JP2010282547A - Input variable selection support apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an input variable selection support apparatus for carrying out support for input variable selection by presenting an index for narrowing down the input variables from input candidate variables by a simple method. <P>SOLUTION: The input variable is selectively presented based on the sensitivity of each input output model by generating a plurality of input output models [j] (j=(1 to J), and J is a natural number of 2 or above) that show the relationship between all input candidate variables and output variables in numerous formats with different model principles by using model information data standardized so that an average value is 0 and a standard differential is 1 and then respectively carrying out sensitivity generation for generating a sensitivity which is an absolute value for an output variable for each input candidate variable of each input output model [j] with respect to each input output models [j]. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to an input variable selection support device that supports input variable selection that determines a preferred input candidate variable from a plurality of input candidate variables of an input / output model and uses it as an input variable.

  The input / output model has a function of calculating an output variable (object variable) from a plurality of input variables (explanatory variables). Input values are substituted into a plurality of input variables of such an input / output model, and predicted values and estimated values are obtained as output variables. Examples of use of such input / output models include, for example, various demand forecasts for electricity, water, general consumer goods, forecasts for control of flow rate, pressure, river flow rate, etc., raw material concentration, product concentration, microbial count, strength For example, a model in which quality identification such as is used as an output variable (prediction target).

  These input / output models are models that have many input variables and output variables, and obtain output values by substituting many input values. In creating such an input / output model, it is often performed to narrow down from a large number of input candidate variables to the minimum necessary input variable, and this narrowing of the input variable is one of important steps in model creation. .

  For example, Patent Document 1 (Japanese Patent Application Laid-Open No. 2002-268703, title of invention “terminal pressure control support device”) is disclosed as a conventional technique relating to such a narrowing of variables. The terminal pressure control support device described in Patent Document 1 is a method in which a user roughly determines (narrows down) a variable to be used first based on a correlation coefficient, and then performs detailed variable setting by a variable increase / decrease method or the like. is there.

  Here, the correlation coefficient generally indicates the magnitude of the correlation between two variables, and is a value between -1 and 1. The closer the correlation coefficient is to 1, the stronger the positive correlation, and the closer to -1, the stronger the negative correlation. Therefore, the closer the absolute value of the correlation coefficient is to 1, the stronger the correlation between the two variables. The terminal pressure control support device described in Patent Document 1 uses this relationship to narrow down variables.

JP 2002-268703 A ([0031] to [0033])

  In the terminal pressure control support device described in Patent Document 1, the variables are narrowed down by utilizing the correlation, but this only looks at the linear relationship between the two variables and changes only sporadically. There is a possibility that the correlation coefficient may be small even if the influence is large in a variable that is not performed, which may cause an important input candidate variable to be overlooked. In addition, when there is a strong correlation between input candidate variables, if both of them are strongly correlated with the output, both will be adopted as input variables. However, the inclusion of both variables is redundant. It was.

  Furthermore, the variable increase / decrease method employed by the terminal pressure control support device described in Patent Document 1 is a method of reducing prediction error (variation) when an input candidate variable is added, and predicting error (variation) when an input candidate variable is deleted. ) Increases the number of input candidate variables. However, in general, the calculation is complicated and takes time.

  Therefore, the present invention has been made in view of the above-described problems, and an object of the present invention is to provide an index for narrowing down input variables from input candidate variables by a simple method and to support input variable selection. It is to provide a support device.

An input variable selection support device according to claim 1 of the present invention is provided.
A data processing unit;
A model information database in which model information data that is actual values for a plurality of input candidate variables and output variables is registered is constructed, and a storage unit in which data is read and written by the data processing unit,
An input unit for inputting to the data processing unit;
An output unit for outputting from the data processing unit;
And an input variable selection support device for selecting an input variable used for creating an input / output model in the prediction device, wherein the data processing unit is
Standardization means for standardizing the model information data so that an average value is 0 and a standard deviation is 1 for each of the output variables and the input candidate variables;
Using the standardized model information data, a plurality of input / output models [j] (j = 1,..., J, where J is a natural number of 2 or more) representing the relationship between all input candidate variables and output variables Is a multi-format input / output model creation means that generates multiple formats with different model principles,
Sensitivity generation for generating for each input candidate variable a sensitivity that is an absolute value of a value obtained by dividing the change amount of the output variable with respect to the change amount of each input candidate variable of the input / output model [j] by the change amount of the input candidate. Sensitivity generating means for each of the input / output model [1],..., The input / output model [j],.
Input variable selection means for selecting an input variable having a high sensitivity of each of the input / output models;
Presenting means for presenting the selected input variable through the output unit;
It is characterized by providing.

An input variable selection support device according to claim 2 of the present invention is
In the input variable selection support device according to claim 1,
The input variable selection means includes
Input candidates in the input / output model [j] of any one of the input / output model [1],..., Input / output model [j],. A sorting means for sorting to sort variables,
Input variable selection means for performing variable selection for selecting input candidate variables rearranged in descending order of sensitivity from a side having a higher sensitivity in a preset number;
It is characterized by providing.

An input variable selection support device according to claim 3 of the present invention is
In the input variable selection support device according to claim 1,
The input variable selection means includes
For the input candidate variables in the input / output model [j], the rearrangement for sorting the input candidate variables in descending order of sensitivity is the input / output model [1],..., The input / output model [j],. J] for each sorting means,
All the input / output models [1],..., Input / output models [j], and so on are selected for selecting the input variables rearranged in descending order of sensitivity from the side with the highest sensitivity in a preset number. ..Input variable selection means for each of the input / output model [J],
It is characterized by providing.

An input variable selection support device according to claim 4 of the present invention is
In the input variable selection support device according to claim 1,
The input variable selection means includes
For the input candidate variables in the input / output model [j], the rearrangement for sorting the input candidate variables in descending order of sensitivity is the input / output model [1],..., The input / output model [j],. J] for each sorting means,
Sorting means for dividing the input / output model [j] into a first group and a second group;
First input variable selection means for performing variable selection for selecting input variables rearranged in descending order of sensitivity for all of the input / output models of the first group from a large number in a preset number;
A second input variable selection means for performing variable selection for selecting one of the input variables rearranged in descending order of the sensitivity of any of the input / output models of the second group from a large number in a preset number;
It is characterized by providing.

An input variable selection support device according to claim 5 of the present invention is
In the input variable selection support device according to claim 3 or 4,
The input variable selection means includes
Determining means for determining an input variable finally selected by an AND set or an OR set of input variables selected for each input / output model [j];
It is characterized by providing.

An input variable selection support device according to claim 6 of the present invention provides:
In the input variable selection support device according to any one of claims 1 to 5,
The input / output model is a combination including at least one of a multiple regression model, a neural network model, a principal component regression model, or a partial least squares model.

An input variable selection support device according to claim 7 of the present invention is
The input variable selection support device according to claim 6,
The input / output model is an input / output model [1] based on a multiple regression model and an input / output model [2] based on a neural network model.

An input variable selection support device according to claim 8 of the present invention provides:
In the input variable selection support device according to claim 7,
The multiple regression model in the input / output model [1] is
It is generated by converting a multiple regression model into a partial least squares model or a principal component regression model.

  ADVANTAGE OF THE INVENTION According to this invention, the parameter | index for narrowing down an input variable from an input candidate variable with a simple method can be shown, and the input variable selection assistance apparatus which assists an input variable selection can be provided.

It is a block diagram of the input variable selection assistance apparatus of the form for implementing this invention. It is a structure figure of a model information database. It is a structure figure of a model information database. It is explanatory drawing explaining selection of an input candidate variable. It is explanatory drawing explaining presentation of an input candidate variable.

  Then, the form for implementing this invention is demonstrated below, referring a figure. First, the overall structure of the input variable selection support device 100 will be described with reference to FIG. As shown in FIG. 1, the input variable selection support apparatus 100 includes at least a data management computer 1, an input unit 2, and an output unit 3. The input variable selection support apparatus 100 of this embodiment is assumed to be a single computer, for example.

  The data management computer 1 further includes a data processing unit 10 and a storage unit 20. The data processing unit 10 is an MPU or a CPU and functions as each unit as will be described later. The storage unit 20 is a large-capacity storage device such as a hard disk, for example, and a database as will be described later is constructed. Note that reading / writing is normally performed between the data processing unit 10 and the storage unit 20, between the data processing unit 10 and the input unit 2, and between the data processing unit 10 and the output unit 3. However, the following explanation will be made while omitting the memory assuming that reading and writing are performed via the memory.

The input unit 2 is, for example, a keyboard or an external hard disk / USB memory capable of transmitting files, and data input from the input unit 2 is processed by the data processing unit 10.
The output unit 3 is a display device, a printer device, or the like, and data output such as screen display / printing is performed by data output from the data processing unit 10.

  Next, actual operation of the input variable selection support device 100 will be described with reference to the drawings. As shown in FIG. 1, the data processing unit 10 of the input variable selection support apparatus 100 includes a model information collection unit 101, a standardization unit 102, a multi-format input / output model creation unit 103, a sensitivity generation unit 104, an input variable selection unit 105, Presenting means 106 is provided. This will be described in order below.

First, the data processing unit 10 functions as a model information collecting unit 101 that registers a plurality of model information data related to past results input from the input unit 2 in the model information database 21.
First, it is assumed that a system administrator designs a required model information database 21 and registers the database structure from the input unit 2 in the model information database 21. Subsequently, the system administrator registers model information data. The model information data may be input through a dedicated screen or a file input in CSV (Comma Separated Value) format.

  The model information data is accumulated in an actual measurement data table of the model information database 21 of the storage unit 20 as shown in FIG. The table structure of the actual measurement data table of the model information database 21 is configured as shown in FIG. 2, for example. In FIG. 2, a number representing an event, input candidate variable data that is a result value for a plurality of input candidate variables, and output variable data that is a result value for an output variable are recorded. For example, the number is given by time. In this way, in the model information database 21, input candidate variable data that is actual values for a plurality of input candidate variables at a given time and output variable data that is actual values for output variables are registered in association with each other, immediately. It is arranged in an accessible state.

  As shown in FIG. 3, the variable table of the model information database 21 also registers input candidate variables, tag names of variables for easy understanding at the time of presentation to be described later, and sensitivity to be described later. Tag names are registered by model and input candidate variable. FIG. 3 illustrates that variable tables for the input / output model [j] are registered. However, variable tables are set for all of the input / output models [1] to [J]. .

Input candidate variables are x ₁ , x ₂ ,..., X _m ,..., X _M (m = 1,... M). The output variable is y. When the number is i, it represents data at a certain time point i. When this number is i, the input candidate variable data is x ₁ (i), x ₂ (i), ... x _m (i), ..., x _M (i) (i = 1, ... , I). The output variable data is y (i) (i = 1,..., I). Here, the number in parentheses represents a number, that is, when the number is i, it represents data at a certain time point i. Data up to number I is accumulated.
Information on model information and variables registered in the model information database 21 is such.

Subsequently, the data processing unit 10 functions as a standardization unit 102 that standardizes model information data so that the average value is 0 and the standard deviation is 1 for each output variable and input candidate variable. The standardized model information data is registered in another standardized data table having the same structure as the table structure of the model information database 21 shown in FIG. Also in this case, the input candidate variables are represented by x ₁ , x ₂ ,..., X _m ,..., X _M (m = 1,... M). The output variable is represented by y. Input candidate variable data is represented by x ₁ (i), x ₂ (i),... X _m (i),..., X _M (i) (i = 1,..., I). . The output variable data is represented by y (i) (i = 1,..., I). Here, the number in parentheses represents a number, that is, when the number is i, it represents data at a certain time point i. Data up to number I is accumulated. Hereinafter, this standardized data is used.

  Subsequently, the data processing unit 10 uses the standardized model information data, and outputs a plurality of input / output models [j] (j = 1,..., J) representing the relationship between all the input candidate variables and the output variables. (Where J is a natural number of 2 or more) functions as the multi-format input / output model creation means 103 that generates various forms with different model principles. An input / output model [1],..., An input / output model [j],..., An input / output model [J] are created using the input standardized variable data and the entire output variable data previously standardized. The plurality of input / output models have different principles. For example, the input / output model [1] is an input / output model based on a neural network, the input / output model [2] is an input / output model based on a multiple regression model,..., And the input / output model [J] is input / output based on a partial least squares model. It is a model. Creation of these input / output models [1],..., Input / output models [j],..., And input / output models [J] is determined by learning and setting described later.

  The created input / output model [1] can be defined as a function of the output variable Y with respect to the input candidate variable X, and is expressed as the following equation.

  Here, X is M input candidate variables, and Y is one output variable. X is represented by the following equation.

  Further, the input / output model [j] can be defined as a function of the output variable Y with respect to the input candidate variable X, and is expressed as the following equation. X is M input candidate variables, and Y is one output variable.

  The input / output model [J] can be defined as a function of the output variable Y with respect to the input candidate variable X, and is expressed as the following equation. X is M input candidate variables, and Y is one output variable.

  Subsequently, the data processing unit 10 determines the sensitivity (input is very small) as an absolute value of a value obtained by dividing the output change amount with respect to the change amount of each input candidate variable of the input / output model [j] by the change amount of the input candidate. The input / output model [1],..., Input sensitivity is generated for each input candidate variable (the absolute value of the ratio obtained by dividing the output change amount by the input change amount). It functions as sensitivity generation means 104 for each of the output models [J]. In this sensitivity generation, a predetermined input value is assigned to a certain input candidate variable, an output value is obtained from the output variable, and subsequently, the input value changed from the predetermined input value to the same input candidate variable with a minute change amount is obtained. Substitution is performed to obtain a new output value from the output variable, and a change amount which is a difference value between these output values is obtained. Then, the sensitivity of the input candidate variable to the output variable is calculated by obtaining the absolute value of the ratio calculated by dividing the change amount of the output value by the change amount of the input value.

This sensitivity generation is performed for all input / output models [1],..., Input / output models [J]. Further, it is performed for all input candidate variables in each input / output model. First, the ratio s _1m for a variable x _m of the input / output model [1] is expressed as the following equation.

Here, the input candidate variable is x _m (m = 1,..., M), X = [x ₁ ,..., X _M ] ^T, and the minute change of the input candidate variable x _m is Δx _m . .
_X 1 Such an input candidate variables input-output model _{[1], ···, x m} , ···, the ratio _s 11 for _{x M, ···, s 1m,} ···, s 1M Is calculated, the absolute value is taken, and the sensitivity | s ₁₁ | , ..., | s _1m |, ..., | s _1M | M are calculated.

Further, the sensitivity s _jm is expressed as follows for a variable x _{m having} the input / output model [j].

_X 1 is the input candidate variables such output model _{[j], ···, x m} , ···, the ratio _s j1 for _{x M, ···, s jm,} ···, s jM M are calculated, the absolute value is taken, and the sensitivity | s _j1 | , ..., | s _jm |, ..., | s _jM | M are calculated.
Further, a variable x _{m having} an input / output model [J] is expressed as a sensitivity s _Jm following equation.

_X 1 is the input candidate variables such output model _{[J], ···, x m} , ···, the ratio _s J1 for _{x M, ···, s Jm,} ···, s JM M are calculated, the absolute value is taken, and the sensitivity | s _J1 | , ..., | s _Jm |, ..., | s _JM | M are calculated.

Thus, in the input / output model [1],..., The input / output model [j],..., The input / output model [J], x _{1 ,.} ,..., X _M ratios s ₁₁ ,..., S _JM are calculated, and absolute values are taken to determine the sensitivity | s ₁₁ | , ..., | s _JM | Are calculated as J × M. These sensitivities are used as indicators. These are registered in the variable table set for each model shown in FIG.

  The “sensitivity” calculated in this way represents the change in the output when the input candidate variable changes by a unit amount, and changes in the positive or negative direction by the amount of its influence. Is.

Subsequently, the data processing unit 10 functions as an input variable selection unit 105 that selects an input variable having a high sensitivity of each input / output model. Although there are various selection methods, for example, it functions as a rearranging means for rearranging input candidate variables in descending order of sensitivity in only the input / output model [j] selected in advance from a plurality of input / output models. Selection may be made by functioning as input variable selection confirmation means for selecting a preset number p of input candidate variables as input variables in the rearranged order. For example, among the input candidate variables in descending order of sensitivity of the input / output model [j] selected in advance as shown in FIG. 4, the number of input variables specified by the user (for example, p input variables). Each variable group (input variable or set of tag names of input variables) is displayed individually.
As a selection criterion for selecting one input / output model [j] from among a plurality of input / output models, for example, an input / output model having the highest sensitivity or an input / output model having a large sum of sensitivities is used. Can do. Since both adopt an input / output model with high sensitivity, an effective input / output model can be selected.

  As another selection method, the data processing unit 10 performs rearrangement for sorting input candidate variables in descending order of sensitivity in the input / output model [j]. The input / output model [1],. ], Each functioning as an input variable selection confirmation means for selecting a preset number of input candidate variables as input variables in the order of rearrangement for all input / output models, You may make it select. For example, as shown in FIG. 4, the input candidate variables in descending order of sensitivity of the input / output model [1],... For example, variable groups (input variables or sets of tag names of input variables) taking p input variables) are individually displayed. Although not shown, these p input variables are further set as a product set (AND set) or a sum set (OR set). You may select in this way.

As another selection method, the data processing unit 10 functions as a group selection unit that divides the input / output model [1],..., The input / output model [J] into a first group and a second group, For the first group, it functions as a first variable selection means for selecting, as an input variable, an input candidate variable whose sensitivity falls within the top p for all of its input / output models, and for any of the input / output models for the second group Functions as second variable selection means for selecting input candidate variables that fall within the top p sensitivities as input variables, and are preset in descending order of sensitivity calculated for the first variable selection means and the second variable selection means. Selection may be made by functioning as variable selection means for selecting input variables by the number.
As a selection criterion for the first group, for example, an input / output model with sensitivity larger than a predetermined value or an input / output model with a sum of sensitivities larger than a predetermined value can be used. As a selection criterion for the second group, for example, an input / output model whose sensitivity is smaller than a predetermined value or an input / output model whose sum of sensitivities is smaller than a predetermined value can be used.

The input / output model [1],..., The input / output model [J] of the first group and the second group is one of the top p input variables in descending order of sensitivity, or the selected input variable An input variable selected as a product set (AND) or union set (OR) is selected. In this way, the final input variable is determined.
An input variable is selected by any one of these methods.

  As described above, the input variable is selected from the input candidate variables based on the sensitivity that directly represents the degree of influence of the input candidate variables on the output. Of the input candidate variables, when actually selecting as the model input, it is extremely reasonable to extract variables that have a large influence on the output. In this case, however, the selected variable depends on the model. Therefore, when it is based only on the sensitivity of one model, there is a risk of bias. Therefore, by performing this based on a plurality of models, it can be said that the selected input candidate variable is a very appropriate method as a method for narrowing down the input candidate variables.

Subsequently, the data processing unit 10 functions as a presentation unit 106 that presents the selected input candidate variable through the output unit 3. For example, the data processing unit 10 causes the output unit 3 to output an input variable selected based on the sensitivity (controls the display device to display the image on a screen or causes the printer to print and print). Display and printing are performed as shown in FIG. At this time, if the sensitivity is displayed in addition to the tag representing the input selection variable, the reason for the selection can be understood. Therefore, the input variable can be selected by changing the user's experience or the like.
The input variable selection support apparatus 100 is like this.

Next, details of the input / output model will be described. Here, it relates to the details of the multi-format input / output model creation means. For example, a multiple regression model is selected as the input / output model. The multiple regression model is linear, and the input / output model is also linear.
This multiple regression model is expressed as follows.

  Here, A is a coefficient vector, and is expressed as follows.

Next, creation of a multiple regression model (learning A) will be described.
The data processing unit 10 functions as means for reading model information data for model creation (learning A) from the standardized data table of the model information database 21. This model information data is data composed of many past samples of the input candidate variable (x) and the output variable (y). Specifically, x is generally an M variable and the number of samples is I. When this model information data is arranged in the form of a matrix, it becomes as follows. Each row represents each sample and each column represents each variable.

  In general, y is a variable, and the model information data is expressed as follows, assuming a vertical vector of I rows × 1 columns.

  The data processing unit 10 functions as a multiple regression model creating unit that creates the input / output model 1 (multiple regression model) using the entire input model information data. Specifically, the multiple regression model is expressed as follows.

  In this case, the coefficient A of the multiple regression model that predicts y from x is obtained by the least square method as follows. For details on how to derive the coefficient A of the multiple regression model, refer to the following document (Chemometrics-Chemical pattern recognition and multivariate analysis, Yoshikatsu Miyashita, Shinichi Sasaki, Kyoritsu Shuppan, 1995). .

  By determining this A, a multiple regression model is determined.

Regarding the sensitivity of such a multiple regression model, when the m-th input candidate variable x _m is changed by Δx _m as shown in the above equation 6, the output changes by a _m Δx _m . Therefore, the sensitivity is | a _m |, and the sensitivity of each input candidate variable matches the absolute value of the coefficient of the coefficient vector A. Therefore, the input candidate variable is selected as the input variable in the priority order of the absolute values of the multiple regression coefficients themselves.

  Subsequently, a neural network model is selected as another input / output model. The neural network model generally has a three-layer neural network structure including an input layer, an intermediate layer, and an output layer. Further, the neural network model is coupled between elements of the input layer and the intermediate layer and between elements of the intermediate layer and the output layer. have. There are as many elements as the number of input variables in the input layer, as many elements as the number of output variables in the output layer, and the intermediate layer is composed of arbitrarily designated elements.

  In this neural network, elements in the input layer correspond to input factors, and elements in the output layer correspond to output factors. The degree of coupling between neurons is represented by a coupling coefficient, and this coupling coefficient is a coefficient for representing the weight of coupling between elements of the neural network. If the coupling coefficient is large, the coupling has a weight, that is, a necessary coupling, and if the coupling coefficient is small, the coupling has no weight, that is, an unnecessary coupling. . By updating the magnitude of the coupling coefficient w, it is possible to learn a nonlinear relationship between input and output.

  As described above, since the neural network model can be modeled from data regardless of linear or non-linear, it is treated as an “input / output model”. The neural network trains the input / output data to be learned in the “learning phase” as “teacher data” and learns its input / output characteristics, and uses the neural network that has completed the learning phase as a “model” for prediction and sensitivity analysis. . Using the data here, each row of X is given as an input variable of teacher data, each row of y corresponding to each row of the input variable is given as an output variable, and the output of the neural network by each row of X becomes a row corresponding to y. The neural network is learned so as to match as much as possible.

Next, learning will be described.
The data processing unit 10 functions as means for inputting model information data for model creation (model learning). This model information data is generally data composed of a large number of past samples of input candidate variables (x) and output variables (y). Specifically, x is generally an M variable, and the past number of samples is I. When this data is arranged in the form of a matrix, Equations 10 and 11 are obtained. Each row represents each sample and each column represents each variable.

  In such a neural network model, nonlinear input / output relationships can be processed by changing the model structure and coupling coefficient. Such an input / output model construction of a neural network is an input layer so that a desired output value can be obtained from an output layer element (output factor) with respect to input values input to a plurality of input layer elements (input factors). And changing the coupling coefficient between the intermediate layer and the intermediate layer and the output layer. As a result, the coupling coefficient is determined. The data processing unit 10 determines the coupling coefficient by substituting the data relating to the actual measurement for the input and the output in I ways. The input / output model of the neural network is determined in this way.

The sensitivity of such a neural network model cannot actually be expressed as a simple expression in a neural network, but is expressed as G (x), and this neural network model is an input / output model [j]. . In this case, the ratio s _{jm with} respect to the variable x _m is expressed as follows.

Here, the input candidate variable is x _m (m = 1,..., M), X = [x ₁ ,..., X _M ] ^T, and the minute change of the input candidate variable x _m is Δx _m . .
_X 1 is the input candidate variables such output model _{[1], ···, x m} , ···, the ratio _s j1 for _{x M, ···, s jm,} ···, s jM Is calculated, the absolute value is taken, and the sensitivity | s _j1 | , ..., | s _jm |, ..., | s _jM | M are calculated. Such sensitivity is calculated for G ₁ (x),..., G _J (x).

  Although it is difficult to predict the sensitivity of such a neural network model, input candidate variables are selected and used as input variables in the order of priority in the order of sensitivity obtained as described above.

  A principal component regression model is selected as the input / output model. The principal component regression model is a linear model obtained by improving the multiple regression model, and is treated as an “input / output model”. In a multiple regression model, when there are many input candidate variables, it is difficult to create a multiple regression model directly from model creation data. Specifically, when a model is created from data for model creation, a multiple regression coefficient is generally calculated by the least square method, but there is a linear dependency or a close relationship (multicollinearity) between input candidate variables. This is because the matrix calculation in the least squares method becomes unstable in some cases (specifically, the calculation process of the least square method includes a calculation corresponding to the inverse matrix calculation, and this inverse matrix calculation is unstable. To become).

  On the other hand, when the principal component regression method is applied, input candidate variables are aggregated into intermediate variables (principal components) that are small in number and uncorrelated with each other, and a multiple regression model from this intermediate variable to the output is created. . Since the relation from the original input candidate variable to the intermediate variable is linear and is obtained as a constant coefficient matrix, this coefficient matrix is combined with a multiple regression coefficient representing the relation from the intermediate variable to the output (matrix product is taken) Thus, a coefficient corresponding to the multiple regression coefficient from the input candidate variable to the output variable is calculated. Since input variables are reduced by removing input variables having multicollinearity in this way, calculation instability does not occur, and model creation calculation can be performed stably. In addition, when each input variable does not have multicollinearity, the number of input variables may not decrease.

  Subsequently, learning of the principal component regression model will be described. The data processing unit 10 receives model information data for model creation (learning). This model information data is generally data composed of a large number of past samples of the input candidate variable (x) and the output variable (y), and is expressed by the above formulas 10 and 11. In the case of this principal component regression model, the model is represented by two matrices P and Q. Here, P is a loading matrix for the input variable (coefficient matrix representing the influence on the principal component aggregated from the input variable), and Q is a multiple regression coefficient from the principal component to the output variable. The input is expressed as:

  The output is expressed as follows:

  Therefore, the relationship between the input and the output is expressed as follows:

  In the case of principal component regression, the matrix P, Q of the model can be used to convert the input variable to the multiple regression coefficient that directly represents the output variable as in the following equation.

Each element of the multiple regression coefficient A calculated by this principal component regression represents the sensitivity of each principal component regression. Take absolute value and sensitivity | s _j1 | , ..., | s _jm |, ..., | s _jM | M are calculated. The sensitivity vector A is displayed with input candidate variables (for example, p) arranged in descending order of absolute values. Only the number specified from the top in descending order of absolute value is adopted as the input variable. For details of the principal component regression method, refer to the following literature (Chemometrics-Chemical pattern recognition and multivariate analysis, Yoshikatsu Miyashita and Shinichi Sasaki, Kyoritsu Shuppan, 1995).

  Also, a partial least squares model is selected as the input / output model. Since the partial least squares model is a linear model that improves the multiple regression model, it is treated as an “input / output model”. In the multiple regression model, when there are many input candidate variables, the matrix calculation in the least squares method is performed when there is a linear dependency or a close relationship (multicollinearity) between the input candidate variables as described above. It becomes unstable (specifically, the calculation process corresponding to the inverse matrix calculation is included in the calculation process of the least square method, and this inverse matrix calculation becomes unstable).

  In contrast, when the partial least squares method is applied, the input candidate variables are aggregated into intermediate variables (latent variables) that are small in number and uncorrelated with each other, and a multiple regression model from this intermediate variable to the output is created. Is done. Since the relation from the original input candidate variable to the intermediate variable is linear and is obtained as a constant coefficient matrix, this coefficient matrix is combined with a multiple regression coefficient representing the relation from the intermediate variable to the output (matrix product is taken) Thus, a coefficient corresponding to the multiple regression coefficient from the input candidate variable to the output variable is calculated. Instability of calculation does not occur in the creation of a model called the partial least square method, so that the model creation calculation can be performed stably.

  Subsequently, learning of the partial least square method model will be described. The data processing unit 10 receives model information data for model creation (learning). This model information data is generally model information data composed of a large number of past samples (I in this embodiment) of the input candidate variable (x) and the output variable (y), and is represented by the above formulas (10) and (11). It is. In the case of the partial least square method, the model is represented by three matrices of P, Q, and W. P is a loading coefficient matrix for the input variable (coefficient matrix representing the degree of influence on the intermediate variable that aggregates the input variables from the input to the latent variable), and Q is a loading coefficient matrix for the output variable (the degree of influence from the latent variable to the output variable). A coefficient matrix), W is a weight matrix. The input is expressed as:

  The output is expressed as follows:

  T and X have the following relationship.

  In the case of the partial least square method, the output variables are directly represented from the input matrix and the matrix P, Q, W of the model. The multiple regression coefficient is expressed by the following equation.

  Here, A is as follows.

Each element of the multiple regression coefficient A calculated by the partial least square method represents the sensitivity of each input candidate variable. Take absolute value and sensitivity | s _j1 | , ..., | s _jm |, ..., | s _jM | M are calculated. The sensitivity vector A is displayed with input candidate variables arranged in descending order of absolute values. Only the number specified from the top in descending order of absolute value is adopted as the input variable. For details on the partial least square method, refer to the following literature (Chemometrics-Chemical pattern recognition and multivariate analysis, Yoshikatsu Miyashita and Shinichi Sasaki, Kyoritsu Shuppan, 1995). In addition, when each input variable does not have multicollinearity, the number of input variables may not decrease.

Next, another embodiment will be described.
In this embodiment, in particular, a linear input / output model and a nonlinear input / output model are combined so that selected input / output variables have different tendencies, and effective input / output variables are selected without omission. It is to make. For example, when J = 2 and two types of models are used, the input / output model [1] may be a multiple regression model and the input / output model [2] may be a neural network model. Since the multiple regression model is linear and the neural network model is non-linear, variable selection is performed from various viewpoints, and effective input / output variables are selected. The input / output model [1] is a principal component regression model, the input / output model [2] is a neural network model, the input / output model [1] is a partial least squares model, and the input / output model [2] is a neural network. It is good as a model.

Next, processing as a prediction device after determining an input variable will be described.
One model for prediction is selected from a plurality of models used when calculating the sensitivity. Specifically, a model to be predicted by the user is determined and registered in advance from a plurality of registered models. Next, using the input variable determined above, a prediction model is generated again. The method for generating the prediction model is the same as that when the model is generated to calculate the sensitivity. A prediction value is output based on a given input using the generated prediction model. In this way, a prediction is made. It is also possible to create a plurality of models from the selected input variables and use the (weighted) average as a predicted value.

  The input variable selection support device 100 of the present invention has been described above. The process of selecting a variable using the sensitivity of the present invention is performed particularly when the prediction apparatus is started up or when the prediction accuracy deteriorates due to a change in the prediction target (a change over time, a physical change, etc.) Is more effective.

  In particular, if there is input candidate variable and output variable data, the impact can be evaluated by evaluating the sensitivity from the input candidate variable to the output variable using multiple models created from all of them. By using it as an index to be adopted, it is possible to select an input variable with higher reliability than when an input variable is selected from only one model.

  The input variable selection support apparatus of the present invention can be applied particularly to the determination of input variables of an input / output model.

100: input variable selection support device 1: data management computer 10: data processing unit 101: model information collection unit 102: standardization unit 103: multi-format input / output model creation unit 104: sensitivity generation unit 105: input variable selection unit 106: Presenting means 20: storage unit 2: input unit 3: output unit

Claims (8)

A data processing unit;
A model information database in which model information data that is actual values for a plurality of input candidate variables and output variables is registered is constructed, and a storage unit in which data is read and written by the data processing unit,
An input unit for inputting to the data processing unit;
An output unit for outputting from the data processing unit;
And an input variable selection support device for selecting an input variable used for creating an input / output model in the prediction device, wherein the data processing unit is
Standardization means for standardizing the model information data so that an average value is 0 and a standard deviation is 1 for each of the output variables and the input candidate variables;
Using the standardized model information data, a plurality of input / output models [j] (j = 1,..., J, where J is a natural number of 2 or more) representing the relationship between all input candidate variables and output variables Is a multi-format input / output model creation means that generates multiple formats with different model principles,
Sensitivity generation for generating for each input candidate variable a sensitivity that is an absolute value of a value obtained by dividing the change amount of the output variable with respect to the change amount of each input candidate variable of the input / output model [j] by the change amount of the input candidate. Sensitivity generating means for each of the input / output model [1],..., The input / output model [j],.
Input variable selection means for selecting an input variable having a high sensitivity of each of the input / output models;
Presenting means for presenting the selected input variable through the output unit;
An input variable selection support device comprising: In the input variable selection support device according to claim 1,
The input variable selection means includes
Input candidates in the input / output model [j] of any one of the input / output model [1],..., Input / output model [j],. A sorting means for sorting to sort variables,
Input variable selection means for performing variable selection for selecting input candidate variables rearranged in descending order of sensitivity from a side having a higher sensitivity in a preset number;
An input variable selection support device comprising: In the input variable selection support device according to claim 1,
The input variable selection means includes
For the input candidate variables in the input / output model [j], the rearrangement for sorting the input candidate variables in descending order of sensitivity is the input / output model [1],..., The input / output model [j],. J] for each sorting means,
All the input / output models [1],..., Input / output models [j], and so on are selected for selecting the input variables rearranged in descending order of sensitivity from the side with the highest sensitivity in a preset number. ..Input variable selection means for each of the input / output model [J],
An input variable selection support device comprising: In the input variable selection support device according to claim 1,
The input variable selection means includes
For the input candidate variables in the input / output model [j], the rearrangement for sorting the input candidate variables in descending order of sensitivity is the input / output model [1],..., The input / output model [j],. J] for each sorting means,
Sorting means for dividing the input / output model [j] into a first group and a second group;
First input variable selection means for performing variable selection for selecting input variables rearranged in descending order of sensitivity for all of the input / output models of the first group from a large number in a preset number;
A second input variable selection means for performing variable selection for selecting one of the input variables rearranged in descending order of the sensitivity of any of the input / output models of the second group from a large number in a preset number;
An input variable selection support device comprising: In the input variable selection support device according to claim 3 or 4,
The input variable selection means includes
Determining means for determining an input variable finally selected by an AND set or an OR set of input variables selected for each input / output model [j];
An input variable selection support device comprising: In the input variable selection support device according to any one of claims 1 to 5,
The input / output model is a combination including at least one of a multiple regression model, a neural network model, a principal component regression model, or a partial least squares model. The input variable selection support device according to claim 6,
The input / output model is an input / output model [1] based on a multiple regression model and an input / output model [2] based on a neural network model. In the input variable selection support device according to claim 7,
The multiple regression model in the input / output model [1] is
An input variable selection support device generated by converting a multiple regression model into a partial least square method model or a principal component regression model.

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