JP7296905B2 - Explanatory variable estimation method, program and device using model addition part - Google Patents

Description

The present invention relates to technology for estimating explanatory variables from the status of objective variables.

Attempts have been made in various fields to analyze the causes or factors of various events or things and realize desired or controlled events or things based on the analysis results.

For example, Patent Literature 1 analyzes the relationship between employee work data and data indicating the actual absence of work, predicts whether or not the employee will take a leave of absence at a predetermined time, and calculates the prediction result. A system intended to be utilized for business management and attendance management is disclosed. In this system, when predicting employees' absence from work, it is possible to derive which part of the work data contributed to the calculation of the risk of absence from work, that is, what factors acted as the cause of the absence from work.

In addition, Non-Patent Document 1 has recently been actively used in various fields as a method of analyzing how explanatory variables such as work data affect objective variables such as the presence or absence of leave of absence. It introduces and explains Activation Maximization, which is a method of calculating inputs (that is, explanatory variables) that minimizes or maximizes outputs (that is, objective variables) in deep learning, which is used.

JP 2019-135662 A

Qiita, "Method for understanding the grounds for deep learning decisions", [searched on February 25, 2020], Internet <URL: https://qiita.com/icoxfog417/items/>

Here, the system described in Cited Document 1 uses a linear discriminator as a predictive model for predicting the objective variable related to absence from work. This linear discriminator is represented by a monotonic function that can determine whether the factor (explanatory variable) acts in the direction of leave or vice versa, depending on the positive or negative coefficient of each factor (explanatory variable) that can be a factor of leave of absence. It is what is done.

As a simple example, let the discriminant of the linear classifier be y=a_1*x_1+a_2*x_2. Here, x_1 and x_2 are explanatory variables (work data), y is an objective variable (risk of absence from work), and a_1 and a_2 are coefficients of x_1 and x_2, respectively. In this case, it is possible to specifically indicate values of work data (explanatory variables) that reduce the calculated risk of absence from work.

For example, if it is defined that the higher the value of y, the higher the risk of absence from work, if a_1>0, it is judged that the risk of absence from work can be reduced by minimizing the work data (explanatory variable) x_1. In other words, with a linear discriminator, it is possible to easily calculate the optimum value for suppressing absence from work in the work data (explanatory variable) that is the cause of absence from work.

However, when using, for example, a deep learning model that is expected to make more accurate predictions for more complex or ambiguous events or things, the factor extraction is not self-evident and usually becomes quite difficult.

In general, a deep learning model contains a large number of parameters and is represented by a multi-layered mapping function. Therefore, it is not easy at all to calculate the optimum value of the work data (explanatory variable) that minimizes the risk of absence from work (objective variable), for example.

On the other hand, Activation Maximization introduced in Non-Patent Document 1 is indeed a method of calculating input (explanatory variable) values that minimize or maximize output (objective variable) in deep learning.

However, the input (explanatory variable) values calculated by Activation Maximization are the optimal values in the trained neural network, and there is no guarantee that they are values that match the real world, that is, values that are actually applicable. I have a problem. For example, the calculated value may output a result such as "(acquire) 20 days of paid leave in a quarter (to minimize the risk of absence from work)". There are quite a few cases where possible and useful results cannot be obtained.

Therefore, the present invention provides an explanatory variable estimation method, a program, and an apparatus capable of estimating an explanatory variable that takes a value within a preset variable value range and outputs an objective variable value that satisfies a predetermined condition. intended to

According to the present invention , for a built model that estimates the objective variable from the explanatory variables,
The variation in the value of the objective variable, which is the output of the constructed model, caused by the variation in the value of the explanatory variable outside the preset variable value range is reduced to approximately zero or zero below a predetermined minute threshold. The model addition part to be suppressed, which is expressed as a function of the explanatory variable
In the model for estimating explanatory variables generated by adding Explanatory variable determination means for determining an explanatory variable value that is estimated to output an objective variable value that satisfies a predetermined condition
An explanatory variable estimation program is provided that causes a computer to function as

Here, it is also preferable that the predetermined condition is set such that the objective variable value is maximized, minimized, maximized or maximized within a predetermined range, or minimized or minimized within a predetermined range.

Further, in the predictor variable estimation program according to the present invention, it is also preferable that the model addition part outputs the same value as the value of the predictor variable within the variable value range.

Furthermore, in the explanatory variable estimation program according to the present invention, it is also preferable that the model addition part is added before the constructed model.

Further, as an embodiment of the explanatory variables according to the present invention, there are a plurality of explanatory variables, and the variable value range for at least one of them is determined by the values taken by the other explanatory variables. is determined, or the presence or absence thereof is also preferably determined.

Furthermore, in the explanatory variable estimation program according to the present invention, the above function is
(a) When the variable value range is from the first value to the larger second value, the partial differential value of the explanatory variable is 1 within the variable value range, and the variable value Outside the range, the function is set so that the partial differential value by the explanatory variable is zero, and
(b) when the variable value range is a range of only one value, the function is set such that the partial differential value of the explanatory variable is zero inside and outside the variable value range;
(c) For the explanatory variables for which the variable value range is not set in advance, it is also preferable to set a function in which the partial differential value of the explanatory variables is 1.

Further, in the explanatory variable estimation model according to the present invention, it is also preferable to determine the estimated explanatory variable value by a gradient method using the gradient of the objective variable.

Furthermore, in the explanatory variable estimation program according to the present invention, specifically,
The objective variable is the probability, score or degree related to a predetermined event or thing, and the explanatory variable is the quantity related to the event or thing that can be related to the predetermined event or thing,
In the explanatory variable estimation model, it is also preferable to determine the value of the quantity related to the event or matter that is estimated to output a value that satisfies a predetermined condition in the probability, score or degree.

According to the present invention, also
For a pre-built model that estimates the target variable from the explanatory variables,
The variation in the value of the objective variable, which is the output of the constructed model, caused by the variation in the value of the explanatory variable outside the preset variable value range is reduced to approximately zero or zero below a predetermined minute threshold. The model addition part to be suppressed, which is expressed as a function of the explanatory variable
In the model for estimating explanatory variables generated by adding Explanatory variable determination means for determining an explanatory variable value that is estimated to output an objective variable value that satisfies a predetermined condition
is provided .

According to the present invention, there is further provided a computer-implemented explanatory variable estimation method comprising:
For a pre-built model that estimates the target variable from the explanatory variables,
The variation in the value of the objective variable, which is the output of the constructed model, caused by the variation in the value of the explanatory variable outside the preset variable value range is reduced to approximately zero or zero below a predetermined minute threshold. The model addition part to be suppressed, which is expressed as a function of the explanatory variable
generating a model for predictor variable estimation by adding
In the explanatory variable estimation model , it is estimated that an objective variable value that satisfies a predetermined condition is to be output based on a change in the value of the output objective variable that occurs when the value of the explanatory variable that is the input is varied. determining the explanatory variable values to be evaluated ; and
A method for predictor estimation is provided.

According to the predictor variable estimation method, program, and apparatus of the present invention, it is possible to estimate the predictor variable that takes a value within a preset variable value range and outputs the predictor variable value that satisfies a predetermined condition. can.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic diagram showing an embodiment of an explanatory variable estimation device that performs explanatory variable estimation processing using an explanatory variable estimation model according to the present invention; FIG. 10 is a graph for explaining possible aspects of a constraint function expressing model additions according to the present invention; FIG. FIG. 10 is a graph for explaining another aspect that the constraint function representing the model addition part according to the present invention can take; FIG.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[Explanatory variable estimation method and device]
FIG. 1 is a schematic diagram showing an embodiment of an explanatory variable estimation device that performs explanatory variable estimation processing using an explanatory variable estimation model according to the present invention.

The explanatory variable estimation device 2 of this embodiment shown in FIG.
(a) has an explanatory variable estimation model 1,
(b) In this explanatory variable estimation model 1, based on the variation in the value of the output "objective variable" that occurs when the value of the input "explanatory variable" is varied, the "objective" that satisfies a predetermined condition is determined. It is a device capable of determining the estimated "explanatory variable" value that causes the output of the "variable" value.

Also, in (b) above, the explanation is defined so that the "explanatory variable" that is estimated to bring about the "objective variable" that satisfies the predetermined condition takes a value within the preset "variable value range". When a variable is included, the determined value of the explanatory variable does not deviate from the "variable value range".

For example, as one case, the explanatory variable estimation device 2 uses an attendance pattern (attendance data group) can be output. That is, in this case, it becomes possible to propose an optimal or ideal attendance pattern that minimizes the predicted risk of absence from work.

Also, in this case, when the attendance pattern to be output/proposed includes, for example, the number of days of paid leave to be taken in a quarter, the explanatory variable estimation device 2 determines a preset range of days that can actually be taken ( For example, it is possible to output the number of paid vacation days within the range of zero to five days as the optimum or ideal number of days for minimizing the risk of absence from work.

In other words, avoid outputting or making proposals that are not realistically feasible, such as “(acquire) 20 days of paid leave in a quarter (to minimize the risk of leave of absence),” It is possible to output and propose explanatory variables that are useful for

Here, in order to enable output and proposal as described above, the explanatory variable estimation device 2:
(A) For the constructed objective variable estimation model 10 that estimates the "objective variable" from the "explanatory variables",
The variation in the value of the "objective variable", which is the output of the constructed objective variable estimation model 10, caused by the fluctuation in the value of the "explanatory variable" outside the preset "variable value range" is suppressed to a predetermined value or less. (For example, it is suppressed below a predetermined minute threshold value, that is, suppressed to approximately zero). generating a variable estimation model 1;
(B) In the generated explanatory variable estimation model 1, the "predetermined condition" is set based on the variation in the value of the output "objective variable" that occurs when the value of the input "explanatory variable" is varied. Determining an "explanatory variable" value that is estimated to cause an output of an "objective variable" value that satisfies the explanatory variable estimation method.

Of these, the constraint condition layer 11, which is the model addition part added to the objective variable estimation model 10 in the above (A), is the "objective Since the influence on "variable" is suppressed, the above processing (B) eventually results in
It is possible to estimate an "explanatory variable" that (a) takes a value within a preset "variable value range" and (b) outputs an "objective variable" value that satisfies a "predetermined condition". of.

Here, the "predetermined condition" in (b) above is set to a condition that the value of the objective variable is maximized, minimized, maximized or maximized within a predetermined range, or minimized or minimized within a predetermined range. be able to. For example, if the 'predetermined condition' is 'minimize risk of absence from work' and the range of 'variable value' is 'range from 0 to 5 days (for paid leave taken)', risk of absence from work (objective variable) It is possible to output the estimation result by setting the number of days of paid leave taken (explanatory variable) that minimizes to, for example, "4 days".

Incidentally, in the present embodiment, the estimated "explanatory variable" value is determined by the gradient method using the gradient of the "objective variable" in the explanatory variable estimation model 1 of (B) above.

Further, as a modification, the step (A) of generating the predictor variable estimation model 1 may be performed outside the predictor variable estimation device 2 . That is, the predictor variable estimation device 2 may take in the predictor variable estimation model 1 generated externally and perform step (B) above.

In addition, as an application case of (the explanatory variable estimation method in) the explanatory variable estimation device 2, the case where the "explanatory variable" is the employee's attendance pattern (attendance data group) and the "objective variable" is the risk of absence from work has already been explained. However, in this case, as described above, it is possible to obtain an attendance pattern that can minimize the risk of absence from work, taking into account various "constraints" in attendance. Here, the "constraints" are, for example, that there is an upper limit on the number of days of paid leave that can be taken, that gender and age are fixed (the gender value and age value as explanatory variables to be input cannot be changed). ) etc. can be set.

Furthermore, by using the attendance patterns obtained in this way, for example, an in-house counselor, in interviews with employees, will be able to provide advice on how to work (attendance patterns), which was conventionally unavoidable to be individualized advice. It is also possible to present proposals with quantitative evidence. Furthermore, it is also possible to automatically present a suitable "working style (attendance pattern)" without taking the form of an interview with a counselor.

Of course, the application cases of (the explanatory variable estimation method in) the explanatory variable estimation device 2 are not limited to those described above. For example, the following (a) to (e) can be cited as other application cases.

(a) Estimate mortality risk and addiction risk as "objective variables" from lifelogs (sleep time, amount of walking, meal content and amount, exercise content and amount, etc.) as "explanatory variables" A case of an insurance business used to calculate insurance premiums. In this case, as a "constraint (explanatory variable value range)", for example, a condition determined from the life rhythm of the individual subject to explanatory variable estimation (range of possible wake-up times, range of days during a week when exercise is possible, , possible food ranges (dietary preferences), etc.) can be employed.

Here, by applying the explanatory variable estimation device 2 (the explanatory variable estimation method in) to such a case, for example, for each individual who is the target of explanatory variable estimation, within a reasonable range for the individual's life rhythm , it is also possible to suggest a lifestyle that reduces the risk of death and addiction, for example, ``waking up one hour earlier to 6:30 am''.

As for the function g(x), which will be explained in detail later, the constraint function g(x) expressing the constraint layer 11 (set for each individual) in this case may be, for example, "wake-up time A function in which the range of ∂g(x _i )/∂x _i =1 in the explanatory variable x _i represented is 6<x _i <8 (from 6:00 a.m. to 8:00 a.m.) can also be adopted.

(b) A case of English conversation education in which a pronunciation evaluation score is calculated and used as an "objective variable" from speech data as an "explanatory variable." In this case, as a “constraint (explanatory variable value range)”, for example, the value of a certain feature value of the speech data for each word of the student whose explanatory variable is to be estimated is the ideal (for example, native) feature value A condition that the value is within a predetermined range around the value can be adopted.

Here, by applying (the explanatory variable estimation method in) the explanatory variable estimation device 2 to such a case, for example, for each student to be the explanatory variable estimation target, an ideal (for example, native) pronunciation can be concretely It is also possible to present

Regarding the function g(x), which will be explained in detail later, as a constraint function g(x) expressing the constraint layer 11 (set in common for all students) in this case, for example "The range of ∂g(x _i )/∂x _i = 1 in the explanatory variable x _i representing the feature is a predetermined (for example, unavoidable ) where ε is the error, a function that satisfies μ−ε<x _i <μ+ε can also be adopted.

(c) A case in the sports industry that calculates and uses performance in a predetermined competition as an "objective variable" from player's vital data and sensing data as an "explanatory variable." In this case, as a "constraint (explanatory variable value range)", for example, a predetermined physical strength value or instantaneous power value has an upper limit (maximum value), or sleep time has an upper limit (maximum value) and a lower limit (minimum value). Furthermore, conditions such as that vital data such as heart rate that cannot be changed at will take a predetermined value (error range around) can be adopted.

Here, by applying the explanatory variable estimation device 2 (the explanatory variable estimation method in) to such a case, for example, for each player to be the explanatory variable estimation target, under the player's current conditions and environment, It will also be possible to propose a training style that maximizes performance within the feasible range.

Regarding the function g(x), which will be explained in detail later, the constraint function g(x) expressing the constraint layer 11 (set for each player) in this case may be, for example, "sleep time It is also possible to adopt a function in which the range of ∂g(x _i )/∂x _i =1 in the explanatory variable x _i represented is 5<x _i <9 (5 hours to 9 hours).

(d) A case in the real estate industry that calculates and uses the price of the property and the gross profit in the business as the "objective variable" from each item related to the location conditions and floor plan of the residential property as the "explanatory variable". In this case, as the "constraint (explanatory variable value range)", for example, a condition such as fixing a predetermined item of the location condition and the predetermined item of the floor plan, which cannot be changed in business, to a predetermined value can be adopted.

Here, by applying (the explanatory variable estimation method in) the explanatory variable estimation device 2 to such a case, for example, for each residential property to be the explanatory variable estimation target, while satisfying the constraint conditions that cannot be changed in business, It is also possible to present proposals for changes such as floor plans that maximize profits.

As for the function g(x), which will be explained in detail later, the constraint function g(x) expressing the constraint layer 11 (set for each residential property) in this case is, for example, "location conditions When the value of the explanatory variable x _i representing whether it is a corner lot is a preset value c, the c value is taken, and when the value of the explanatory variable x _i is in a range other than c, ∂g(x _i ) /∂x _i =0” can also be adopted.

(e) Clicks as an "objective variable" from explanatory texts and photos (features of) of posted products as "explanatory variables" and purchase history information and attribute information of users who are the main destinations of the site This is a case in the EC (Electronic Commerce) industry that estimates the presence or absence of conversions (for example, purchases) and uses them for site management. In this case, as the "constraint (explanatory variable value range)", for example, the user's purchase history and attribute information values can be fixed to predetermined values (because the system cannot control them, of course). can.

Here, by applying (the explanatory variable estimation method in) the explanatory variable estimation device 2 to such a case, for each listed product subject to the explanatory variable estimation, under the premise constraint conditions, the purchase possibility It is also possible to determine the mode of the posted sentences and photographs that are the most popular.

Regarding the function g(x), which will be explained in detail later, as the constraint function g(x) expressing the constraint layer 11 (set for each posted product) in this case, for example, "user's When the value of the explanatory variable x _i representing the purchase history is a preset value c, the c value is taken, and the value of the explanatory variable x _i is in a range other than c, ∂g(x _i )/∂x _i = A function that becomes 0 can also be adopted.

In any case, the explanatory variable estimation device 2 (the explanatory variable estimation method in)
(a) Let the "objective variable" be the "probability, score or degree" of a given event or thing,
(b) "Explanatory variables" are "quantities related to events or things" that can be related to the above-mentioned predetermined events or things,
(c) In the explanatory variable estimation model 1, it is possible to determine the value of the "quantity related to the event or thing" that is estimated to output a value that satisfies a predetermined condition in the "probability, score or degree". Therefore, it can be applied to various fields, businesses, and sites.

[Model configuration, device configuration. Explanatory variable estimation program]
Similarly, according to FIG. 1, the explanatory variable estimation model 1 is
(a) an input layer;
(b) a constraint layer 11 that is a model addition part;
(c) an objective variable estimation model 10; Here, the objective variable estimation model 10, the constraint layer 11 (model addition part), and the explanatory variable estimation model 1 generated from these can be models (parts) embodied by a machine learning algorithm. In this embodiment, the model (part) is based on a deep neural network (DNN, Deep Neural Networks) algorithm.

Also in FIG. 1, the explanatory variable estimation device 2 includes an input unit 21, a model construction unit 22, an explanatory variable determination unit 23, and an output unit 24. Of these, the model construction unit 22
(as shown in (A) above) a functional configuration unit that performs a step of generating the explanatory variable estimation model 1 by adding the constraint layer 11, which is the model addition part, to the objective variable estimation model 10; On the other hand, the explanatory variable determination unit 23 is
(As shown in (B) above) is a functional configuration unit that performs a step of determining an explanatory variable value that is estimated to output an objective variable value that satisfies the "predetermined condition".

That is, the model construction unit 22 and the explanatory variable determination unit 23 are main units for implementing an embodiment of the explanatory variable estimation method according to the present invention, and a processor storing an embodiment of the explanatory variable estimation program according to the present invention.・It can be regarded as a memory function. For this reason, the predictor variable estimation device 2 may be a dedicated device for predictor variable estimation, but it may be a cloud server, a non-cloud server device, a personal computer ( PC), a notebook or tablet computer, or a smart phone.

<Objective variable estimation model>
Each component described above will be described below. First, the objective variable estimation model 10 converts a set of m (m is a positive integer) explanatory variables x (=(x ₁ , x ₂ , . . . , x _m )) as an input into It is a pre-built model that estimates the target variable y. Of course, y may also be a set of objective variables, that is, y=(y ₁ , y ₂ , . . . , y _l ) (l is a positive integer).

Specifically, in the objective variable estimation model 10, the mapping function of the layer k (=1, 2, . where the subscript k is the layer index and N is the number of layers that make up the model 10 . In this case, the objective variable y, which is the model output, is given by the following equation (1) y＝F(x)
＝(f_1*f_2*・・・*f_N)(x)
is expressed as where f_p*f_q is a composite function of f_p and f_q.

By the way, the DNN model can take a functional form corresponding to various layer configurations other than the above formula (1), but in any case, the objective variable estimation model 10 can be described as y = F (x) become a model.

The objective variable estimation model 10 inputs learning data from the input layer given to the top of the model expressed by the above equation (1), and uses error backpropagation or the like to calculate the internal parameters of each layer in the model. It is constructed by learning (by the way, the “objective variable estimation model 10” refers to the main body of the model other than the input layer given at the top). Therefore, hereinafter, the function expressing the objective variable estimation model 10 is assumed to be F ^* (.) using " ^* " indicating that learning has been completed. In this case, the output from the objective variable estimation model 10, that is, the objective variable y is given by the following equation (2) y=F ^* (x)
It is calculated with

Now, consider deriving the explanatory variable x ^* that minimizes or maximizes the objective variable y using the above equation (2). As described above, in the case where the explanatory variable x is "attendance pattern (attendance data group)" and the objective variable y is "risk of absence from work", for example, "attendance It becomes a problem of deriving x ^* , which is a "pattern". In any case, in this case, x ^* to be obtained is expressed by the following equation (3) x ^* =argmin_{x}F ^* (x), or x ^* =argmax_{x}F ^* (x)
can be expressed as

Gradient methods such as the steepest descent method and the stochastic gradient method (SGD) can generally be used to obtain such an optimal input x ^* in a DNN model. Calculate x ^* based on the gradient method. Here, the gradient method performs partial differentiation with respect to x on y represented by the above equation (2), calculates ∂y/∂x, that is, ∂F ^* (x)/∂x, and calculates this y This is a method of determining x ^* such that the partial differential value representing the gradient of converges to zero as much as possible.

However, the x ^* derived in this way, for example, the “ideal attendance pattern (that minimizes the risk of absence from work)” is only the optimal result of a trained neural network, that is, the optimal result of computer simulation. . Therefore, conventionally, there have been many cases where the derived x ^* value itself is not realistic and cannot be actually realized or applied, that is, it cannot be said to be useful at all.

For example, it is possible that the calculated x ^* value is "(to take) 20 days of paid leave in a quarter (to minimize the risk of absence from work)", which is actually applicable and useful There were quite a few situations in which we could not obtain good results.

In addition, the problem of such derived x ^* value is based on converging the gradient ∂y/∂x to zero as much as possible, and the domain of x is basically not considered or is difficult to guarantee (steepest descent This is a problem unique to the gradient method (including the method and SGD).

In addition, there are various explanatory variables x that can cause such problems in various cases. and/or have constraints such as lower bounds.

For example, in the case where the above-mentioned objective variable y is "risk of absence from work", the explanatory variable x is (a) "sex" and "commuting time", which are the attribute information for risk estimation, and (b) "monthly It is also possible to adopt "overtime hours" and "number of paid holidays taken in a quarter". in this case,
(a') The explanatory variable (input to the model) in (a) above takes a fixed value that cannot be changed, i.e., a value within a "variable value range" that includes only this fixed value, and the derived x ^* value is also should be the fixed value,
(b′) The explanatory variables (inputs to the model) in (b) above have a practical domain defined by predetermined upper and/or lower limits, i.e., a preset “variable value range” , and the derived x ^* value should also be a value within the "variable value range".

Here, the constraint layer 11, which is the next part of the model addition, functions to exactly solve the problem of x ^* values as explained above.

<Model addition part, explanatory variable estimation model>
Similarly in FIG. 1, the constraint layer 11 receives from the input layer the value of each explanatory variable x _i in m explanatory variables (set) x (=(x ₁ , x ₂ , ..., x _m )) is loaded into each neuron. Here, the constraint layer ₁₁ has the partial differential value ∂g(x)/∂x _i |x _i =x_ex at x _i _ex, which is the x _i value outside the “variable value range”, for the captured explanatory variable x i . , is a layer represented by a constraint function g(x) that is zero.

This constraint function g(x) is, in short, the value of the objective variable y, which is the output of the objective variable estimation model 10, caused by fluctuations in the value of the explanatory variable x _i outside the preset "variable value range". It is a function that suppresses the variation ∂y/∂x _i in ∂y/∂xi to a predetermined value or less (for example, to a predetermined minute threshold or less, that is, to approximately zero).

In the present embodiment, such a constraint layer 11 is arranged in the preceding stage of the objective variable estimation model 10 having the problem of the x ^* value and immediately after the input layer to solve the problem of the x ^* value. I do.

Specifically, the explanatory variable estimation model 1 generated by arranging this constraint condition layer 11 in front of the objective variable estimation model 10 is expressed by the following equation (4) y=(g*F ^* )(x)=F ^* (g(x))
is expressed as In addition, the partial differential of y with respect to the explanatory variable _xi , that is, the gradient of y with respect to _xi , which is important in the gradient method, follows the differential formula of the composite function, and is given by the following formula (5) ∂y/∂x _i =∂F ^* (g(x))／∂g(x)・∂g(x)／∂x _i
is represented as

Here, consider the case where the explanatory variable _xi is a variable for which a "variable value range" is set. ∂g(x)/∂x _i , which is the latter half of the right side of the above equation (5 ₎ , is defined as becomes zero. Therefore, in this case, the gradient ∂y/∂x _i is also necessarily zero. As a result, in the gradient method, the amount of displacement (proportional to the gradient) when the x ^* value is obtained and the x _i value is displaced outside the "variable value range" is zero, so in effect, x _i The step of tentatively setting the value to a value outside the "variable value range" and trying to minimize/maximize y does not work.

In this way, the constraint layer 11 (the constraint function g(x) representing) minimizes or maximizes y (for example, the risk of absence from work) for each explanatory variable x _i (for example, each attendance data) that is an input. It is an important part of the model that applies appropriate limits to the gradient of y so that the x _i ^* value such that In other words, it is a model part that compensates for the weaknesses of the gradient method and makes it possible to estimate useful explanatory variables that can actually be taken.

Further, as a result, finally, for explanatory variables x _i for which a “variable value range” is set, the x _i ^* value is derived as a value within the “variable value range”. As a result, for example, it is possible to derive an actually adoptable x _i ^* value such as "(taking) 3.5 days of paid leave in a quarter (to minimize the risk of absence from work)."

In summary, in the explanatory variable estimation model 1 to which the constraint layer 11 is added, the variation in the output objective variable y that occurs when the explanatory variable x _i for which the “variable value range” is set is changed That is, based on the slope ∂y/ _∂xi , it is possible to determine the x _i ^* values within the "variable value range" that are presumed to cause the output of the y value that satisfies the "predetermined condition".

Here, the above-mentioned "predetermined condition" is a condition of the gradient method adopted in this embodiment, and the objective variable y is (a) maximum, (b) minimum, (c) maximum or The condition is set to be the maximum within a predetermined range, or (d) be the minimum or the minimum within a predetermined range. Of these, (c) and (d) are set based on the limitations of the gradient method or based on the judgment that there is no problem or sufficient in application to actual cases.

In addition, the "variable value range" of the explanatory variable x may be set as a common value for the entire group (e.g. company) according to specific application cases, or may be set for each subgroup (e.g. internal department) or per group element (eg, individual employee). Accordingly, the constraint layer 11, that is, the constraint function g(x) may be prepared in common for the entire group, or preferably prepared for each subgroup or each group element.

Furthermore, in this case, a general-purpose objective variable estimation model 10 (for example, built with learning data including data from multiple domestic companies) is used, and the constraint layer 11 is used as an explanatory variable estimation target (for example, an original ideal attendance pattern It is also possible to generate the predictor variable estimation model 1 dedicated to the predictor variable estimation target only by setting and preparing according to the one company searching for the predictor variable. In addition, this makes it possible to obtain explanatory variable estimation models 1 that match individual cases with a relatively small processing load.

Furthermore, although this is an embodiment different from the above embodiment in which the constraint condition layer 11 is arranged in the preceding stage of the objective variable estimation model 10, the feature value generated in a certain intermediate layer constituting the objective variable estimation model 10 is clearly grasped including the constraint conditions, it is also preferable to add the constraint condition layer 11 expressing the constraint conditions of the feature quantity immediately after the intermediate layer. This also makes it possible to adjust the effect of backpropagation in the gradient method appropriately and reliably just before the intermediate layer.

Various modes that the constraint function g(x) representing the constraint layer 11 can take will be described below with reference to FIGS.

FIG. 2 is a graph for explaining possible aspects of the constraint function g(x) expressing the constraint layer 11. In FIG.

First, FIG. 2( _A ) shows g( x _i ) and ∂g(x _i )/∂x _i . Here, g(x _i ) is a function corresponding to each neuron i (i=1, 2, . . . , m) in the constraint layer 11 represented by the constraint function g(x). .

In addition, as an example of the explanatory variable x _i that takes a fixed value c, in the case where the above objective variable y is "risk of absence from work", "gender", "age", "place of residence", "years of service", " Static attribute information such as "job rank/class", "commuting time", and "questionnaire response (selected response symbol string)" corresponds to such explanatory variables x _i .

As shown in FIG. 2A, in this case, g(x _i ) receives only x _i =c and takes the value c (=g(c)). On the other hand, in the gradient method algorithm, ∂g(x _i )/∂x _i is set to zero for all possible values of x _i (including the value c). As a result, from the above equation (5), the gradient ∂y/∂x _i is always zero, so when the x ^* value is obtained and the x _i value is displaced, the displacement (proportional to the gradient) is zero. , after all, the step of trying to minimize/maximize y by shifting the x _i value from the value c does not work. As a result, it is possible to determine the x _i ^* value that takes the value c.

Next, FIG. 2B shows the actual domain defined by the explanatory variable x _i with a predetermined lower limit value a (first value) and upper limit value b (second value), That is, in the case of having a preset variable value range (a ≤ x _i ≤ b), one aspect of the function form of g(x _i ) and ∂g(x _i )/∂x _i is graphed is shown. Here, for example, in the above case where the objective variable y is "risk of absence from work", "monthly working hours", "monthly overtime hours", "number of paid holidays taken in a quarter", etc. It corresponds to the explanatory variable x _i .

As _shown in FIG. 2(B), in this case, g(x _{i )} is the value x_ab (=g(x_ab) ). Also, it takes the value a when _xi is less than a, and takes the value b when _xi is greater than b. On the other hand, ∂g(x _i )/∂x _i is 1 when _xi is a<x _i <b and is zero when _xi is _xi ≤ a or b ≤ _xi set.

As a result, when the explanatory variable x _i takes a value outside the variable value range (a ≤ x _i ≤ b), ∂g(x)/∂x _i is always zero from the above equation (5), so x ^* When finding a value and displacing the x _i value outside the variable value range (a ≤ x _i ≤ b), the displacement (proportional to the slope) becomes zero, and after all, the x _i value becomes the “variable value Trying to minimize/maximize y by tentatively setting it to a value out of range doesn't work. As a result, it is possible to determine x _i ^* values that take values within the variable value range (a≦x _i ≦b).

Incidentally, even if the set variable value range is defined only by the lower limit value a (a ≤ x _i ) or is defined only by the upper limit value b (x _i ≤ b), g (x _i ) takes the same value as the explanatory variable x _i within the variable value range, while taking the same value as the lower limit value a/upper limit value b outside the variable value range, and ∂g(x _i )/∂x _i can be set to be 1 within the variable value range excluding the endpoints, while being zero outside the variable value range and at the endpoints.

Finally, FIG. 2(C) shows one aspect of the functional form of g(x _i ) and ∂g(x _i )/∂x _i when the variable value range is not set for the explanatory variable x _i . This is shown graphically. In this case, the x ^* value problem described above does not occur for this explanatory variable x _i , so g(・) is the expression of the identity map, and g(x _i ) is always the value of the explanatory variable x _i . can be set to be equal, and ∂g(x _i )/∂x _i can also be set to always equal one.

That is, in this case, the constraint layer 11 is set to the model portion that outputs the same value as the input value. As a result, even if the constraint layer 11 is added, the estimation process can be preferably performed without changing the dynamism of predictor variable estimation in the gradient method.

Note that g(·) is usually a function g(x) of a set of multiple explanatory variables x (=(x ₁ , x ₂ , . . . , x _m )). Therefore, in this _case , for example, g(x _{3 )} , g(x ₅ ), . is a function of the form shown in FIG. 2(B), and g(x ₄ ) is a function of the form shown in FIG. 2(C). For each explanatory variable _xi , a specific mode is embodied according to the variable value range of the explanatory variable.

<Other embodiments of model addition part>
FIG. 3 is a graph for explaining another aspect that the constraint function g(x) expressing the constraint layer 11 can take.

The constraint function g(x) shown in FIG. 3 is a function of multiple explanatory variables including the explanatory variable x _i and the explanatory variable x _j , and at least one explanatory variable (in FIG. 3, the explanatory variable x The variable value range for _i ) is determined by the values of other explanatory variables (explanatory variables x _j in FIG. 3), or the presence or absence thereof.

By the way, as an example of such an explanatory variable, for example, if the explanatory variable x _j is a variable that indicates the length of service and the explanatory variable x _i is a variable that indicates the number of days of paid leave taken, it is possible to take In the case where the number of days of paid leave is decided, the variable value range of the explanatory variable x _i will change depending on the value of the explanatory variable x _j .

Specifically, according to FIG. 3, the variable value range (actual domain) of the explanatory variable x _i is
(a) When the explanatory variable x _j takes a value within the x _j value setting range 1 (the value is c in FIG. 3), the x _i value setting range is 1 (p≦x _i ≦q),
(b) When explanatory variable x _j takes a value within x _j value setting range 2 (value b in FIG. 3), x _i value setting range 2 (r≦x _i ≦ s),
(c) If the explanatory variable x _j takes the value a (takes a value within the setting range including only the value a), the setting is unspecified.

Along with this, regarding the constraint condition function g(x), in the case of (a) above, g(x _i ) takes the value x _i within the x _i value setting range 1 (p ≤ x _i ≤ q), On the other hand, outside the x _i value setting range 1 (p≤x _i ≤q), the value p is set when x _i <p, and the value q is set when q < x _i . Also, g(x _i )/∂x _i is 1 when _xi is p<x _i <q, while _xi is 0 when xi ≤ _p or q ≤ _xi It is set as follows.

Furthermore, regarding the constraint function g(x), in the case of (b) above, g(x _i ) takes the value x _i within the x _i value setting range 2 (r≦x _i ≦ s), while x Outside _{the i} value setting range 2 (r≤x _i ≤s), it is set to take the value r when x _i <r and the value s when s < x _i . Also, g(x _i )/∂x _i is 1 when _xi is r<x _i <s, while _xi is zero when xi ≤ _r or s ≤ _xi It is set as follows.

Furthermore, regarding the constraint function g(x), in case (c) above, g(x _i ) is always set equal to the value of the explanatory variable x _i , and ∂g(x _i )/∂ x _i is also set to always be 1.

By setting the constraint function g(x) as described above, even for explanatory variables whose variable value range is affected by the values of other explanatory variables, it is within the specified variable value range. It becomes possible to determine the x ^* value.

Needless to say, the constraint function g(x), which is a function of explanatory variables affected by the values of other explanatory variables, is not limited to the above embodiment shown in FIG. For example, depending on the value of the explanatory variable x _j in FIG. 3, the explanatory variable x _i may take a fixed value c, and the constraint function g(x) as shown in FIG. 2(A) may be set. It is possible. As a further modification, the variable value range or the presence/absence of one explanatory variable may be determined by the values of a plurality of other explanatory variables.

<Explanatory variable estimation device, explanatory variable estimation program>
Hereinafter, returning to FIG. 1, the model 1 for estimating explanatory variables as described above is installed, and an explanatory variable (for example, attendance pattern ) will be described.

In FIG. 1, the input unit 21 of the explanatory variable estimation device 2 is equipped with a communication function. The explanatory variable (for example, attendance pattern) information to which the correct label (for example, presence or absence of leave of absence) is attached is received, converted into a predetermined data format, and stored in the model construction unit 22 .

In addition, the input unit 21 receives constraint conditions (conditions related to the variable value range of each explanatory variable) information for generating the constraint condition layer 11 (constraint condition function g(x)) input by the operator, for example, Output to the model construction unit 22 . Further, it receives information on a predetermined condition (for example, minimization of the risk of absence from work) for predicting explanatory variables input by an operator, and outputs the information to the explanatory variable determination unit 23 .

The model construction unit 22
(a) Construct an objective variable estimation model 10 using explanatory variables (for example, attendance pattern) information with a correct label that is stored by itself,
(b) using the received constraint information, generate a constraint layer 11 that matches the estimation target (e.g., an employee of the α division);
(c) Add the constraint layer 11 of (b) above to the objective variable estimation model 10 of (a) above to generate the explanatory variable estimation model 1 and output it to the explanatory variable determination unit 23 .

The explanatory variable determination unit 23 uses the received explanatory variable estimation model 1 to use the explanatory variable (for example, ideal attendance pattern) information is determined and output to the output unit 94 .

The output unit 94 displays the received explanatory variable (for example, ideal attendance pattern) information that satisfies the predetermined condition, for example, on a display, or transmits it to an external information processing device (if it has a communication function). do. Here, the explanatory variable information to be displayed/sent is, for example, ``For employees of the α division, it is preferable to take four days (or more) of paid leave in a quarter (to minimize the risk of absence from work)''. information.

As described in detail above, according to the present invention, by using the "explanatory variable estimation model" generated by adding the "model addition part" to the model for estimating the objective variable from the explanatory variables, It is possible to estimate an explanatory variable that takes a value within a preset variable value range and outputs an objective variable value that satisfies a predetermined condition.

In addition, such explanatory variable estimation processing according to the present invention can provide information related to how to control the causes and factors of a certain event or matter, for example, in order to control the event or matter in a desired form. It's becoming Therefore, the present invention is highly capable of solving problems in various fields, businesses, and sites, such as companies promoting work style reform, hospitals and nursing facilities promoting next-generation healthcare including mental health. It has versatility.

For the various embodiments of the present invention described above, various changes, modifications and omissions within the spirit and scope of the present invention can be easily made by those skilled in the art. The foregoing description is exemplary only and is not intended to be limiting. The invention is to be limited only as limited by the claims and the equivalents thereof.

1 Explanatory variable estimation model 10 Objective variable estimation model 11 Constraint condition layer (model addition part)
2 explanatory variable estimation device 21 input unit 22 model construction unit 23 explanatory variable determination unit 24 output unit

Claims (10)

For a pre-built model that estimates the target variable from the explanatory variables,
The variation in the value of the objective variable, which is the output of the constructed model, caused by the variation in the value of the explanatory variable outside the preset variable value range is reduced to approximately zero or zero below a predetermined minute threshold. The model addition part to be suppressed, which is expressed as a function of the explanatory variable
In the model for estimating explanatory variables generated by adding Explanatory variable determination means for determining an explanatory variable value that is estimated to output an objective variable value that satisfies a predetermined condition
An explanatory variable estimation program characterized by causing a computer to function as The predetermined condition is set such that the target variable value is maximized, minimized, maximized or maximized within a predetermined range, or minimized or minimized within a predetermined range. 1. The explanatory variable estimation program according to 1. 3. The predictor variable estimation program according to claim 1, wherein the model addition part outputs the same value as the value of the predictor variable within the variable value range. 4. The predictor variable estimation program according to any one of claims 1 to 3, wherein the model addition part is added before the constructed model. There are a plurality of explanatory variables, and the variable value range of at least one of the explanatory variables is determined by the values of the other explanatory variables, or the presence or absence thereof is determined. The explanatory variable estimation program according to any one of claims 1 to 4. In the function, when the variable value range is from a first value to a larger second value, the partial differential value of the explanatory variable is 1 within the variable value range, and the variable Outside the value range, the partial differential value of the explanatory variable is set to zero, and if the variable value range is a range of only one value, the partial differential value of the explanatory variable is set inside and outside the variable value range. is set to a function in which is zero, and further, for the explanatory variable for which the variable value range is not set in advance, the function is set to a function in which the partial differential value by the explanatory variable is 1. 6. The explanatory variable estimation program according to any one of 5 from to 5. 7. The explanatory variable according to any one of claims 1 to 6, wherein the estimated explanatory variable value is determined by a gradient method using a gradient for the objective variable in the explanatory variable estimation model. estimation program . The objective variable is the probability, score or degree related to a predetermined event or thing, and the explanatory variable is the quantity related to the event or thing that can be related to the predetermined event or thing,
8. In the predictor variable estimation model, a value of quantity related to the event or thing that is estimated to output a value that satisfies a predetermined condition in the probability, score or degree is determined. The explanatory variable estimation program according to any one of the above. For a pre-built model that estimates the target variable from the explanatory variables,
The variation in the value of the objective variable, which is the output of the constructed model, caused by the variation in the value of the explanatory variable outside the preset variable value range is reduced to approximately zero or zero below a predetermined minute threshold. The model addition part to be suppressed, which is expressed as a function of the explanatory variable
In the model for estimating explanatory variables generated by adding Explanatory variable determination means for determining an explanatory variable value that is estimated to output an objective variable value that satisfies a predetermined condition
An explanatory variable estimation device characterized by having For a pre-built model that estimates the target variable from the explanatory variables,
The variation in the value of the objective variable, which is the output of the constructed model, caused by the variation in the value of the explanatory variable outside the preset variable value range is reduced to approximately zero or zero below a predetermined minute threshold. The model addition part to be suppressed, which is expressed as a function of the explanatory variable
generating a model for predictor variable estimation by adding
In the explanatory variable estimation model , it is estimated that an objective variable value that satisfies a predetermined condition is to be output based on a change in the value of the output objective variable that occurs when the value of the explanatory variable that is the input is changed. determining the explanatory variable values to be evaluated ; and
A computer-implemented explanatory variable estimation method , comprising:

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