f _q (x, θ) effective only in the vicinity of the request point x _q is obtained, and then the local prediction model f _q ( x, theta) to complete the requested point x _q, calculates a predicted value of the objective variable y _q 'to the request point x _q. Note that the subscript n represents the number of actual data, and the subscript k represents the number of neighboring data.

This prediction method is called Model on Demand or Just in Time Model because a prediction model is recreated every time a new request point _xq is obtained. By creating a local prediction model f _q (x, θ) that is effective only in the vicinity of the request point x _q instead of creating a prediction model f (x, θ) for the entire space, the input / output characteristics have non-linearity. Even in some cases, it is possible to accurately predict with a simple prediction model. Further, if the actual value y _q target variable to the request point x _q is obtained, (deleting the oldest data if necessary) by adding the actual data {x _q, y _q} in the database It is possible to follow changes in input / output characteristics.

Here, in order to realize a highly accurate database-type prediction method, (a) the number S of actual data, (b) the number K of neighboring data, (c) the selection method of neighboring data, (d) the local prediction model It is necessary to set the function form of etc. appropriately.
As the function form of the local prediction model in (d), since it is not necessary to cover the entire space, a linear model in which the function form is set in advance is used, and it is common to obtain the parameter θ using the neighborhood data. is there.
Further, the number S of actual data (a) and the number K of neighboring data (b) are often determined by trial and error while checking the accuracy of the prediction model.
The most difficult adjustment is the method of selecting neighborhood data in (c).

As a selection method of the neighborhood data, a distance function d (x _q , x _n ) between the request point x _q and the explanatory variable x _n of the actual data is defined, and the distance function d (x _q , X _n ) is generally selected from the performance data in ascending order of the distance calculated. x _q (= [x _q1 x _q2 ... x _qM ] ^T _∈R ^M ) is a vector representing the request point x _q , and x _n (= [x _n1 x _n2 ... x _nM ] ^T ∈R ^M ) is A vector representing the explanatory variable x _n of the actual data, L is a matrix that linearly maps the vector, and is generally a real symmetric matrix (referred to herein as a distance weight matrix). M is the number of explanatory variables, that is, the number of dimensions of the vector.

JP 7-164267 A JP 2006233333 A JP 2004-355189 A JP 2004-99698 A

As a method for selecting neighborhood data, Patent Document 1 discloses using Euclidean distance. In this case, the distance weight matrix L is a unit matrix as shown in Equation (3). diag () is a function for calculating a diagonal matrix.
L = diag (1, 1,..., 1) (3)

Patent Document 2 discloses that the explanatory variable is normalized and then the Euclidean distance is calculated (normalized Euclidean distance). In this case, the distance weight matrix L is a diagonal matrix whose diagonal element is the reciprocal of the standard deviation σ _m of the explanatory variable, as in Expression (4). The subscript m represents an explanatory variable number (vector element number).
L = diag (1 / σ ₁ , 1 / σ ₂ ,..., 1 / σ _m ,..., 1 / σ _M ) (4)

Patent Document 3 discloses that a partial regression coefficient vector is used as an influence coefficient used for distance calculation. In this case, the distance weight matrix L is a diagonal matrix having a partial regression coefficient with respect to the objective variable of the explanatory variable as a diagonal element, as in Expression (5).
L = diag (a ₁ , a ₂ ,..., A _m ,..., A _M ) (5)

The distance weight matrix L in Patent Documents 1 to 3 is a diagonal matrix, but Patent Document 4 discloses using the Mahalanobis distance. In this case, the distance weight matrix L is the inverse of the covariance matrix of the explanatory variable matrix X (= [x ₁ x ₂ ... X _S ] ^T ∈R ^{S × M} ) of the actual data as shown in the equation (6). The square root of the matrix (L ^T L is the inverse of the covariance matrix of the explanatory variable matrix X). cov () is a function for calculating a covariance matrix.
L ^T L = cov (X) ⁻¹ (6)

However, all of the conventional methods use the distance function d (x _q , x _n ) in Expression (2), that is, the distance between the request point x _q and the explanatory variable x _n of the actual data, and the objective variable is directly set. Not used.
Patent documents 1, 2, and 4 do not use the objective variable at all when selecting the neighborhood data. Normally, the explanatory variables are usually selected as items that have a correlation with the objective variable, so these methods treat the strength of the correlation between the objective variable and the explanatory variable equally in all explanatory variables. It corresponds to.
On the other hand, Patent Document 3 uses partial regression coefficients of an objective variable and an explanatory variable when calculating the distance weight matrix L. However, since it is a partial regression coefficient for the entire space of the objective variable and the explanatory variable, if the nonlinear relationship between the objective variable and the explanatory variable is strong, depending on the request point, it may be an explanatory variable with a weak correlation with the objective variable. The neighborhood data may be selected with a large weight, and it is not suitable to use as the distance weight matrix L. In addition, if there is a correlation between explanatory variables, the partial regression coefficient does not correctly represent the strength of the correlation with the objective variable. Therefore, it is not appropriate to use the partial regression coefficient in the distance weight matrix L even in such a case.

  As described above, in the conventional neighborhood data selection method, the neighborhood data is selected without using the objective variable of the actual data at all, or is used only for the calculation of the distance weight matrix L (as the request point). However, it is difficult to predict the objective variable for the required point with high accuracy in the neighborhood data selected in this way.

  The present invention has been made in view of the above points, and it is an object of the present invention to select appropriate neighborhood data when calculating predicted values of objective variables using actual data.

距離ｄ（ｘ_q，ｘ_n，ｙ_q1’，ｙ_n）が小さい順に複数の実績データを近傍データとして選択することを特徴とする［１］又は［２］に記載の予測装置。
［４］ 距離重み行列Ｐは、式（ｂ）のように、
Ｐ^TＰ＝cov（［Ｘ Ｙ］）^-1・・・（ｂ）
実績データの個数Ｓとして、実績データの説明変数行列Ｘ（＝［ｘ₁ ｘ₂・・・ｘ_S］^Tと実績データの目的変数ベクトルＹ＝［ｙ₁ ｙ₂・・・ｙ_S］^Tとを合わせた行列［Ｘ Ｙ］の共分散行列の逆行列で与えられることを特徴とする［３］に記載の予測装置。
［５］ 距離重み行列Ｐは、所定の値を対角要素とする対角行列で与えられることを特徴とする［３］に記載の予測装置。
［６］ 距離重み行列Ｐの対角要素は、説明変数の標準偏差の逆数と、目的変数の標準偏差の逆数とで与えられることを特徴とする［５］に記載の予測装置。
［７］ 距離重み行列Ｐの対角要素は、説明変数の目的変数に対する偏回帰係数と、目的変数自身の目的変数に対する偏回帰係数とで与えられることを特徴とする［５］に記載の予測装置。
［８］ 前記初期予測値算出手段で算出した初期予測値と、前記予測値算出手段で算出した予測値との差が所定の値を下回れば、前記予測値算出手段で算出した予測値を採用し、前記所定の値以上であれば、前記初期予測値算出手段で算出した初期予測値と、前記予測値算出手段で算出した予測値とを按分した値を算出し、
該按分で得た値を新たな初期予測値として、前記近傍データ選択手段の処理、前記局所予測モデル作成手段の処理、及び前記予測値算出手段の処理を行い、該新たな初期予測値と、前記予測値算出手段で今回算出した予測値との差が前記所定の値を下回れば、前記予測値算出手段で今回算出した予測値を採用し、前記所定の値以上であれば、該新たな初期予測値と、前記予測値算出手段で今回算出した予測値とを按分した値を算出し、
これを、前記所定の値を下回るまで、又は所定の繰り返し回数に達するまで繰り返すことを特徴とする［１］乃至［７］のいずれか一つに記載の予測装置。
［９］ 前記局所予測モデル作成手段は、前記近傍データ選択手段で選択した複数の近傍データを用いて、局所予測モデルとして予め関数形が設定された線形モデルのパラメータを求めることを特徴とする［１］乃至［８］のいずれか一つに記載の予測装置。
［１０］ 実績データ格納手段に格納された、説明変数及び目的変数の実績値の組合せからなる実績データを利用して、予測対象の説明変数に対する目的変数の予測値を算出する予測方法であって、
初期予測値算出手段が、前記実績データ格納手段に格納された実績データに基づいて、予測対象の説明変数に対する目的変数の初期予測値を算出するステップと、
近傍データ選択手段が、予測対象の説明変数と初期予測値とを合わせたベクトルと、前記実績データ格納手段に格納された実績データの説明変数と実績データの目的変数とを合わせたベクトルとの距離を算出し、距離が小さい順に複数の実績データを近傍データとして選択するステップと、
局所予測モデル作成手段が、前記近傍データ選択手段で選択した複数の近傍データを用いて局所予測モデルを作成するステップと、
予測値算出手段が、前記局所予測モデル作成手段で作成した局所予測モデルに予測対象の説明変数を入力して、予測対象の説明変数に対する目的変数の予測値を算出するステップとを有することを特徴とする予測方法。
［１１］ 実績データ格納手段に格納された、説明変数及び目的変数の実績値の組合せからなる績データを利用して、予測対象の説明変数に対する目的変数の予測値を算出するためのプログラムであって、
前記実績データ格納手段に格納された実績データに基づいて、予測対象の説明変数に対する目的変数の初期予測値を算出する初期予測値算出手段と、
予測対象の説明変数と初期予測値とを合わせたベクトルと、前記実績データ格納手段に格納された実績データの説明変数と実績データの目的変数とを合わせたベクトルとの距離を算出し、距離が小さい順に複数の実績データを近傍データとして選択する近傍データ選択手段と、
前記近傍データ選択手段で選択した複数の近傍データを用いて局所予測モデルを作成する局所予測モデル作成手段と、
前記局所予測モデル作成手段で作成した局所予測モデルに予測対象の説明変数を入力して、予測対象の説明変数に対する目的変数の予測値を算出する予測値算出手段としてコンピュータを機能させるためのプログラム。 The gist of the present invention for solving the above problems is as follows.
[1] A prediction device that calculates a predicted value of an objective variable for an explanatory variable to be predicted using actual data that is a combination of actual values of explanatory variables and objective variables stored in actual data storage means. ,
An initial predicted value calculating means for calculating an initial predicted value of the objective variable for the explanatory variable to be predicted based on the actual data stored in the actual data storing means;
The distance between the vector combining the explanatory variable to be predicted and the initial predicted value, and the vector combining the explanatory variable of the actual data stored in the actual data storage means and the objective variable of the actual data is calculated. Neighborhood data selection means for selecting a plurality of results data as neighborhood data in ascending order;
Local prediction model creation means for creating a local prediction model using a plurality of neighborhood data selected by the neighborhood data selection means;
Prediction value calculating means for inputting a prediction target explanatory variable to the local prediction model created by the local prediction model creating means and calculating a predicted value of an objective variable for the explanatory variable of the prediction target. Prediction device.
[2] The initial predicted value calculating means calculates a distance between the explanatory variable of the prediction target and the explanatory variable of the actual data, and selects a plurality of actual data as the neighboring data from the actual data storing means in order of increasing distance. The prediction according to [1], wherein a local prediction model is created using a plurality of selected neighborhood data, an explanatory variable to be predicted is input to the local prediction model, and an initial prediction value is calculated. apparatus.
[3] The neighborhood data selection means includes a vector [x _q ^T y _q1 '] ^T obtained by combining the explanatory variable x _q to be predicted and the initial predicted value y _q1 ′, the explanatory variable x _n of the actual data, and the actual data Using the distance weight matrix P, which is a matrix that linearly maps the vector, using the vector [x _n ^T y _n ] ^T combined with the objective variable y _n of the distance d (x _q , X _n , y _q1 ′, y _n )

The prediction apparatus according to [1] or [2], wherein a plurality of performance data are selected as neighboring data in ascending order of distance d (x _q , x _n , y _q1 ′, y _n ).
[4] The distance weight matrix P is as shown in equation (b).
P ^T P = cov ([XY]) ⁻¹ (b)
As the number S of the actual data, and the target variable vector of explanatory variable matrix _{X (= [x 1 x 2} ··· x S] T and actual data of actual data _{Y = [y 1 y 2 ···} y S] T The prediction device according to [3], which is given by an inverse matrix of a covariance matrix of a matrix [XY] combined with
[5] The prediction apparatus according to [3], wherein the distance weight matrix P is given as a diagonal matrix having a predetermined value as a diagonal element.
[6] The prediction device according to [5], wherein the diagonal elements of the distance weight matrix P are given by the reciprocal of the standard deviation of the explanatory variable and the reciprocal of the standard deviation of the objective variable.
[7] The prediction according to [5], wherein the diagonal elements of the distance weight matrix P are given by a partial regression coefficient for the objective variable of the explanatory variable and a partial regression coefficient for the objective variable of the objective variable itself. apparatus.
[8] If the difference between the initial predicted value calculated by the initial predicted value calculating means and the predicted value calculated by the predicted value calculating means falls below a predetermined value, the predicted value calculated by the predicted value calculating means is adopted. If the value is equal to or greater than the predetermined value, a value obtained by apportioning the initial predicted value calculated by the initial predicted value calculating unit and the predicted value calculated by the predicted value calculating unit is calculated.
The value obtained by the apportioning is used as a new initial predicted value, the processing of the neighborhood data selecting means, the processing of the local prediction model creating means, and the processing of the predicted value calculating means, and the new initial predicted value, If the difference between the predicted value calculated this time by the predicted value calculating means is less than the predetermined value, the predicted value calculated this time by the predicted value calculating means is adopted, and if it is greater than or equal to the predetermined value, the new value Calculate a value obtained by apportioning the initial predicted value and the predicted value calculated this time by the predicted value calculation means,
The prediction apparatus according to any one of [1] to [7], wherein this is repeated until the value falls below the predetermined value or until a predetermined number of repetitions is reached.
[9] The local prediction model creation means uses the plurality of neighborhood data selected by the neighborhood data selection means to obtain parameters of a linear model in which a function form is set in advance as a local prediction model. [1] The prediction device according to any one of [8].
[10] A prediction method for calculating a predicted value of an objective variable for an explanatory variable to be predicted, using actual data that is a combination of actual values of explanatory variables and objective variables stored in actual data storage means. ,
An initial predicted value calculating unit calculating an initial predicted value of an objective variable for an explanatory variable to be predicted based on the actual data stored in the actual data storing unit;
The distance between the vector in which the neighborhood data selection unit combines the explanatory variable to be predicted and the initial predicted value, and the vector in which the explanatory variable of the actual data stored in the actual data storage unit and the objective variable of the actual data are combined Calculating a plurality of performance data as the neighborhood data in ascending order of distance;
A step of creating a local prediction model using a plurality of neighborhood data selected by the neighborhood data selection means, the local prediction model creation means;
A prediction value calculating means including a step of inputting an explanatory variable to be predicted to the local prediction model created by the local prediction model creating means and calculating a predicted value of an objective variable for the explanatory variable to be predicted. The prediction method.
[11] A program for calculating a predicted value of an objective variable with respect to an explanatory variable to be predicted using performance data that is a combination of actual values of explanatory variables and objective variables stored in actual data storage means. And
An initial predicted value calculating means for calculating an initial predicted value of the objective variable for the explanatory variable to be predicted based on the actual data stored in the actual data storing means;
The distance between the vector combining the explanatory variable to be predicted and the initial predicted value, and the vector combining the explanatory variable of the actual data stored in the actual data storage means and the objective variable of the actual data is calculated. Neighborhood data selection means for selecting a plurality of results data as neighborhood data in ascending order;
Local prediction model creation means for creating a local prediction model using a plurality of neighborhood data selected by the neighborhood data selection means;
A program for causing a computer to function as a prediction value calculation unit that inputs an explanatory variable to be predicted to a local prediction model created by the local prediction model creation unit and calculates a predicted value of an objective variable for the explanatory variable to be predicted.

  According to the present invention, by using the objective variable of the performance data, appropriate neighborhood data can be selected, and the objective variable can be predicted with high accuracy.

It is a figure which shows the function structure of the prediction apparatus which concerns on embodiment. It is a flowchart which shows the process which the prediction apparatus which concerns on embodiment performs. It is a schematic diagram for demonstrating the difference between the selection method of the conventional neighborhood data, and the selection method of the neighborhood data to which this invention is applied.

Preferred embodiments of the present invention will be described below with reference to the accompanying drawings.
FIG. 1 shows a functional configuration of the prediction apparatus 100 according to the embodiment. The prediction device 100 is used to predict a certain prediction target, for example, to predict properties such as quality and dimensions of a product manufactured by a production process.

First, as a preparation, assuming that a variable to be predicted, that is, an objective variable is naturally determined, the user needs to determine a variable that is necessary for predicting the objective variable, that is, an explanatory variable. As explanatory variables, a plurality of variables correlated with the objective variable are selected. An explanatory variable may be selected from physical knowledge or empirical knowledge, or a variable having a high correlation coefficient with the objective variable may be used as the explanatory variable based on the actual data. Then, the combination {x _n , y _n } of the actual values of the explanatory variable x and the objective variable y already obtained from the manufacturing performance or the like is stored and accumulated in the database 200 as the actual data storage means.

Reference numeral 101 denotes an initial predicted value calculation unit, which is an initial predicted value calculation means, which calculates an initial predicted value y _q1 ′ of an objective variable for the requested point x _q based on the actual data stored in the database 200.
The initial prediction value calculation unit 101 includes a first neighborhood data selection unit 101a, a first local prediction model creation unit 101b, and a first prediction value calculation unit 101c. The first neighborhood data selection unit 101a calculates the distance between the request point _xq and the explanation variable _xn of the record data, and selects a plurality of record data from the database 200 as the neighbor data in order of increasing distance. The first local prediction model creation unit 101b creates a local prediction model using a plurality of neighborhood data selected by the first neighborhood data selection unit 101a. The first predicted value calculation unit 101c inputs the request point x _q to the local prediction model created by the first local prediction model creation unit 101b, and calculates the initial predicted value y _q1 ′.

Reference numeral 102 denotes a second neighborhood data selection unit which is a neighborhood data selection means, and a vector obtained by combining the request point x _q and the initial predicted value y _q1 ′, an explanatory variable x _n of the actual data stored in the database 200, and calculating a distance between vectors obtained by combining the objective variable y _n of the actual data, to select the distance a plurality of actual data in ascending order as the proximate data.

  Reference numeral 103 denotes a second local prediction model creation unit which is a local prediction model creation unit, which creates a local prediction model using a plurality of neighborhood data selected by the second neighborhood data selection unit 102.

Reference numeral 104 denotes a second prediction value calculation unit which is a prediction value calculation unit. The request point _xq is input to the local prediction model created by the second local prediction model creation unit 103, and an objective variable corresponding to the request point _{xq is obtained} . The predicted value of is calculated.

FIG. 2 is a flowchart illustrating processing executed by the prediction device 100 according to the embodiment.
Steps S <b> 1 to S <b> 3 are initial prediction value calculation processing by the initial prediction value calculation unit 101.
In step S <b _> 1, the first neighborhood data selection unit 101 a selects K neighborhood data {x _k , y _k } from the actual data {x _n , y _n } stored in the database 200.
Here, the neighborhood data {x _k , y _k } similar to the request point x _q may be selected using any of the methods disclosed in Patent Documents 1 to 4, and the distance function of Expression (2) is used. K results data is selected as the neighborhood data in ascending order of the distance calculated by d (x _q , x _n ).
The distance weight matrix L in Expression (2) is determined by any one of Expressions (3) to (6). The number S of actual data and the number K of neighboring data are set in advance, and S = 20,000 and K = 100 are set as initial values, and may be adjusted by trial and error while looking at the prediction accuracy. For example, the number K is decreased when it is desired to improve the followability to the latest data, and the number K is increased when the robustness is desired to be increased. Further, the number S is a value determined by the presence or absence of a long-term trend such as secular change. If such a trend is small, the number S is increased, and if the trend is large, the number S is decreased.

In step S2, the first local prediction model creation unit 101b uses the K pieces of neighboring data {x _k , y _k } selected in step S1, and the local prediction model f _q1 effective only in the vicinity of the request point x _q. The local prediction model f _q1 (x, θ) is created by _obtaining the parameter θ of (x, θ).
The function form of the local prediction model is set in advance, but the local prediction model only needs to be established in the vicinity of the request point x _q , and thus does not need to be a complicated function form. For example, a linear model (including a model having only the constant term θ ₀ ) as in Expression (7) is used, and the parameter θ = [θ ₀ θ ₁ ... Θ _M ] ^T is calculated from the neighborhood data.
y ′ = θ ₀ + θ ₁ x ₁ + θ ₂ x ₂ +... + θ _M x _M (7)

The parameter θ is the predicted value y _k ′ of the target variable calculated by inputting the target variable y _k of the neighboring data and the explanatory variable x _k of the neighboring data to the local prediction model of the formula (7) as in the formula (8). Is determined so that the error sum of squares J is minimized.
J = Σ (y _k −y _k ′) ² (8)
The method for determining the parameter θ may be determined so as to minimize the error absolute value sum as in the equation (9), or the value of the parameter θ as in the equations (10) and (11). It may be determined to minimize the evaluation value to which the regularization term for suppressing the above is added.
J = Σ | y _k −y _k ′ | (9)
J = Σ (y _k −y _k ′) ² + λΣ | θ _k | (10)
J = Σ (y _k −y _k ′) ² + λΣθ _k ² (11)

In step S3, the first predicted value calculation unit 101c inputs a request point x _q topical prediction model f _q1 created (x, theta) in step S2, calculating the predicted value of the dependent variable for the request points x _q The initial predicted value y _q1 ′ is used.

In step S <b _> 4, the second neighboring data selection unit 102 selects K neighboring data {x _k , y _k } from the actual data {x _n , y _n } stored in the database 200.
Here, combined with 'vector [x _q ^T y _q1 a combination of the'] ^T and the required point x _q initial prediction value y _q1, the objective variable y _n explanatory variable x _n and the actual data of the actual data vector The distance d (x _q , x _n , y _q1 ′, y _n ) from [x _n ^T y _n ] ^T is calculated by the equation (13) using the distance weight matrix P, and the distance d (x _q , X pieces of performance data are selected as the neighborhood data in ascending order of x _n , y _q1 ′, y _n ).

When using the Mahalanobis distance as the distance above description of actual data variable matrix _{X = [x 1 x 2 ···} x S] T and an object variable vector of actual data _{Y = [y 1 y 2 ···} y S ] A covariance matrix cov ([XY]) of a matrix [XY] combined with ^T is obtained. This is a matrix representing the strength of the correlation between the objective variable and the explanatory variable, and using this covariance matrix, the distance d (x _q , x _n , y _q1 ′ is given by the equations (12) and (13). , Y _n ).
P ^T P = cov ([XY]) ⁻¹ (12)

Thus, the point of calculating the distance using not only the explanatory variable x _n of the actual data but also the objective variable y _n of the actual data is a point that is greatly different from the conventional method. In addition, since the matrix P ^T P is an inverse matrix of the covariance matrix of the explanatory variable and the objective variable, the explanatory variable having a strong correlation between the explanatory variable and the objective variable is taken into consideration after considering the strength of the correlation between the explanatory variables. Neighboring data can be selected with emphasis on, and a highly accurate local prediction model can be created.

FIG. 3 schematically shows a difference between a conventional neighborhood data selection method and a neighborhood data selection method to which the present invention is applied. Since the conventional neighborhood data selection method does not directly use the objective variable of the performance data, as shown in the colored range in FIG. 3A, the description of the performance data that is simply close to the required point _xq is shown. Variables are extracted and neighborhood data is selected. For this reason, the correlation between the explanatory variable and the objective variable is not taken into account.For example, actual data with a significant deviation from the objective variable may be selected as the neighborhood data, and the neighborhood data suitable for building a highly accurate local prediction model is selected. It may not be possible to select.
In contrast, the present invention in the applied proximate data selection method, 'sought after, and requests point x _q initial prediction value y _q1' initial prediction value of the objective variable y _q1 to the request point x _q as a reference and (☆ marks in FIG. 3B), it is possible to select the neighborhood data in consideration of the correlation between the explanatory variable and the objective variable. In this case, as shown in the colored range in FIG. 3 (b), the contour lines representing the equidistant distance (the ellipses having the same distance and the ellipse indicated by the solid line in the figure are also one of the contour lines) exist in the actual data. Neighboring data suitable for constructing a highly accurate local prediction model can be selected.

In step S5, the second local prediction model creation unit 103 uses the K pieces of neighborhood data {x _k , y _k } selected in step S4, and the local prediction model f _q2 effective only in the vicinity of the request point x _q. The local prediction model f _q2 (x, θ) is created by _obtaining the parameter θ of (x, θ). Note that the process of step S5 is the same as the process of step S2, and a detailed description thereof will be omitted.

In step S6, the second predicted value calculation unit 104, the local predictive model f _q2 (x, θ) created in step S5 to enter a request point x _q, the predicted value y _q target variable to the request point x _q 'Is calculated. Note that the process of step S6 is the same as the process of step S3, and a detailed description thereof will be omitted.

In step S7, a convergence determination is performed. If converged, the process ends. If not converged, the process proceeds to step S8.
First, the initial predicted value y _q1 ′ calculated in step S3 is compared with the predicted value y _q ′ calculated in step S6. If both are close (the difference between the two is less than a predetermined value), there is no problem, so the predicted value y _q ′ calculated in step S6 is adopted and output, and this processing is terminated. If the difference between the two is not less than a predetermined value, there is a possibility that appropriate neighborhood data has not been selected. In this case, the process proceeds to step S8, and a value obtained by apportioning the initial predicted value y _q1 ′ calculated in step S3 and the predicted value y _q ′ calculated in step S6 is calculated as shown in equation (14). The process returns to step S4 as a new initial predicted value y _q1 ′.
y _q1 ′ = a · y _q ′ + (1−a) · y _q1 ′ (14)

In the second and subsequent loops, the new initial predicted value y _q1 ′ calculated in step S8 of the previous loop is compared with the predicted value y _q ′ calculated in the current step S6. If both are close (the difference between the two is less than a predetermined value), the predicted value y _q ′ calculated in step S6 is employed and output, and the process is terminated. If the difference between the two is equal to or greater than a predetermined value, the process proceeds to step S8, and the new initial predicted value y _q1 ′ calculated in step S8 of the previous loop and the current step S6 are calculated as in equation (14). A value obtained by apportioning the predicted value y _q ′ is calculated, and this is used as a new initial predicted value y _q1 ′, and the process returns to step S4.
This is repeated until the difference between the initial predicted value y _q1 ′ and the predicted value y _q ′ becomes a predetermined value or less.

Here, a in equation (14) is a coefficient that takes a value between 0 and 1 for adjusting the convergence speed of the initial predicted value y _q1 ′. When the coefficient a is increased (for example, if a = 1, y _q ′ calculated in the current loop is set to y _q1 ′ in the next loop), the convergence works faster. Hunting may occur (the predicted value repeats two values alternately). Hunting is more difficult when the convergence speed is relaxed, and it is generally better to set a = 0.5.
Further, since there may be cases where convergence does not occur no matter how many times it is repeated, it may be considered that if it has been repeated a predetermined number of times, it has been converged and the repetition may be forcibly terminated.

If the actual value y _q target variable to the request point x _q is obtained, adding the actual data {x _q, y _q} in the database 200. The next time the predicted value is calculated, the neighborhood data may be selected from the S + 1 results data including the newly added results data combination, or the oldest data is selected as the neighborhood data. It may be excluded from the target and always select the neighborhood data from the S pieces of actual data. Since the actual data that is not selected is not used for the calculation of the predicted value, the actual data may be deleted. If the storage capacity of the database 200 is sufficient, the actual data may not be deleted.

As described above, by using the objective variable y _n of the actual data, can select the appropriate neighborhood data, it is possible to predict the target variable with high accuracy to the request point x _q.
That is, in the conventional method, historical data having similar values of explanatory variables is selected as the neighborhood data, whereas in the method to which the present invention is applied, the request point x _q and the initial predicted value y _q1 ′ are combined. Using the distance between the vector [x _q ^T y _q1 '] ^T and the vector [x _n ^T y _n ] ^T that combines the explanatory data x _n of the actual data and the objective variable y _{n of the} actual data, Select. In this way, since the explanatory data and the value of the objective variable are both close (the objective variable is close to the actual value and the predicted value), it is possible to create a local prediction model with higher accuracy than the conventional method. Thus, a highly accurate predicted value can be calculated.

In the present embodiment, the initial predicted value y _q1 ′ of the objective variable for the request point x _q is calculated by the conventional database type prediction method, but may be calculated by another method. For example using the S actual data stored in the database 200, calculates the predicted value of the dependent variable for the request points x _q by multiple regression techniques, it may be an initial prediction value y _q1 '.

In the present embodiment, the example in which the convergence determination is performed in step S7 and the calculation is repeatedly performed until the difference between the initial predicted value y _q1 ′ and the predicted value y _q ′ becomes small has been described. Although it is possible to obtain highly accurate neighborhood data by performing repeated calculations, a calculation load is applied instead. In order to reduce the calculation load, it is only necessary to reduce the number of repetitions. When it is necessary to minimize the calculation load, it is not necessary to perform the repeated calculation. Even if iterative calculation is not performed, a predicted value with higher accuracy than the conventional method can be obtained.

In this embodiment, the example in which the Mahalanobis distance is used as the neighborhood data selection method in the second neighborhood data selection unit 102 has been described. However, the present invention is not limited to this.
For example, the normalized Euclidean distance using the diagonal matrix calculated by Expression (15) as the distance weight matrix P may be used. Here, σ _m is the standard deviation of the explanatory variable x _m (subscript m represents the number of the explanatory variable (vector element number)), and σ _Y is the standard deviation of the objective variable.
P = diag (1 / σ ₁ , 1 / σ ₂ ,..., 1 / σ _m ,..., 1 / σ _M , 1 / σ _Y ) (15)

Also, partial regression coefficients for the objective variable explanatory variable _{x m (a 1, a 2} , ··, a m, ··, a M, a Y) determine the Euclidean that the weight of the explanatory variables and the partial regression coefficients A diagonal matrix having a partial regression coefficient as a diagonal element may be given as the distance weighting matrix P, as in the equation (16). Here, the partial regression coefficient a _Y is a partial regression coefficient with respect to the objective variable of the objective variable itself, and corresponds to a correlation coefficient between the objective variable and the objective variable (correlation coefficient with itself). It becomes 1 as shown in Expression (16).
P = diag (a ₁ , a ₂ ,..., A _m ,..., A _M , 1) (16)

In addition to the above method, the weight of each explanatory variable and the objective variable is determined based on physical knowledge and empirical knowledge as shown in Expression (17), and the diagonal matrix using these as diagonal elements is the distance weight. It may be given as a matrix P.
P = diag (w ₁ , w ₂ ,..., W _M , w _Y ) (17)

A model for predicting the steel temperature after machining in a steel process was studied. As explanatory variables, 15 types such as the dimensions of the steel material before and after processing and the steel material temperature before processing were selected from physical knowledge.
Objective variable: Steel material temperature after processing Explanation variable: Dimensions of steel material before and after processing, steel material temperature before processing, conveyance / processing time, tool shape, ... (15 types = M)
The half-year performance data was divided into two, the performance data for 4 months was stored in the database in advance, the predicted value for the performance data for the remaining 2 months was calculated, and the accuracy was evaluated. The evaluated performance data was sequentially added to the database, and the performance data was constantly updated.
Learning data: 26411 operation data for 4 months Evaluation data: 13306 operation data for 2 months

Table 1 shows the result of comparing the prediction accuracy between the conventional method and the method of the present invention.
The conventional method uses Euclidean distance weighted by typical normalized Euclidean distance, Mahalanobis distance, and partial regression coefficient for selection of neighborhood data.
In the method of the present invention, the Mahalanobis distance is used for selection of neighborhood data in the initial predicted value calculation unit 101 and the second neighborhood data selection unit 102, and there is no repetition (no convergence calculation) and there is repetition (with convergence calculation). did.
The numerical values in Table 1 are normalized to mean zero and standard deviation 1. The number S of actual data is 20,000, the number K of neighboring data is 100, the upper limit of the number of repetitions of steps S4 to S8 in FIG. 2 is 100, and the value of the coefficient a in equation (14) is 0.5. .
As shown in Table 1, the method of the present invention has the best RMSE (root mean square error between the actual value and the predicted value) compared with the conventional method, and the weight of the partial regression coefficient that is the most accurate in the conventional method. Even when compared with the Euclidean distance, the accuracy was improved by 9.3% (= (0.290−0.263) × 100 / 0.290) in the case of repetition. Note that the average error has a small value in any of the methods, so it can be said that there is no problem.

Although the present invention has been described together with the embodiments, the above-described embodiments are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention is interpreted in a limited manner by these. It must not be. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.
The prediction device to which the present invention is applied is realized by a computer device including a CPU, a ROM, a RAM, and the like, for example. In FIG. 1, the prediction device 100 is illustrated as a single device, but may be configured by a plurality of devices, for example.
The present invention also provides software (program) that implements the functions of the present invention to a system or apparatus via a network or various storage media, and the system or apparatus computer reads out and executes the program. It is feasible.

DESCRIPTION OF SYMBOLS 100: Prediction apparatus 101: Initial prediction value calculation part 101a: 1st neighborhood data selection part 101b: 1st local prediction model preparation part 101c: 1st prediction value calculation part 102: 2nd neighborhood data selection part 103: Second local prediction model creation unit 104: second prediction value calculation unit

Claims (11)

A prediction device that calculates a predicted value of an objective variable for an explanatory variable to be predicted using actual data that is a combination of actual values of explanatory variables and objective variables stored in actual data storage means,
An initial predicted value calculating means for calculating an initial predicted value of the objective variable for the explanatory variable to be predicted based on the actual data stored in the actual data storing means;
The distance between the vector combining the explanatory variable to be predicted and the initial predicted value, and the vector combining the explanatory variable of the actual data stored in the actual data storage means and the objective variable of the actual data is calculated. Neighborhood data selection means for selecting a plurality of results data as neighborhood data in ascending order;
Local prediction model creation means for creating a local prediction model using a plurality of neighborhood data selected by the neighborhood data selection means;
Prediction value calculating means for inputting a prediction target explanatory variable to the local prediction model created by the local prediction model creating means and calculating a predicted value of an objective variable for the explanatory variable of the prediction target. Prediction device.   The initial predicted value calculating means calculates a distance between the explanatory variable of the prediction target and the explanatory variable of the actual data, selects a plurality of actual data as the neighboring data from the actual data storing means in order of increasing distance, and then selects The prediction apparatus according to claim 1, wherein a local prediction model is created using a plurality of neighboring data, an explanatory variable to be predicted is input to the local prediction model, and an initial prediction value is calculated. The neighborhood data selection means includes a vector [x _q ^T y _q1 '] ^T combining the explanatory variable x _q to be predicted and the initial predicted value y _q1 ′, an explanatory variable x _n of actual data, and an objective variable of actual data Using a vector [x _n ^T y _n ] ^T combined with y _n and using a distance weight matrix P which is a matrix for linear mapping of the vector, the distance d (x _q , x _n , Y _q1 ′, y _n )

The distance _{d (x q, x n,} y q1 ', y n) predicting apparatus according to claim 1 or 2, characterized in that selected as proximate data a plurality of actual data in ascending order. The distance weight matrix P is expressed by the following equation (b).
P ^T P = cov ([XY]) ⁻¹ (b)
As the number S of the actual data, and the target variable vector of explanatory variable matrix _{X (= [x 1 x 2} ··· x S] T and actual data of actual data _{Y = [y 1 y 2 ···} y S] T The prediction apparatus according to claim 3, wherein the prediction apparatus is given by an inverse matrix of a covariance matrix of a matrix [XY] that is combined.   The prediction apparatus according to claim 3, wherein the distance weight matrix P is given as a diagonal matrix having a predetermined value as a diagonal element.   6. The prediction apparatus according to claim 5, wherein the diagonal elements of the distance weight matrix P are given by an inverse number of the standard deviation of the explanatory variable and an inverse number of the standard deviation of the objective variable.   6. The prediction apparatus according to claim 5, wherein the diagonal elements of the distance weight matrix P are given by a partial regression coefficient for the objective variable of the explanatory variable and a partial regression coefficient for the objective variable of the objective variable itself. If the difference between the initial predicted value calculated by the initial predicted value calculating means and the predicted value calculated by the predicted value calculating means is less than a predetermined value, the predicted value calculated by the predicted value calculating means is adopted, If the value is equal to or greater than a predetermined value, a value obtained by apportioning the initial predicted value calculated by the initial predicted value calculating unit and the predicted value calculated by the predicted value calculating unit is calculated.
The value obtained by the apportioning is used as a new initial predicted value, the processing of the neighborhood data selecting means, the processing of the local prediction model creating means, and the processing of the predicted value calculating means, and the new initial predicted value, If the difference between the predicted value calculated this time by the predicted value calculating means is less than the predetermined value, the predicted value calculated this time by the predicted value calculating means is adopted, and if it is greater than or equal to the predetermined value, the new value Calculate a value obtained by apportioning the initial predicted value and the predicted value calculated this time by the predicted value calculation means,
The prediction apparatus according to claim 1, wherein the prediction apparatus repeats this until the predetermined value is reached or until a predetermined number of repetitions is reached.   2. The local prediction model creation unit obtains a parameter of a linear model in which a function form is set in advance as a local prediction model using a plurality of pieces of neighborhood data selected by the neighborhood data selection unit. The prediction apparatus according to any one of 8. A prediction method for calculating a predicted value of an objective variable for an explanatory variable to be predicted using actual data that is a combination of actual values of explanatory variables and objective variables stored in actual data storage means,
An initial predicted value calculating unit calculating an initial predicted value of an objective variable for an explanatory variable to be predicted based on the actual data stored in the actual data storing unit;
The distance between the vector in which the neighborhood data selection unit combines the explanatory variable to be predicted and the initial predicted value, and the vector in which the explanatory variable of the actual data stored in the actual data storage unit and the objective variable of the actual data are combined Calculating a plurality of performance data as the neighborhood data in ascending order of distance;
A step of creating a local prediction model using a plurality of neighborhood data selected by the neighborhood data selection means, the local prediction model creation means;
A prediction value calculating means including a step of inputting an explanatory variable to be predicted to the local prediction model created by the local prediction model creating means and calculating a predicted value of an objective variable for the explanatory variable to be predicted. The prediction method. A program for calculating a predicted value of an objective variable with respect to an explanatory variable to be predicted using performance data that is a combination of an actual value of an explanatory variable and an objective variable stored in the actual data storage means,
An initial predicted value calculating means for calculating an initial predicted value of the objective variable for the explanatory variable to be predicted based on the actual data stored in the actual data storing means;
The distance between the vector combining the explanatory variable to be predicted and the initial predicted value, and the vector combining the explanatory variable of the actual data stored in the actual data storage means and the objective variable of the actual data is calculated. Neighborhood data selection means for selecting a plurality of results data as neighborhood data in ascending order;
Local prediction model creation means for creating a local prediction model using a plurality of neighborhood data selected by the neighborhood data selection means;
A program for causing a computer to function as a prediction value calculation unit that inputs an explanatory variable to be predicted to a local prediction model created by the local prediction model creation unit and calculates a predicted value of an objective variable for the explanatory variable to be predicted.

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