Variable relationship display device, method and program

Abstract

To provide a variable relation display device, method, and program that can display the relation of importance between variables in a model obtained by modeling a predetermined event.SOLUTION: A variable relation display device A of the present invention executes processing of generating a partial model of an explanatory variable and one second component of an objective variable by a random forest for every second component of the objective variable for all the second components, thereby generating a model composed of a plurality of partial models, obtains an importance that is an index representing the degree of magnitude of an influence of the explanatory variable imposed on the objective variable for every first component of the explanatory variable, based on the degree of impurity of the partial models, and displays each obtained importance in matrix in a two-dimensional space with the first component of the explanatory variable on one axis and the second component of the objective variable on the other axis.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a variable relationship display device, a variable relationship display method, and a variable relationship display program that display the relationship between variables having one or more components (factors, items) in a model that models a predetermined phenomenon. [Background technology]

[0002] When simulating (numerical experimenting) a predetermined event, the predetermined event is modeled and a model relating to the predetermined event is generated. This modeling utilizes various techniques such as support vector machines, clustering, Bayesian estimation, and neural networks, one of which is the random forest disclosed in, for example, Non-Patent Document 1 and Non-Patent Document 2.

[0003] Random forests are a type of ensemble learning and can be used for classification and regression. A random forest generally includes multiple decision trees (a group of decision trees) that serve as weak classifiers for the ensemble learning. The model output is determined by averaging the results of the multiple decision trees. Input data is input to the root of each decision tree, and the output results of the decision trees are provided to the leaves of each decision tree. Between the root and the leaves, nodes consisting of one or more layers are provided. In the node, data is input to a higher-level node (root or node), and this data is input to one of the lower-level nodes (nodes or leaves) depending on the evaluation result of a partitioning function. This process is repeated recursively from the root to the leaves. The evaluation function is learned and determined for each individual decision tree using training data. In the random forest, randomness is introduced during this learning process. This randomness is introduced in two ways: randomly extracting training data S0(∈S) from multiple training data S to be used for training the decision tree, and randomly selecting and using a portion T0(∈T) of the set T of possible values ​​for the parameters of the partitioning function. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Hitoshi Habe, "Random Forests," Information Processing Society of Japan Research Report, Vol. 2021-CVIM-182, No. 31, May 23, 2021 [Non-patent document 2] Hitoshi Habe, "Fundamentals and Recent Trends of Random Forests," Journal of the Institute of Image Information and Television Engineers, Vol. 70, No. 5, pp. 788-791 (2016) Summary of the Invention [Problem to be solved by the invention]

[0005] Incidentally, when the explanatory variables of a model that models a given phenomenon consist of multiple components (factors, items) (first components) and the objective variable of the model consists of one or multiple components (second components), being able to visualize the magnitude of the influence (degree of influence, importance) of the components of the explanatory variables on the components of the objective variable is useful for understanding causal relationships, contributes to the analysis of the given phenomenon, and is useful for the development of products that cause the given phenomenon. In particular, when one or multiple intermediate variables that are linked in series between the explanatory variables and the objective variable are present, many different routes can be envisioned that lead from the explanatory variables to the intermediate variables and then to the objective variable. Therefore, being able to visualize important routes in the process from the explanatory variables to the intermediate variables and then to the objective variable can greatly contribute to the analysis of the given phenomenon.

[0006] The present invention has been made in consideration of the above circumstances, and its object is to provide a variable relationship display device, a variable relationship display method, and a variable relationship display program that can display the relationship of importance between variables in a model that models a specified phenomenon. [Means for solving the problem]

[0007] As a result of various studies, the inventors have found that the above object can be achieved by the present invention described below. That is, a variable relationship display device according to one aspect of the present invention is a device for displaying inter-variable relationships between explanatory variables each consisting of a predetermined number of first components and a dependent variable each consisting of one or more second components in a model that models a predetermined phenomenon, the device comprising: a display unit that performs a display; a model generation unit that performs a model generation process that generates partial models of the explanatory variables and one second component of the dependent variable using a random forest, for each second component of the dependent variable, by performing a process for generating the model consisting of a plurality of partial models; an importance processing unit that performs an importance processing that calculates, for each first component of the explanatory variables, an importance that is an index representing the magnitude of the influence of the explanatory variables on the dependent variable based on the impurity of the partial models; and a display processing unit that displays, on the display unit, the importance calculated by the importance processing unit in a matrix in a two-dimensional space with the first component of the explanatory variables as one axis and the second component of the dependent variable as the other axis.

[0008] Such a variable relationship display device generates a model consisting of multiple partial models using a random forest, calculates the importance of each first component of the explanatory variable based on the impurity of the partial model, and displays each importance in a matrix in a two-dimensional space with the first component of the explanatory variable on one axis and the second component of the target variable on the other axis, thereby making it possible to display the relationship of importance between variables in a model that models a specified phenomenon.

[0009] In another aspect, the variable relation display device described above further includes an input unit that receives inputs of a threshold value of importance to be displayed and a second component, and the display processing unit associates a first component of the explanatory variable having an importance equal to or greater than the threshold value received by the input unit with the second component received by the input unit, and displays the first component and the second component together with their importance on the display unit. Preferably, in the variable relation display device described above, the association between the first component of the explanatory variable having an importance equal to or greater than the threshold value and the second component received by the input unit is represented by a line segment (edge), and the importance is represented by a thickness of the line segment. Preferably, in the variable relation display device described above, the association between the first component of the explanatory variable having an importance equal to or greater than the threshold value and the second component received by the input unit is represented by a line segment (edge), and the importance is represented by a numerical value.

[0010] Such a variable relationship display device further includes an input unit that accepts inputs of the threshold of importance and second components to be displayed, and therefore can display first components having importance equal to or greater than the threshold for a specific second component focused on by the user, thereby visualizing first components that are important for the specific second component.

[0011] In another aspect, in the above-mentioned variable relation display device, the display processing unit further displays on the display unit a correlation coefficient between a first component of the explanatory variable having an importance equal to or greater than a threshold value received by the input unit and a second component of the target variable. Preferably, in the above-mentioned variable relation display device, the correspondence between the first component of the explanatory variable having an importance equal to or greater than the threshold value and the second component received by the input unit is represented by a line segment (edge), the importance is represented by the thickness of the line segment, and the correlation coefficient is represented by its numerical value around the line segment.

[0012] Such a variable relationship display device further displays a correlation coefficient in addition to the importance, and therefore, based on the correlation coefficient, it is possible to recognize the linearity between the first component of the explanatory variable having an importance equal to or greater than the threshold and the second component received by the input unit. The larger the absolute value of the correlation coefficient, the higher the linearity, and conversely, the smaller the absolute value of the correlation coefficient, the lower the linearity (in other words, the higher the nonlinearity).

[0013] In another aspect, the above-described variable relationship display device further includes one or more intermediate variables that are arranged in series in a chain between the explanatory variables and the objective variable, and the model generation unit and the importance processing unit each perform the model generation process and the importance processing for each pair of variables extending from the explanatory variables via the intermediate variables to the objective variable, sequentially from the objective variable to the explanatory variable, by provisionally regarding the preceding variable as an explanatory variable and the succeeding variable as an objective variable, and the display processing unit displays the importance determined by the importance processing unit for each pair of variables on the display unit.

[0014] Such a variable relationship display device can display the relationships of importance between variables in a model in which a cause appears as a result through a series of intermediates.

[0015] In another aspect, the above-mentioned variable relation display device further includes an explanatory variable selection unit that selects, as a predetermined number of first components in the explanatory variables, the predetermined number of initial components from a plurality of initial components that constitute initial explanatory variables, and the explanatory variable selection unit generates, from the plurality of initial components, a plurality of sets each having a combination of the predetermined number of initial components that are different from each other, and each time a set is generated when generating the plurality of sets, causes the model generation unit to perform the model generation process by assuming that the initial component of the set is a first component of the explanatory variables, thereby generating the model consisting of a plurality of partial models. The system is equipped with a candidate generation unit that performs a candidate generation process to generate a candidate model for the one pair, and a selection unit that performs a selection process to select a candidate model that gives the best evaluation using a predetermined evaluation function from among a plurality of candidate models corresponding to each of the plurality of pairs generated by the candidate generation unit, and select the predetermined number of initial components of the pair corresponding to the selected candidate model as the predetermined number of first components, wherein the predetermined evaluation function is a function based on the estimation accuracy of the candidate model generated by the candidate generation unit, and the model generation unit generates the model using the predetermined number of first components selected by the selection unit as first components of the explanatory variables.

[0016] When modeling a given phenomenon, the number of components in the explanatory variables may be enormous, for example, thousands, tens of thousands, or hundreds of thousands. In such cases, not all components in the explanatory variables necessarily affect the objective variable equally. Therefore, if important components that significantly affect the objective variable can be selected (extracted or selected), the given phenomenon can be modeled using a relatively simple model, and such selection is desirable. On the other hand, by obtaining principal components using so-called principal component analysis, the space formed by the principal components can be reduced in dimension below the dimension of the explanatory variables, which are represented by the number of components in the explanatory variables. However, since the space formed by the explanatory variables is converted into a space formed by the principal components, interpretation of the principal components becomes necessary. For this reason, the selection is desirable while maintaining the components of the explanatory variables as they are. The variable relationship display device further includes an explanatory variable selection unit that selects a candidate model that provides the best evaluation using an evaluation function based on the estimation accuracy of the candidate model generated by the candidate generation unit, and selects a predetermined number of initial components of a set corresponding to the selected candidate model from multiple initial components as first components, thereby enabling more appropriate selection of the predetermined number of first components.

[0017] In another aspect, the above-mentioned variable relation display device further comprises one or more intermediate variables arranged in series in a chain between the initial explanatory variables and the objective variable, and the candidate generation unit and the selection unit each perform the candidate generation process and the selection process for each variable between the objective variable and the initial explanatory variables, by provisionally regarding a preceding variable as an initial explanatory variable and a succeeding variable as an objective variable, in order from the objective variable to the initial explanatory variable, and the model generation unit performs the candidate generation process and the selection process for each variable between the objective variable and the initial explanatory variables, by provisionally regarding a preceding variable as an initial explanatory variable and a succeeding variable as an objective variable, in order from the objective variable to the initial explanatory variable, and The model is generated by provisionally regarding the preceding variable as an initial explanatory variable and the succeeding variable as a dependent variable, sequentially moving toward the initial explanatory variable, and using the predetermined number of first components selected by the selection unit as first components of the explanatory variables, and the importance processing unit performs the importance processing for each pair of variables from the initial explanatory variable through the intermediate variables to the dependent variable, sequentially moving from the dependent variable to the initial explanatory variable, by provisionally regarding the preceding variable as an initial explanatory variable and the succeeding variable as a dependent variable, and the display processing unit displays each importance determined by the importance processing unit for each pair of variables on the display unit.

[0018] Such a variable relationship display device can more appropriately select a predetermined number of first components in each model when modeling an event in which a cause appears as a result through a series of intermediates, and can display each relationship of importance between each variable in each model.

[0019] In another aspect, in the above-mentioned variable relationship display device, the predetermined event is road noise heard by a vehicle occupant due to vibration input to a tire in response to unevenness in a road surface. Preferably, in the above-mentioned variable relationship display device, the explanatory variables or the initial explanatory variables are a plurality of different component plate thicknesses of a front suspension component and a main body frame component of a vehicle, the target variable is a sound pressure transmission characteristic (Sound Pressure Level (SPL)) at the position of the occupant's ear, the intermediate variables include first and second intermediate variables arranged in series in a chain, the first intermediate variable is an excitation point response characteristic (point inertance (P / I)) at a plurality of points (evaluation points, measurement points) set on the front suspension component and the main body frame component, and the second intermediate variable is a vibration transmission characteristic (A / F) at the plurality of points with a tire contact point as the excitation point.

[0020] This makes it possible to provide a variable relationship display device that can display the relationship of importance between variables in a model that models road noise.

[0021] A variable relationship display method according to another aspect of the present invention is a method for displaying the relationship between explanatory variables consisting of a predetermined number of first components and a dependent variable consisting of one or more second components in a model that models a predetermined phenomenon, and includes the following steps: a model generation step for generating partial models of the explanatory variables and one second component of the dependent variable using a random forest, the process being performed for each second component of the dependent variable, thereby generating the model consisting of a plurality of partial models; an importance processing step for calculating, for each first component of the explanatory variables, an importance that is an index representing the degree of influence that the explanatory variables have on the dependent variable based on the impurity of the partial models; and a display processing step for displaying, on a display unit, the importance calculated in the importance processing step in a matrix form in a two-dimensional space with the first component of the explanatory variables as one axis and the second component of the dependent variable as the other axis.

[0022] A variable relationship display program according to another aspect of the present invention is a program for displaying the relationship between explanatory variables consisting of a predetermined number of first components and a dependent variable consisting of one or more second components in a model that models a predetermined phenomenon, and causes a computer to execute the following steps: a model generation step for generating partial models of the explanatory variables and one second component of the dependent variable using a random forest, for each second component of the dependent variable, by performing the process for all second components of the dependent variable, thereby generating the model consisting of a plurality of partial models; an importance processing step for calculating, for each first component of the explanatory variables, an importance that is an index representing the degree of influence of the explanatory variables on the dependent variable based on the impurity of the partial models; and a display processing step for displaying, on a display unit, the importance calculated in the importance processing step in a matrix form in a two-dimensional space with the first component of the explanatory variables as one axis and the second component of the dependent variable as the other axis.

[0023] Such a variable relationship display method and variable relationship display program uses a random forest to generate a model consisting of multiple partial models, calculates the importance of each first component of an explanatory variable based on the impurity of the partial model, and displays each importance in a matrix in a two-dimensional space with the first component of the explanatory variable on one axis and the second component of the target variable on the other axis, thereby making it possible to display the relationship of importance between variables in a model that models a specified phenomenon. [Effects of the Invention]

[0024] The variable relation display device, variable relation display method, and variable relation display program according to the present invention can display the relationship of importance between variables in a model that models a predetermined phenomenon. [Brief explanation of the drawings]

[0025] [Figure 1] FIG. 1 is a block diagram showing a configuration of a variable relationship display device with an explanatory variable selection function in an embodiment. [Figure 2] 5 is a diagram for explaining generation of a partial model in the variable relationship display device. FIG. [Figure 3] FIG. 10 is a diagram for explaining an importance map. [Figure 4] FIG. 10 is a diagram for explaining an importance graph. [Figure 5] As an example, this is a diagram for explaining how important components between variables are extracted for a specified second component in a response variable. [Figure 6] 10 is a flowchart showing the operation of the variable relationship display device regarding the selection of explanatory variables and the display of variable relationships. [Figure 7] FIG. 1 is a diagram illustrating, as an example, parts of a vehicle to be evaluated. [Figure 8] FIG. 10 is a diagram for explaining evaluation points (measurement points, data acquisition points) as an example. [Figure 9] FIG. 10 is a diagram showing the comparison results of sound pressure transmission characteristics (SPL) as an example. [Figure 10] As an example, this figure shows the evaluation results of the accuracy of the model evaluated by the coefficient of determination (R2). [Figure 11] As an example, this is a diagram showing an importance graph for a specified second component in a response variable. [Figure 12] FIG. 12 is a diagram for explaining components having importance of 0.6 or more in FIG. 11. DETAILED DESCRIPTION OF THE INVENTION

[0026] Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. In addition, components with the same reference numerals in each drawing indicate the same components, and their description will be omitted as appropriate. In this specification, when referring to a general term, a reference numeral without a subscript is used, and when referring to an individual component, a reference numeral with a subscript is used.

[0027] A variable relation display device according to an embodiment displays the inter-variable relations between explanatory variables, each consisting of a predetermined number of first components, and a dependent variable, each consisting of one or more second components, in a model that models a predetermined phenomenon. The variable relation display device includes a display unit that displays the inter-variable relations; a model generation unit that performs a model generation process that generates partial models of the explanatory variables and one second component of the dependent variable using a random forest, for each second component of the dependent variable, thereby generating the model consisting of multiple partial models; an importance processing unit that performs an importance processing that calculates, for each first component of the explanatory variables, an importance, which is an index representing the degree of influence of the explanatory variables on the dependent variable, based on the impurity of the partial models; and a display processing unit that displays, on the display unit, the importances calculated by the importance processing unit in a matrix in a two-dimensional space, with the first component of the explanatory variables as one axis and the second component of the dependent variable as the other axis. The variable relation display device will be described in more detail below.

[0028] FIG. 1 is a block diagram showing the configuration of a variable relation display device with an explanatory variable selection function according to an embodiment. FIG. 2 is a diagram illustrating the generation of a partial model in the variable relation display device. FIG. 2A is a diagram illustrating initial explanatory variables, intermediate variables, and dependent variables, and FIG. 2B is a diagram illustrating the generation of a partial model using a random forest. Note that "T" in "Terr 1,T," "Result 1,T," "Terr dn,T," and "Result dn,T" in FIG. 2B refers to the number of decision trees generated in each random forest model. FIG. 3 is a diagram illustrating an importance map. FIG. 4 is a diagram illustrating an importance graph. FIG. 5 is a diagram illustrating, as an example, the extraction of important components between variables for a specified second component in the dependent variable.

[0029] The variable relationship display device A in the embodiment is a device that displays the relationship between explanatory variables consisting of a predetermined number of first components in a model that models a predetermined phenomenon and a target variable consisting of one or more second components, and in this embodiment, further includes an explanatory variable selection function that selects a predetermined number of initial components from a plurality of initial components that constitute initial explanatory variables as the predetermined number of first components in the explanatory variables. Such a variable relationship display device A includes, for example, a data acquisition unit 1, a control processing unit 2, an input unit 3, a display unit 4, an interface unit 5, and a storage unit 6, as shown in FIG.

[0030] The data acquisition unit 1 is connected to the control processing unit 2 and is a device that acquires data on initial explanatory variables and response variables under the control of the control processing unit 2 to model a predetermined phenomenon using a model including explanatory variables each consisting of a predetermined number of first components and response variables each consisting of one or more second components. In this embodiment, the data acquisition unit 1 also acquires data on one or more intermediate variables that are arranged in a serial chain between the initial explanatory variables and the response variable. Each of these intermediate variables consists of one or more intermediate components. The intermediate variables are variables located between the initial explanatory variable (or explanatory variable) and the response variable, and are connected in series. Adjacent variables have an input-output relationship preset by the user (i.e., the previous variable is the input to the subsequent variable and the subsequent variable is the output of the previous variable). This input-output relationship preset by the user may be a causal relationship based on a physical phenomenon, but is not limited to such a causal relationship based on a physical phenomenon and may also include a relationship based on a hypothesis. The number of intermediate components for each intermediate variable may be the same or different. If the variable relationship display device A does not have an explanatory variable selection function, data on explanatory variables is acquired instead of the data on the initial explanatory variables.

[0031] The predetermined event may be any event (matter, phenomenon) as long as multiple initial components in the initial explanatory variables and one or multiple second components of the target variable can be quantified. In this embodiment, since there are also intermediate variables, the predetermined event may be any event as long as the intermediate components of the intermediate variables can also be quantified.

[0032] The data acquisition unit 1 may be, for example, a measuring instrument that directly or indirectly measures data on the initial components of the initial explanatory variables, data on the intermediate components of the intermediate variables, and data on the second component of the target variable. The measurement results obtained by the measuring instrument are stored and accumulated in the storage unit 6 to generate partial models and to be used as a training data set for generating a candidate model (or a model).

[0033] The data on the initial components of the initial explanatory variables, the data on the intermediate components of the intermediate variables, and the data on the second component of the response variable may be data on simulation results obtained by CAE (Computer Aided Engineering). Alternatively, for example, the data acquisition unit 1 may be an input unit that inputs data on simulation results obtained by CAE, and in this case, the data acquisition unit 1 may also serve as the input unit 3 described below. The input data on the simulation results is stored in the storage unit 6 for use as a learning dataset. The CAE is disclosed, for example, in "Kano Katsuhito et al., 'Evolution of CAE in Crash Safety Development,' Mazda Technical Review, No. 30 (2012), pp. 151-155," and is generally a simulation of a large-scale finite element model using nonlinear analysis software LS-DYNA (LSTC-Livemore Software Technology Crops).

[0034] Alternatively, for example, the data acquisition unit 1 may be an interface circuit that inputs and outputs data to and from an external device. In this case, the external device is a storage medium that stores data on the initial components of the initial explanatory variables, the intermediate components of the intermediate variables, and the second component of the response variable, which are obtained from the measurement results or the simulation results. The storage medium may be, for example, a Universal Serial Bus (USB) memory or an SD card (registered trademark). Alternatively, for example, the data acquisition unit 1 may be a drive device that reads data from a storage medium that stores data on the initial components of the initial explanatory variables, the intermediate components of the intermediate variables, and the second component of the response variable, which are obtained from the measurement results or the simulation results. In this case, the storage medium may be, for example, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Compact Disc Recordable), a DVD-ROM (Digital Versatile Disc Read Only Memory), or a DVD-R (Digital Versatile Disc Recordable). Alternatively, for example, the data acquisition unit 1 may be a communication interface circuit that transmits and receives communication signals to and from an external device. In this case, the external device is a server device that is connected to the communication interface circuit via a network (such as a WAN (Wide Area Network, including a public communication network) or a LAN (Local Area Network)) and manages data on initial components of initial explanatory variables, data on intermediate components of intermediate variables, and data on second components of target variables obtained from the measurement results or the simulation results. When the data acquisition unit 1 is the interface circuit or communication interface circuit described above, the data acquisition unit 1 may also serve as the IF unit 5 described below.

[0035] The input unit 3 is connected to the control processing unit 2 and is a device that inputs various commands, such as a command to start displaying variable relationships, and various data necessary for operating the variable relationship display device A, such as the name of a model, to the variable relationship display device A, and is, for example, a plurality of input switches to which predetermined functions are assigned, a keyboard, a mouse, etc. The display unit 4 is connected to the control processing unit 2 and is, under the control of the control processing unit 2, a device that displays the commands and data, variable relationships, etc. input from the input unit 3, and is, for example, a display device such as a CRT display, an LCD (liquid crystal display), or an organic EL display.

[0036] The input unit 3 and the display unit 4 may be configured as a touch panel. In the case of configuring this touch panel, the input unit 3 is a position input device that detects an operation position and inputs, for example, a resistive film type or a capacitive type. In this touch panel, a position input device is provided on the display surface of the display unit 4, and one or more input content candidates that can be input are displayed on the display unit 4. When the user touches the display position displaying the input content they want to input, the position is detected by the position input device, and the display content displayed at the detected position is input to the variable relation display device A as the user's operation input content. With such a touch panel, the user can easily intuitively understand the input operation, and therefore a variable relation display device A that is easy for the user to use is provided.

[0037] The IF unit 5 is connected to the control processing unit 2 and is a circuit that inputs and outputs data to and from, for example, an external device under the control of the control processing unit 2, and is, for example, an interface circuit for RS-232C, which is a serial communication method, an interface circuit using the Bluetooth (registered trademark) standard, an interface circuit using the USB standard, etc. The IF unit 5 may also be, for example, a communication interface circuit that transmits and receives communication signals to and from an external device, such as a data communication card or a communication interface circuit conforming to the IEEE802.11 standard, etc.

[0038] The storage unit 6 is connected to the control processing unit 2 and is a circuit that stores various predetermined programs and various predetermined data under the control of the control processing unit 2. The various predetermined programs include, for example, a control processing program, which controls each of the units 1, 3 to 6 of the variable relationship display device A in accordance with the function of each unit; a model generation program that generates a model consisting of a plurality of partial models by performing a process of generating partial models of the explanatory variables and one second component of the objective variable using a random forest for each second component of the objective variable, for each second component of the objective variable; an importance processing program that calculates, for each first component of the explanatory variables, an importance that is an index representing the degree of influence of the explanatory variables on the objective variable based on the impurity of the partial models; a display processing program that displays the importance calculated by the importance processing program on the display unit 4 in a matrix in a two-dimensional space with the first component of the explanatory variables as one axis and the second component of the objective variable as the other axis; and an explanatory variable selection program that selects, as a predetermined number of first components of the explanatory variables, the predetermined number of initial components from a plurality of initial components that constitute initial explanatory variables. The various types of predetermined data include, for example, data necessary for executing each of these programs, such as a training dataset (data on the initial components of the initial explanatory variables, data on the intermediate components of the intermediate variables, and data on the second component of the target variable) and the name of the model. Such storage unit 6 includes, for example, a ROM (Read Only Memory), which is a nonvolatile storage element, and an EEPROM (Electrically Erasable Programmable Read Only Memory), which is a rewritable nonvolatile storage element. The storage unit 6 also includes a RAM (Random Access Memory), which serves as a working memory for the control processing unit 2 and stores data generated during execution of the predetermined programs. The storage unit 6 may also be configured with a hard disk drive with a relatively large storage capacity.

[0039] The control processing unit 2 is a circuit that controls each of the units 1, 3 to 6 of the variable relationship display device A according to the function of each unit, displays the relationship between explanatory variables consisting of a predetermined number of first components in a model that models a predetermined phenomenon and a target variable consisting of one or more second components, and, when displaying, selects the predetermined number of initial components as the first components from multiple initial components that make up the initial explanatory variables, and generates a model using the explanatory variables of the selected first components. The control processing unit 2 is configured, for example, with a CPU (Central Processing Unit) and its peripheral circuits. By executing a control processing program, the control processing unit 2 functionally comprises a control unit 21, a model generation unit 22, an importance processing unit 23, a display processing unit 24, and an explanatory variable selection unit 25.

[0040] The control unit 21 controls each of the units 1, 3 to 6 of the variable relationship display device A according to the function of each unit, and controls the variable relationship display device A as a whole.

[0041] The model generation unit 22 performs a model generation process to generate a model consisting of multiple partial models by performing a process of generating partial models of the explanatory variables and one second component of the objective variable using a random forest for each second component of the objective variable and for all second components.

[0042] The importance processing unit 23 performs importance processing to determine the importance, which is an index representing the degree of influence that the explanatory variable has on the target variable, for each first component of the explanatory variable based on the impurity of the partial model.

[0043] The display processing unit 24 displays the importance levels calculated by the importance processing unit 23 on the display unit 4 in a matrix format in a two-dimensional space with the first component of the explanatory variable as one axis and the second component of the target variable as the other axis.

[0044] In the case where the model that models the predetermined phenomenon further includes one or more intermediate variables that are arranged in series in a chain between the explanatory variable and the objective variable, the model generation unit 22 and the importance processing unit 23 each perform the model generation process and the importance processing for each variable between the explanatory variable, via the intermediate variable, and the objective variable, sequentially from the objective variable to the explanatory variable, by provisionally regarding the preceding variable as the explanatory variable and the succeeding variable as the objective variable, and the display processing unit 24 displays each importance calculated by the importance processing unit 23 for each variable between the variables on the display unit 4.

[0045] In this embodiment, the above-mentioned processes will be described in more detail using an example in which the first component of the explanatory variable is selected from the initial components of the initial explanatory variable.

[0046] The explanatory variable selection unit 25 selects a predetermined number of initial components from a plurality of initial components constituting the initial explanatory variables as a predetermined number of first components in the explanatory variables. More specifically, the explanatory variable selection unit 25 functionally includes a candidate generation unit 251 and a selection unit 252.

[0047] The candidate generation unit 251 generates a plurality of sets, each having a combination of the predetermined number of initial components that are different from each other, from the plurality of initial components, and each time a set is generated when generating the plurality of sets, the candidate generation unit 251 causes the model generation unit 22 to perform the model generation process by assuming that the initial components of the set are first components of the explanatory variables, thereby generating the model consisting of a plurality of partial models as a candidate model for the one set. That is, the candidate generation unit 251 generates a plurality of sets, each having a combination of the predetermined number of initial components that are different from each other, from the plurality of initial components, and each time a set is generated when generating the plurality of sets, the candidate generation unit 251 performs the process of generating partial models of the initial explanatory variables and one second component of the objective variable by using a random forest for each second component of the objective variable, by using the model generation unit 22, thereby generating a candidate model consisting of a plurality of partial models for the one set.

[0048] The predetermined number may be any number as long as it is smaller than the number of initial components. The predetermined number may be appropriately set in advance, but in this embodiment, it is input by the user via the input unit 3.

[0049] The selection unit 252 selects a candidate model that gives the best evaluation using a predetermined evaluation function from among a plurality of candidate models corresponding to each of the plurality of pairs generated by the candidate generation unit 251, and performs a selection process to select the predetermined number of initial components of the pair corresponding to the selected candidate model as the predetermined number of first components.

[0050] The predetermined evaluation function is a function based on the estimation accuracy (prediction error) of the candidate model generated by the candidate generation unit.

[0051] The model generation unit 22 generates the model using the predetermined number of first components selected by the selection unit 252 as first components of the explanatory variables.

[0052] In this embodiment, since there are intermediate variables, the candidate generation unit 251 and the selection unit 252 each perform the candidate generation process and the selection process for each of the variables between the initial explanatory variable and the intermediate variable and the variable between the subsequent variables as the dependent variable, sequentially from the dependent variable to the initial explanatory variable. The model generation unit 22 generates the model by using the predetermined number of first components selected by the selection unit 252 as first components of the explanatory variables for each of the variables between the initial explanatory variable and the subsequent variables as the dependent variable, sequentially from the dependent variable to the initial explanatory variable and the variable between the subsequent variables as the dependent variable. The importance processing unit 23 performs the importance processing for each of the variables between the initial explanatory variable, the intermediate variable, and the objective variable, sequentially from the objective variable to the initial explanatory variable, by provisionally regarding the preceding variable as the initial explanatory variable and the succeeding variable as the objective variable. The display processing unit 24 displays the importance calculated by the importance processing unit 23 for each of the variables.

[0053] For example, as shown in Figure 2A, multiple dx initial components (x1, x2, . . . , x dx ), the initial explanatory variable X consists of multiple dy second components (y1, y2, . . . , y dy ), and multiple n intermediate variables C1,...,C n In this case, the candidate generation process and selection process are performed sequentially from the objective variable Y to the initial explanatory variable X, and then the objective variable Y and the intermediate variable C n Between variables, intermediate variable C n and the intermediate variable C n-1, between the variables C1 and C2 (not shown), and between the variables C1 and the initial explanatory variable X. In the example shown in FIG. 2A, although there are multiple intermediate variables C, there may be only one. Although there are multiple second components y of the response variable Y, there may be only one. The number dx of the initial components x of the initial explanatory variable X, the number d of the intermediate components c of each intermediate variable C, and the number dy of the second components y of the response variable Y may all be the same number, may be different numbers, or may be the same number partially. In other words, as long as there are multiple initial components x, they are arbitrary.

[0054] In this process between variables, the candidate generation process and the selection process are carried out by assuming that the variables in the preceding stage are initial explanatory variables and that the variables in the following stage are objective variables. More specifically, for example, the objective variable Y and the intermediate variable C n Between the variables, the intermediate variable C n is assumed to be the initial explanatory variable, the subsequent dependent variable Y is assumed to be the dependent variable (although assumed to be the dependent variable, in this case it is the dependent variable Y itself), and the intermediate variable C n and the intermediate variable C n-1 Between the variables, the intermediate variable C n-1 is assumed to be the initial explanatory variable, and the intermediate variable C n is provisionally regarded as the dependent variable, and between the variables of the intermediate variables C2 and C1 shown in the figure, the intermediate variable C1 in the previous stage is provisionally regarded as the initial explanatory variable, and the intermediate variable C2 in the subsequent stage is provisionally regarded as the dependent variable, and between the variables of the intermediate variable C1 and the initial explanatory variable X, the initial explanatory variable X in the previous stage is provisionally regarded as the initial explanatory variable (although provisionally regarded as the initial explanatory variable, in this case it is the initial explanatory variable X itself), and the intermediate variable C1 in the subsequent stage is provisionally regarded as the dependent variable.

[0055] The candidate generator 251 first calculates the target variable Y and the intermediate variable C n Between the variables, the intermediate variable C n Multiple intermediate components in (c n1 , c n2 ,···,c ndn) (the intermediate components tentatively regarded as the initial components), a set (first set) of the predetermined number of intermediate variables is generated.

[0056] Next, the candidate generation unit 251 uses the model generation unit 22 to generate the intermediate variable C n and one second component y of the dependent variable Y are generated by a random forest. As a result, a partial model for one second component y of the dependent variable Y is generated.

[0057] Then, the candidate generating unit 251 performs this process for each second component y of the objective variable Y and for all the second components y.

[0058] As a result, the intermediate variable C consisting of a plurality of dy partial models for the generated first set is n A candidate model (first candidate model) of the objective variable Y is generated.

[0059] Next, the candidate generator 251 generates a set (second set) of intermediate component combinations different from the combination of intermediate components (intermediate components assumed to be initial components) in the generated first set, and performs the above-mentioned processes. As a result, for the generated one second set, a set of intermediate variables C n and the objective variable Y, a candidate model (second candidate model) is generated.

[0060] Next, the candidate generator 251 generates a set (third set) of intermediate component combinations different from the combinations of intermediate components (intermediate components assumed to be initial components) in the first and second sets generated above, and performs the above-mentioned processes. As a result, for the generated third set, a set of intermediate variables C n and the objective variable Y, a candidate model (third candidate model) is generated.

[0061] The above-described process is performed for a plurality of pairs, thereby generating a plurality of candidate models corresponding to the plurality of pairs shown in FIG. 2B, for example.

[0062] The plurality of sets may be generated for all combinations of a predetermined number of initial components, or, to obtain an approximate solution or an optimal solution, the number of sets may be appropriately set by a user, and the predetermined number of initial components may be randomly extracted from a plurality of initial components to generate the number of sets set by the user. In this embodiment, as will be described later, these generation and selection processes are reduced to an extraction problem, and a so-called genetic algorithm is used.

[0063] The selection unit 252 calculates an evaluation value using the predetermined evaluation function for each of the plurality of candidate models corresponding to each of the plurality of pairs generated by the candidate generation unit 251 as described above. In this embodiment, the predetermined evaluation function is estimation accuracy (prediction error), and is the average value (the division result of dividing the sum of the estimation accuracy of each second component by the total number dy of second components) of each second component obtained by subtracting each value y of each second component from each estimated value (prediction value) y^ of each second component obtained by inputting a predetermined number of intermediate components c in the pair to each partial model (evaluation value q=(Σ(y^-y) 2 ) / dy, the smaller the evaluation value q, the higher the evaluation).

[0064] Then, the selection unit 252 compares these estimation accuracies (evaluation values ​​q), selects the candidate model that gives the best evaluation, and selects the predetermined number of intermediate components c of the set corresponding to this selected candidate model as the predetermined number of first components.

[0065] This will give us the target variable Y and the intermediate variable C n The first component of the model between variables is selected.

[0066] Then, each of the above-described processes is performed sequentially between each variable, from the response variable to the initial explanatory variable, and the first component of each model between each variable is selected.

[0067] The process of selecting the predetermined number of first components as described above can be reduced as follows.

[0068] Now, a c×a matrix consisting of a combinations of variables and their c values is defined as U, a c×b matrix obtained by partially extracting only b columns (b < a) from U is defined as U', and a target variable representing another c×d matrix is defined as V. When a random forest regression model is specified with matrix U' as the input and q columns (q ≤ d) of matrix V specified by the user as the output, the objective function Q is defined as follows, where the average of the estimation accuracy (prediction error) (for a total of q columns) is represented by the following Equation 1.

[0069]

Equation

[0070] The problem of extracting the best matrix U' that minimizes this objective function Q (that is, a combinatorial optimization problem of selecting the best b columns from the columns of matrix U and converting them into matrix U') is solved using, for example, a genetic algorithm. The genetic algorithm is a well-known algorithm usually used for searching for approximate solutions, and generally, a plurality of candidate individuals are prepared, and the individuals with high fitness are preferentially selected, and the solution is searched while repeating operations such as crossover and mutation (while alternating generations).

[0071] 1 , for each pair of variables extending from the initial explanatory variables through the intermediate variables to the dependent variable, the model generation unit 22 provisionally regards the preceding variable as the initial explanatory variable and the succeeding variable as the dependent variable, in order from the dependent variable to the initial explanatory variable, and generates a model between the variables using the predetermined number of first components selected by the selection unit 252 as first components of the dependent variables. A model between the variables may be generated using the training dataset, or the candidate model providing the best evaluation selected by the selection unit 252 may be used as the model between the variables.

[0072] The importance processor 23 calculates the importance between each of the variables between the initial explanatory variables, the intermediate variables, and the objective variable, sequentially from the objective variable to the initial explanatory variable, by provisionally regarding the preceding variable as the initial explanatory variable and the succeeding variable as the objective variable, based on the impurity of the partial model in the model between the variables. Algorithms for implementing random forests include, for example, ID3 (Iterative Dichotomizer 3), C4.5, C5.0, CART, and CHAID. For example, when using CART, each decision tree selects a condition for the explanatory variables so as to maximize the reduction in the Gini coefficient (information gain) at each branch, and repeatedly divides the sample (input from the upper node) into two according to the condition. The impurity represents the degree of improvement in error before and after branching. In terms of the Gini coefficient, the impurity ΔGI(t) is the reduction in the Gini coefficient (Gini impurity), and ΔGI(t)=P t GI(t)-P L GI(t L )-P R GI(t R ) and the Gini coefficient GI(t) is GI(t)=1-Σp(k|t) 2 where p(k|t) is the proportion of correctly classified class k in node t, and GI(t L ) is the Gini coefficient of the branch to the left of the node, and GI(t R) is the Gini coefficient of the branch to the right of the node, and P t is the ratio of the number of samples before splitting, and P L is the proportion of samples on the left side after the split, and P R is the proportion of samples on the right side after division. In the group of decision trees for the partial model generated as described above, the average value of the Gini impurities due to the selected first components can be treated as the importance of each first component for determining the second component. Therefore, in this embodiment, the importance processing unit 23 calculates the average value of the Gini impurities due to the selected first components and normalizes the average value to a range between 0 and 1 to calculate the importance.

[0073] Then, the display processing unit 24 displays the importance between the variables calculated by the importance processing unit 23 on the display unit 4 as an importance map (importance heat map) in a matrix in a two-dimensional space with the first component of the explanatory variable as one axis and the second component of the objective variable as the other axis. An example of this is shown in FIG. 3. In FIG. 3, the intermediate variable C n-1 and intermediate variable C n The importance of the variables is shown in the figure, and the intermediate variable C n-1 is considered as an explanatory variable and is set as the vertical axis of one axis, and the intermediate variable C n is assumed to be the objective variable and the horizontal axis of the other axis. n-1 and intermediate variable C n The predetermined number of intermediate variables C selected as the first components between the variables n-1 A predetermined number of intermediate components are arranged in the horizontal axis, and the intermediate variable C n and the target variable Y, and the intermediate variable C selected as the predetermined number of first components n A predetermined number of intermediate components in are arranged. Each importance value is expressed in grayscale (shade), with 1 being the darkest black and 0 being the lightest white.

[0074] In this embodiment, the input unit 3 further receives inputs of the threshold value of importance to be displayed and the second component, and the display processing unit 24 further associates the first component of the explanatory variable having an importance equal to or greater than the threshold value received by the input unit 3 with the second component received by the input unit 3, and displays the first component and the second component together with their importance on the display unit 4. More specifically, the association between the first component of the explanatory variable having an importance equal to or greater than the threshold value and the second component received by the input unit 3 is represented by a line segment (edge), and the importance is represented by the thickness of the line segment. An example of this is shown on the left side of FIG. 4 in plan view. On the right side of FIG. 4 in plan view, an intermediate variable C' k-1 and intermediate variable C” k In the example shown in Figure 4, the importance map between the intermediate variable C k The mth intermediate variable m in th is designated and input as the second component to be displayed, 0.6 is designated and input as the threshold value of the importance to be displayed, and the intermediate variable C' k-1 The first, third and sixteenth intermediate variables C' in k-1 [1], C' k-1 [3], C' k-1

[16] was extracted as the first component with an importance level of 0.6 or more, and the first intermediate variable C' k-1 Node ND' representing [1] k-1 [1] is the mth intermediate variable C” k Node ND” representing [m] k [m] corresponds to the line segment LN1, and the third intermediate variable C' k-1 Node ND' representing [3] k-1 [3] is the node ND k [m] corresponds to the line segment LN2, and the 16th intermediate variable C' k-1 Node ND' representing

[16] k-1

[16] is the node ND k[m] corresponds to the line segment LN3. The larger the importance value, the thicker the line segment LN (the smaller the importance value, the thinner the line segment LN). Note that the manner in which importance is displayed is not limited to the manner in which it is represented by the thickness of the line segment, or, for example, the importance may be associated with the line segment LN by a lead line from the line segment LN or the arrangement around the line segment, and may be directly represented by a numerical value.

[0075] When there are intermediate variables, selection of a component having an importance equal to or greater than the threshold value received by the input unit 3 with respect to the second component received by the input unit 3 is performed as shown in Fig. 5. The upper part of Fig. 5 illustrates an importance map (first importance map; X → C1) between the explanatory variable X and the first intermediate variable C1, the middle part of Fig. 5 illustrates an importance map (second importance map; C1 → C2) between the first intermediate variable C1 and the second intermediate variable C2, and the lower part of Fig. 5 illustrates an importance map (third importance map; C2 → Y) between the second intermediate variable C2 and the dependent variable Y. The horizontal axis of the third importance map; C2 → Y lists the second components y of the dependent variable Y in order from 1 to dy, and the vertical axis lists the second intermediate components c of the second intermediate variable C2 selected as the first component between the second intermediate variable C2 and the dependent variable Y in order from 1 to β. On the horizontal axis of the second importance map; C1 → C2, the second intermediate components c of the second intermediate variable C2 that were arranged on the vertical axis of the third importance map; C2 → Y are arranged in order from 1 to β, and on the vertical axis thereof, the first intermediate components c of the first intermediate variable C1 selected as the first component between the first intermediate variable C1 and the second intermediate variable C2 are arranged in order from 1 to α. On the horizontal axis of the first importance map; X → C1, the first intermediate components c of the first intermediate variable C1 that were arranged on the vertical axis of the second importance map; C1 → C2 are arranged in order from 1 to α, and on the vertical axis thereof, the first components x of the explanatory variable X selected as the first component between the explanatory variable X and the first intermediate variable C1 are arranged in order from 1 to 28. If the predetermined number of first components to be selected between each variable is, for example, 250, then α = β = 250. The threshold of importance to be displayed is 0.6, and the second component to be displayed is Y k If so, first, select Y from the second components arranged on the horizontal axis of the third importance map; C2 → Yk is selected, and this selected Y k From the importance levels in the column, an importance level of 0.6 or higher is selected, and the second intermediate component c having this importance level of 0.6 or higher is selected. In the example shown in FIG. 5, one second intermediate component c 2e Next, from each second intermediate component c of the second intermediate variable C2 arranged on the horizontal axis of the second importance map; C1 → C2, the second intermediate component c 2e is selected, and this selected second intermediate component c 2e From the weights arranged in the column, weights of 0.6 or more are selected, and the first intermediate component c having this weight of 0.6 or more is selected. In the example shown in FIG. 5, one first intermediate component c 1e Then, from each first intermediate component c of the first intermediate variable C1 arranged on the horizontal axis of the first importance map; X → C1, 1e is selected, and this selected first intermediate component c 1e From the importance levels in the column, the importance level of 0.6 or higher is selected, and the first component x having the importance level of 0.6 or higher is selected. In the example shown in FIG. 5, two first components x f , x g is selected. This allows us to estimate the second component Y of the response variable Y. k The component that influences the second intermediate variable C2 is the second intermediate component c 2e In the first intermediate variable C1, the first intermediate component c 1e In the explanatory variable X, the first two components x f , x g This becomes:

[0076] Then, the display processing unit 24 calculates the two first components x in the explanatory variable X. f , x g and the first intermediate component c of the first intermediate variable C1 1e and are connected by a line segment of a thickness according to their importance, and the first intermediate component c of the first intermediate variable C1 is 1e and the second intermediate component c of the second intermediate variable C2 2e and are connected by a line segment of a thickness according to their importance, and the second intermediate variable C2 is connected by the second intermediate component c 2e and the second component Y of the response variable Y kDisplay in the display unit 4 an importance graph in which the above are connected by line segments having thicknesses corresponding to their importance levels.

[0077] The process of structuring and visualizing important variables (intermediate components or first components having an importance level equal to or higher than a threshold value) in a chain from one second component in the target variable, through intermediate variables, to explanatory variables can be reduced as follows.

[0078] By the above selection process, assume that there is currently a random forest regression model group consisting of a total of N + 1 groups between the explanatory variable X and the target variable Y (the number of models included in each group is d’1, d’2, ···, d’ N , dy). Let the matrix that gives the importance map of the input variables for the random forest regression model group corresponding to the s-th group counted from the explanatory variable X side be I s . Represent it by I s . More specifically, the matrix I x is represented by a d’ s-1 × d’1 matrix when s = 1, and by a d’<​​​​​​​​​​​​​​​​​​​​​​​​​​​​One target variable (in the case of k=N+1, C" is selected as the node representing the second component (goal indicator) that constitutes the objective variable Y. k C” is the m-th column vector of k [m] is specified. Then, this node C” k A set S consisting of all nodes to which edges should be connected to [m] k-1、m is selected as follows: k I' is the m-th column vector of k [m] (d k-1 ) and extract only the components with importance equal to or greater than the threshold t, the row vector with all the corresponding indices arranged horizontally is M k、m The dimension (i.e., the number of indices) is d” k-1、m It is said that. Naturally, d” k-1,m ≦d' k-1 and the row vector M k、m 1 x d” k-1,m This represents the matrix Equation 4:

[0083]

number

[0084] Based on these, C' k-1 Total d” from k-1、m Column vectors C' k-1 [M k、m [1]], C' k-1 [M k、m [2]], ···, C' k-1 [M k、m [d” k-1、m The following expression 5, which is a set of partial extracted nodes, is selected as the appropriate node set.

[0085]

number

[0086] S k-1、m Each node of is input, and node C” k[m] is the output, and the input / output relationship is visualized by connecting edges (line segments) of thickness proportional to the importance between them. k、m The index set that collects the components of is also defined as the following equation 6.

[0087]

number

[0088] Then, in the second process, m is changed so that the first process has a total of d k-1 After that, the number of indexes excluding duplicates that belong to the union of the following formula 7 is d k-1 It is defined as R k is the set {1, 2, , d' k-1}, it is expressed by the following formula 8.

[0089]

number

[0090]

number

[0091] Similarly, considering the union of the following equation 9, S k The number of nodes belonging to d” (excluding duplicates) is also k-1 Therefore, these nodes are expressed as N s N-dimensional column vectors arranged side by side s ×d” k-1 The matrix is ​​defined by the following equation 10. When k≧2, I' k-1 I k-1 From d” k-1 d' with only columns partially extracted k-2 ×d” k-1 The matrix is ​​defined as follows:

[0092]

number

[0093]

number

[0094]

number

[0095] By executing the first and second processes in descending order of k = N, N-1, . . . , 2, 1, the input-output relationship is successively expanded, and finally, when k = 1, the input-output relationship from explanatory variable X through intermediate variable C to target variable Y is visualized as a chain structure with importance represented by the thickness of the edge. Note that the larger the importance threshold t, the smaller the total number of nodes that appear in the chain structure, making it easier to interpret the relationships between each component of each variable.

[0096] The control processing unit 2, input unit 3, display unit 4, IF unit 5 and storage unit 6 can be configured by, for example, a desktop, notebook or tablet computer.

[0097] Next, the operation of this embodiment will be described below: Fig. 6 is a flowchart showing the operation of the variable relationship display device regarding the selection of explanatory variables and the display of variable relationships.

[0098] When the variable relationship display device A having such a configuration is powered on, it initializes the necessary parts and starts operation. By executing the control processing program, the control processing unit 2 is functionally configured with a control unit 21, a model generation unit 22, an importance processing unit 23, a display processing unit 24, and an explanatory variable selection unit 25, and the explanatory variable selection unit 25 is functionally configured with a candidate generation unit 251 and a selection unit 252.

[0099] 6, when an operator (user) inputs an instruction to start displaying the variable relationships from the input unit 3, first, the variable relationship display device A acquires data on the initial explanatory variables and the objective variables from the data acquisition unit 1 by the control unit 21 of the control processing unit 2, and accepts the predetermined number of inputs from the input unit 3 (S1). Data on intermediate variables is also acquired as necessary.

[0100] Next, the variable relationship display device A generates, from the plurality of initial components, a plurality of sets having different combinations of the predetermined number of initial components using the candidate generation unit 251 of the explanatory variable selection unit 25 in the control processing unit 2, and generates a plurality of candidate models for each of these plurality of sets (S2).

[0101] Next, the variable relationship display device A selects, by the selection unit 252 of the explanatory variable selection unit 25 in the control processing unit 2, from among the plurality of candidate models corresponding to each of the plurality of pairs generated by the candidate generation unit 251 in process S2, the candidate model that gives the best evaluation by a predetermined evaluation function, and selects the predetermined number of initial components of the pair corresponding to this selected candidate model as the predetermined number of first components (S3).

[0102] Next, the variable relationship display device A generates a model of the specified event using the specified number of first components selected by the selection unit 252 in process S3 as explanatory variables using the model generation unit 22 of the control processing unit 2 (S4).

[0103] Next, the variable relationship display device A calculates the importance of each of the predetermined number of first components selected by the selection unit 252 in process S3 based on the impurity of the partial model using the importance processing unit 23 of the control processing unit 2 (S5).

[0104] When an intermediate variable C is present, each of the processes S2 to S5 is executed for each variable between the initial explanatory variable X, via the intermediate variable C, and the objective variable Y, sequentially from the objective variable Y to the initial explanatory variable X, with the preceding variable provisionally regarded as the initial explanatory variable and the subsequent variable provisionally regarded as the objective variable.

[0105] Next, the variable relationship display device A receives inputs of the threshold value of the importance to be displayed and the second component from the input unit 3 by the control unit 21 of the control processing unit 2 (S6).

[0106] Next, the variable relationship display device A displays an importance map, for example, as shown in Fig. 3, by the display processing unit 24 of the control processing unit 2, and displays an importance graph, for example, as shown in Fig. 4, for the second component received in process S6 (S7). If there is an intermediate variable C, an importance map for each variable is displayed, and an importance graph, for example, as shown in Fig. 11 described later, is displayed, which shows the relationship between each component in a chain manner between each variable from the explanatory variable X through the intermediate variables to the target variable Y. Note that the importance map and importance graph may be output from the IF unit 5 to an external device as needed.

[0107] Then, the variable relationship display device A determines whether or not to end the process using the control unit 21 of the control processing unit 2. For example, if a predetermined first input operation instructing to end, such as inputting the "Y" key, is received, the variable relationship display device A determines to end (Yes) and ends this process. On the other hand, if a predetermined second input operation instructing to continue, such as inputting the "N" key, is received, the variable relationship display device A determines not to end (No) and returns the process to process S6. This allows the user to analyze new, different importance thresholds and second components to be displayed.

[0108] Next, an example will be described. FIG. 7 is a diagram illustrating, as an example, a vehicle part to be evaluated. FIG. 8 is a diagram illustrating, as an example, evaluation points (measurement points, data acquisition points). FIG. 9 is a diagram illustrating, as an example, the comparison results of sound pressure transmission characteristics (SPL). The horizontal axis of FIG. 9 is frequency, and the vertical axis is SPL. FIG. 10 is, as an example, a diagram illustrating the accuracy of the model using the coefficient of determination (R 2 10 is a diagram showing the evaluation results evaluated by the following formula. The horizontal axis of FIG. 10 represents the type, and from left to right in a plan view, it represents P / I, A / F, and SPL, and the vertical axis represents the coefficient of determination (R 2 ) As an example, FIG. 11 is a diagram showing an importance graph for a specified second component in the dependent variable. FIG. 12 is a diagram for explaining components in FIG. 11 that have an importance of 0.6 or more.

[0109] In this example, the predetermined event is road noise heard by a vehicle occupant due to vibration input to the tires in response to road surface irregularities, the initial explanatory variable X is the plate thickness (dx=28) of 28 parts including the front suspension cross member and the main body frame parts shown in FIG. 7, and the objective variable Y is the sound pressure transmission characteristic (SPL) at the position of the occupant's ears. The intermediate variables C are P / I (excitation point response characteristics (point inertance), first intermediate variable C1) and A / F (vibration transmission characteristics with the tire contact point as the excitation point, second intermediate variable C2) at the 105 evaluation points (measurement points) shown in Figure 8. Three levels of component thickness were set between 0.5 and 2.9 [mm], and the CAE analysis results for 211 specifications were used as the learning data set. At each evaluation point, the frequency was set in 2 [Hz] increments between 2 and 450 [Hz], and the number of first intermediate components of the first intermediate variable C1 was d1 = 23625, and the number of second intermediate components of the second intermediate variable C2 was d2 = 23625. In selecting explanatory variables from the initial explanatory variables, for explanatory variable X, d'x = The first intermediate variable C1 was d'1 = 150 (H1 = {1, 2, . . . , d'1}), and the second intermediate variable C2 was d'2 = 150 (H2 = {1, 2, . . . , d'2}). The objective variable Y was the SPL between 2 and 420 Hz in 2 Hz increments, and Hy = {45, 46, . . . , 80} (i.e., Hy is a set of indices corresponding to the SPL in the frequency range from 90 Hz to 160 Hz). The accuracy of the model was evaluated based on the expressive power of the model (i.e., the estimation accuracy of C1, C2, and Y when X from the given training dataset was input into the model) to evaluate the reliability of the importance analysis based on the training dataset.

[0110] The comparison results of sound pressure transmission characteristics (SPL) are shown in FIG. 9. The comparison is made with the CAE results, and the solid line in FIG. 9 is the estimation result of the model according to this embodiment, and the dashed line is the CAE result. The accuracy of the model is evaluated using the coefficient of determination (R 2 The results of evaluating the expressiveness of each variable of P / I, A / F, and SPL using the RI are shown in Figure 10. The bar graph in Figure 10 shows the vertical axis as R 2For P / I and A / F, the R corresponding to each of the 150 selected variables is 2 The average value of SPL is R 2 The error bars indicate the mean value of R 2 9 and 10, the variable relationship display device A of this embodiment is able to appropriately select explanatory variables and model road noise.

[0111] As shown in Figure 9, when 100 [Hz] where the SPL is the maximum is set as the second component (goal index) to be displayed and the threshold of importance to be displayed is set to 0.6, the importance graph is shown in Figure 11, and the measurement points of the components with importance of 0.6 or more shown in Figure 11 are shown in Figure 12. For the response variable Y, the second component 100 [Hz] to be displayed is influenced more by the 114 [Hz] component of the Top Ceiling (RH) of the A / F, the 78 [Hz] component of the Fr Window Lwr (LH), the 114 [Hz] component of the Fr Header (RH), and the 188 [Hz] component of the Fr frame Fr (LH) of the second intermediate variable C2 than by the other second intermediate variables C2. In the first intermediate variable C1;P / I, the 90[Hz] component of the Roof Rail (RH), the 94[Hz] component of the Roof Rail (LH), the 114[Hz] component of the Fr Window Lwr(RH), and the 40[Hz] component of the Fr Window Lwr(RH) influence the 114[Hz] component of the Top Ceiling (RH) of the second intermediate variable C2;A / F more than the other first intermediate variables C1. The 114[Hz] component of the Fr Window Lwr(RH), the 40[Hz] component of the Fr Window Lwr(RH), and the 282[Hz] component of the Dash Lwr Panel (Ctr) influence the 78[Hz] component of the Fr Window Lwr(LH) of the second intermediate variable C2;A / F more than the other first intermediate variables C1. The 40[Hz] component of the Fr Window Lwr(RH) and the Dash Lwr The 282 [Hz] component of Panel influences the 114 [Hz] component of Fr Header (RH) of the second intermediate variable C2; ​​A / F more than the other first intermediate variables C1, and the 76 [Hz] component of Fr frame Rr (RH), the 432 [Hz] component of Fr frame Fr (RH), and the 320 [Hz] component of Fr frame Rr (LH) influence the 188 [Hz] component of Fr frame Fr (LH) of the second intermediate variable C2; ​​A / F more than the other first intermediate variables C1.Among the explanatory variables, the P13 component has a greater influence on the 90[Hz] component of the Roof Rail (RH) and the 94[Hz] component of the Roof Rail (LH) of the first intermediate variable C1;P / I than the other explanatory variables, the P25 component has a greater influence on the 114[Hz] component of the Fr Window Lwr (RH), the 40[Hz] component of the Fr Window Lwr (RH), and the 282[Hz] component of the Dash Lwr Panel of the first intermediate variable C1;P / I than the other explanatory variables, and the P01 component has a greater influence on the 76[Hz] component of the Fr frame Rr (RH), the 432[Hz] component of the Fr frame Fr (RH), and the 320[Hz] component of the FR frame Rr (LH) of the first intermediate variable C1;P / I than the other explanatory variables. 11, the SPL of cowl plate thickness - front window P / I - front header A / F - 100 [Hz] can be confirmed as a chain structure with high importance, and this is a conventionally known empirical relationship. As a result, the variable relationship display device A in this embodiment can appropriately select explanatory variables, model road noise, and visualize the chain of relationships between each component among each variable from explanatory variable X through intermediate variables to target variable Y.

[0112] As described above, the variable relationship display device A in the embodiment and the variable relationship display method and variable relationship display program implemented therein generate a model consisting of multiple partial models using a random forest, calculate the importance of each first component of the explanatory variable based on the impurity of the partial model, and display each importance in a matrix in a two-dimensional space with the first component of the explanatory variable on one axis and the second component of the target variable on the other axis, thereby making it possible to display the relationship of importance between variables in a model that models a specified phenomenon.

[0113] The above-mentioned variable relationship display device A, variable relationship display method, and variable relationship display program accept inputs of a threshold value of importance and second components to be displayed, and can display first components having an importance equal to or greater than the threshold value for a specific second component focused on by the user, thereby visualizing first components that are important for the specific second component.

[0114] The variable relationship display device A, the variable relationship display method, and the variable relationship display program can handle cases where there are one or more intermediate variables that are linked in series between an explanatory variable (initial explanatory variable) and a target variable, and can therefore display the relationships of importance between the variables in a model that models an event in which a cause passes through intermediate variables in sequence and appears as a result.

[0115] When modeling a given phenomenon, the number of components in the explanatory variables can be enormous, for example, thousands, tens of thousands, or hundreds of thousands. In such cases, not all components in the explanatory variables necessarily affect the target variable equally. Therefore, if important components that significantly affect the target variable can be selected (extracted or selected), the given phenomenon can be modeled using a relatively simple model, and such selection is desirable. On the other hand, by determining principal components using so-called principal component analysis, the space formed by the principal components can be reduced in dimension below the dimension of the explanatory variables, which are represented by the number of components in the explanatory variables. However, because the space formed by the explanatory variables is converted into a space formed by the principal components, interpretation of the principal components becomes necessary. For this reason, the selection is desirable while retaining the components of the explanatory variables. The variable relationship display device A, variable relationship display method, and variable relationship display program select a candidate model that provides the best evaluation using an evaluation function based on the estimation accuracy of the candidate model, and select a predetermined number of initial components of a set corresponding to the selected candidate model from multiple initial components as first components, thereby enabling more appropriate selection of the predetermined number of first components. The above-mentioned variable relation display device A, variable relation display method, and variable relation display program select the first component as the initial component. Therefore, while in so-called principal component analysis, an interpretation of the principal components is required, such interpretation is not required, and the user can intuitively recognize the first component that affects the target variable.

[0116] According to the example of the embodiment, it is possible to provide a variable relationship display device A that can display the relationship of importance between variables in a model that models road noise.

[0117] In the above-described embodiment, the display processing unit 24 may further display on the display unit 4 a correlation coefficient between the first component x of the explanatory variable X having an importance equal to or greater than the threshold value received by the input unit 3 and the second component y of the target variable Y. For example, the correlation coefficient is represented by a numerical value around a line segment (edge) that associates the first component x of the explanatory variable X having an importance equal to or greater than the threshold value with the second component y received by the input unit 3. The correlation coefficient is calculated by a well-known, conventional method of dividing the covariance by the standard deviation of each variable. Such variable relationship display device A, variable relationship display method, and variable relationship display program further display the correlation coefficient in addition to the importance. Therefore, based on the correlation coefficient, it is possible to recognize the linearity between the first component x of the explanatory variable X having an importance equal to or greater than the threshold value and the second component y received by the input unit 3. The larger the absolute value of the correlation coefficient, the higher the linearity. Conversely, the smaller the absolute value of the correlation coefficient, the lower the linearity (in other words, the higher the nonlinearity).

[0118] In order to express the present invention, the present invention has been properly and sufficiently described above through the embodiments with reference to the drawings, but it should be recognized that those skilled in the art can easily change and / or improve the above-mentioned embodiments. Therefore, unless the changes or improvements made by those skilled in the art are at a level that causes departure from the scope of the claims described in the claims, such changes or improvements are interpreted as being included in the scope of the claims. [Explanation of symbols]

[0119] A Variable Relationship Display Device 1 Data acquisition section 2. Control processing section 3 Input section 4 Display 5 Interface section (IF section) 6 Memory section 21 Control section 22 Model Generation Unit 23 Importance processing section 24 Display processing section 25 Explanatory Variable Selection Section 251 Candidate generation section 252 Selected Team

Claims

1. A variable relationship display device that displays a relationship between explanatory variables consisting of a predetermined number of first components and a response variable consisting of one or more second components in a model that models a predetermined phenomenon, a display unit for displaying; a model generation unit that performs a model generation process for generating the model consisting of a plurality of partial models by performing a process of generating a partial model of the explanatory variable and the second component of the dependent variable using a random forest for the second component of the dependent variable when there is one second component, and for generating the model consisting of a plurality of partial models by performing a process of generating a partial model of the explanatory variable and one second component of the dependent variable using a random forest for each second component of the dependent variable when there is a plurality of second components; an importance processing unit that performs importance processing for determining, for each first component of the explanatory variables, importance as an index representing the degree of influence of the explanatory variables on the objective variable based on the impurity of the partial model; a display processing unit that displays, on the display unit, the importance levels calculated by the importance level processing unit in a matrix form in a two-dimensional space in which a first component of the explanatory variable is on one axis and a second component of the objective variable is on the other axis; an input unit that receives inputs of a threshold value of importance to be displayed and a second component; the display processing unit further displays, on the display unit, a correlation coefficient between a first component of the explanatory variable having an importance equal to or greater than the threshold value received by the input unit and a second component of the dependent variable. Variable relationship display device.

2. The display processing unit associates a first component of the explanatory variable having an importance equal to or greater than a threshold value received by the input unit with respect to the second component received by the input unit, and displays the second component received by the input unit together with its importance on the display unit. The variable relationship display device according to claim 1 .

3. The correspondence between the first component of the explanatory variable having an importance equal to or greater than the threshold and the second component received by the input unit is represented by a line segment, the importance is represented by the thickness of the line segment, and the correlation coefficient is represented by a numerical value around the line segment.

3. The variable relationship display device according to claim 1 or 2.

4. further comprising one or more intermediate variables arranged in series in a chain between the explanatory variables and the objective variable, the model generation unit and the importance processing unit perform the model generation process and the importance processing, respectively, for each of the variables between the explanatory variables and the intermediate variables leading to the objective variable, sequentially from the objective variable to the explanatory variable, by provisionally regarding the preceding variable as an explanatory variable and provisionally regarding the subsequent variable as an objective variable; the display processing unit displays, on the display unit, each importance calculated by the importance processing unit for each of the variables. The variable relationship display device according to any one of claims 1 to 3.

5. an explanatory variable selection unit that selects, as a predetermined number of first components in the explanatory variables, the predetermined number of initial components from a plurality of initial components that constitute initial explanatory variables; The explanatory variable selection unit a candidate generation unit that generates a plurality of sets, each having a combination of the predetermined number of initial components that are different from each other, from the plurality of initial components, and each time a set is generated when generating the plurality of sets, causes the model generation unit to perform the model generation process by assuming that the initial component of the set is a first component of the explanatory variable, thereby generating the model consisting of a plurality of partial models as a candidate model for the one set; a selection unit that performs a selection process to select a candidate model that provides the best evaluation using a predetermined evaluation function from among a plurality of candidate models corresponding to each of the plurality of sets generated by the candidate generation unit, and to select the predetermined number of initial components of the set corresponding to the selected candidate model as the predetermined number of first components, the predetermined evaluation function is a function based on estimation accuracy of the candidate model generated by the candidate generation unit, the model generation unit generates the model using the predetermined number of first components selected by the selection unit as first components of the explanatory variables. The variable relationship display device according to any one of claims 1 to 3.

6. further comprising one or more intermediate variables arranged in series in a chain between the initial explanatory variables and the objective variable, the candidate generation unit and the selection unit each perform the candidate generation process and the selection process for each of the variables between the initial explanatory variable, via the intermediate variable, and the dependent variable, sequentially from the dependent variable to the initial explanatory variable, by provisionally regarding the preceding variable as an initial explanatory variable and the subsequent variable as a dependent variable; the model generation unit generates the model by using the predetermined number of first components selected by the selection unit as first components of the explanatory variables, sequentially from the objective variable to the initial explanatory variable, for each variable between the objective variable and the initial explanatory variable via the intermediate variables, by provisionally regarding a variable in a preceding stage as an initial explanatory variable and a variable in a subsequent stage as an objective variable, and the importance processing unit performs the importance processing for each of the variables between the initial explanatory variable and the intermediate variable and between the objective variable and the initial explanatory variable, sequentially from the objective variable to the initial explanatory variable, by provisionally regarding a preceding variable as an initial explanatory variable and a subsequent variable as an objective variable; the display processing unit displays, on the display unit, each importance calculated by the importance processing unit for each of the variables. The variable relationship display device according to claim 5 .

7. the predetermined event is road noise that is heard by a vehicle occupant due to vibration input to a tire in response to unevenness of a road surface; The variable relationship display device according to any one of claims 1 to 6.

8. A variable relationship display method for displaying a relationship between explanatory variables consisting of a predetermined number of first components and a response variable consisting of one or more second components in a model that models a predetermined phenomenon, comprising: a model generation step of generating the model consisting of a plurality of partial models by performing a process of generating a partial model of the explanatory variable and the second component of the dependent variable using a random forest for the second component of the dependent variable when there is one second component, and generating the model consisting of a plurality of partial models by performing a process of generating a partial model of the explanatory variable and one second component of the dependent variable using a random forest for each second component of the dependent variable when there is a plurality of second components; an importance processing step of calculating, for each first component of the explanatory variables, an importance which is an index representing the degree of influence of the explanatory variables on the objective variable based on the impurity of the partial model; a display processing step of displaying the importance levels calculated in the importance level processing step in a matrix on a display unit in a two-dimensional space with a first component of the explanatory variable as one axis and a second component of the objective variable as the other axis; an input step of receiving inputs of a threshold value of the importance to be displayed and the second component; the display processing step further displays on the display unit a correlation coefficient between a first component of the explanatory variable having an importance equal to or greater than the threshold value received in the input step and a second component of the dependent variable. How to display variable relationships.

9. A variable relationship display program that displays a relationship between explanatory variables consisting of a predetermined number of first components and a response variable consisting of one or more second components in a model that models a predetermined phenomenon, On the computer, a model generation step of generating the model consisting of a plurality of partial models by performing a process of generating a partial model of the explanatory variable and the second component of the dependent variable using a random forest for the second component of the dependent variable when there is one second component, and generating the model consisting of a plurality of partial models by performing a process of generating a partial model of the explanatory variable and one second component of the dependent variable using a random forest for each second component of the dependent variable when there is a plurality of second components; an importance processing step of calculating, for each first component of the explanatory variables, an importance which is an index representing the degree of influence of the explanatory variables on the objective variable based on the impurity of the partial model; a display processing step of displaying the importance levels calculated in the importance level processing step in a matrix on a display unit in a two-dimensional space with a first component of the explanatory variable as one axis and a second component of the objective variable as the other axis; an input step of receiving inputs of a threshold value of importance to be displayed and a second component, The display processing step further displays on the display unit a correlation coefficient between a first component of the explanatory variable having an importance equal to or greater than the threshold value received in the input step and a second component of the target variable.

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