JP6358581B2 - Model estimation method, optimization method, apparatus, and program - Google Patents

Description

  The present invention relates to a model estimation method, an optimization method, an apparatus, and a program, and more particularly, to a model estimation method, an optimization method, an apparatus, and a program for predicting the behavior of an individual that has touched a stimulus.

  There are various situations that stimulate humans for the purpose of causing a certain decision (action). Note that the target to be stimulated for the purpose of causing decision making (behavior) may be a living organism (animal or the like) other than a human being.

  For example, contact with direct mail, contact with a TV / web advertisement for a product, purchase the product, contact with a travel advertisement for a region, and decide to travel to the region. To click on the homepage address of a specific company. In addition, in a complex event venue that is crowded with participants, it may be possible to induce individual participants by event information distribution to eliminate congestion in the venue. Alternatively, there is an example in which a human being is guided to a desirable behavior, such as awakening from sleep by an alarm clock or ingesting a desired food by a software agent proposal.

  Various studies have been conducted on the effect of stimulating contact that expresses the probability of human action with respect to stimulating contact. In such studies, it has been found that the stimulus contact effect has properties such as threshold value, wearout (aversion), and forgetting property.

  The threshold property of the stimulation contact effect is a property that a certain amount or more of stimulation is necessary to obtain the effect by stimulation contact. Further, the wear-out or aversion of the stimulation contact effect is a property that excessive stimulation contact reduces the stimulation contact effect. In advertisement research (stimulus = advertisement, effect = sales or market share), the existence of these two properties has been pointed out for some time (for example, Non-Patent Documents 1 and 2).

  The forgetting property of the stimulus contact effect is a property in which the effect of the stimulus touched at a certain time attenuates with time. This property is widely recognized as an advertising effect (for example, Non-Patent Documents 3 and 4), an influence from others (for example, Non-Patent Documents 5 and 6) in purchasing behavior and email transmission behavior. It is often assumed even in animal selection behavior (eg, Non-Patent Document 7). It has also been confirmed by psychological experiments (for example, Non-Patent Document 8).

  In addition, there is a technique for predicting purchase time by adopting marketing stimulus of e-mail, direct mail, TV advertisement and interaction between customers as a variable factor (for example, Non-Patent Document 2). However, the magnitude of interaction between customers is estimated from the data and does not take into account the dependence of purchase history.

N. Terui, M. Ban, G. M. Allenby, “The effect of Media Advertising on Brand Consideration and Choice”, Marketing Science, Vol. 30, No. 1, pp.74-91, 2011. C. Pechmann, D. W. Stewart, “Advertising Repetition: A Critical Review of Wearin and Wearout”, Current Issues and Research in Advertising, Vol. 11, Issue 1-2, pp.285-329, 1988. D. G. Clarke, “Econometric Measurement of the Duration of Advertising Effect on Sales”, Journal of Advertising Research, Vol. 13, No. 4, pp.345-357, 1976. P. Manchanda, J. Dube, K. Y. Goh, R. K. Chintagunta, “The Effect of Banner Advertising on Internet Purchasing”, Journal of Marketing Research, Vol. 43, No. 1, pp. 98-108, 2006. Rikiya Takahashi, Hideyuki Mizuta, Naoki Abe, Ruby L. Kennedy, Vincent J. Jeffs, Ravi Shah, Robert H. Crites, “Collective Response Spike Prediction for Mutually Interacting Consumers”, Data Mining (ICDM), 2013 IEEE 13th International Conference on , pp.727-736, 2013. C. Blundell, J. Beck, K. A. Heller, “Modeling reciprocating relationships with Hawkes processes”, Advances in Neural Information Processing Systems, pp. 2600-2608, 2012. R. Ratcliff, G. McKoon, “The diffusion decision model: theory and data for two-choice decision tasks”, Neural Computation, Vol. 20, No. 4, pp.873-922, 2008. J. T. Wixted, “Analyzing the empirical course of forgetting”, Journal of Experimental Psychology, Vol. 16, No. 5, pp.927-935, 1990. R. E. Bucklin, S. Gupta, “Brand choice, Purchase incidence, and segmentation: an integrated modeling approach”, Journal of Marketing Research, Vol. 29, pp. 201-215, 1992.

  However, in Non-Patent Documents 4, 5, and 6, which are devices that measure the stimulus contact effect on the occurrence of decision-making, all of threshold value, wearout, and forgetting property of the stimulus contact effect are not considered at the same time. The stimulus contact effect cannot be measured or optimized. For example, ignoring wear-out results in an erroneous conclusion (for example, Non-Patent Document 1) that a greater effect is expected as the number of stimulation contacts increases, leading to a lot of useless stimulation contacts. There is a problem that.

  The apparatus for measuring the stimulus contact effect on the occurrence of decision making is a device for measuring the stimulus contact effect on “occurrence / non-occurrence” of human decision making. In other words, decision-making options must be one choice (such as purchasing a specific product). Therefore, this apparatus alone has a problem that it is not possible to handle a situation in which decision making content is selected from two or more options when decision making occurs.

  As an example of the above situation, it is possible to measure the effect of advertising contact on the purchase / non-purchase of a specific product category (such as milk and coffee). It is possible to measure the effect of advertising contact on whether to purchase the above option). Even if a device that measures the advertising contact effect for each of the three brands A, B, and C of milk is prepared using a device that measures the stimulating contact effect on the occurrence of decision making, it is actually present. Any one of A, B, and C is purchased at the time, and the exclusivity of the selection cannot be considered. When an operator measures the advertising contact effect, the operator wants to know the superiority of its own brand over other brands, and in that respect, the device that measures the stimulating contact effect on the occurrence of decision-making is not an ad contact alone. It is insufficient as an effect measuring device.

  Moreover, although the measurement apparatus of the stimulation contact effect with respect to selection of the decision-making content has already been proposed (Non-Patent Document 1), it does not consider all of the threshold property, wearout, and forgetting property of the stimulation contact effect at the same time. There is a problem that the stimulus contact effect cannot be accurately measured or optimized.

  In order to solve the above problems, firstly, a stimulus contact effect measuring device for occurrence of decision making, considering all the stimulus contact effects of threshold value, wearout, and forgetting property at the same time, is constructed. A measuring device for stimulating contact effects on selected behavior (from two or more options) may be incorporated. The stimulating contact effect measuring device for the selected behavior can be considered when considering all stimulating contact effects of threshold value, wearout and forgetting simultaneously, and considering only one or only two. Although there is already an apparatus (hereinafter referred to as an integrated model) that incorporates both the presence / absence of decision-making and selection of decision-making contents (hereinafter referred to as an integrated model), the threshold property, which is the three properties of stimulation contact, An integrated model that considers both wear-out and forgetting has not yet been proposed.

  The present invention has been made in view of the above circumstances, and estimates the stimulus contact effect on the selected action in consideration of the threshold property of the stimulus contact effect, the wearout of the stimulus contact effect, and the forgetting property of the stimulus contact effect. It is an object of the present invention to provide a model estimation method, apparatus, and program capable of obtaining parameters for the above.

  In addition, an optimization method capable of optimizing a stimulus for causing an individual to perform a specific selection behavior in consideration of a threshold property of the stimulus contact effect, wearout of the stimulus contact effect, and forgetting property of the stimulus contact effect An object is to provide a device and a program.

To achieve the above object, a model estimation method according to the present invention is a model estimation method in a model estimation apparatus including an input unit and a parameter estimation unit, wherein the input unit is observed for each of a plurality of individuals. Behavior data including behavior time series data representing a sequence of times when the individual has acted, and selection sequence data representing a sequence of behavior selection contents when the individual acts, and each of the plurality of individuals Receiving stimulus data representing a sequence of times when the individual contacts the stimulus, and observed for each action option; and the parameter estimation unit is configured to preliminarily store the individual for each of a plurality of individuals. When contacted with a stimulus greater than a predetermined first amount, the stimulus contact effect representing the degree to which the individual takes action by contact with the stimulus is increased. The stimulus contact effect is reduced when the individual comes into contact with a predetermined amount of stimulus or more, and the stimulus contact effect is attenuated according to the elapsed time of contact with the individual's stimulus. Thus, a model relating to the occurrence of an individual's behavior modeling the rate at which the individual takes action per unit time at time t, and each option z when the individual takes action at time t a model relating to selection when an individual action occurs, modeling a selection probability p _l (t) for selecting _l , a parameter relating to a model relating to the occurrence of the individual action for each of the plurality of individuals, and A model that individual parameters that represent parameters related to selection when individual behavior occurs are generated according to the distribution represented by the overall parameters Based on the model related to the individual parameter generation process and the behavior data and the stimulus data received by the input unit, the overall parameter and the individual parameter for each of the plurality of individuals are estimated. And a step.

In addition, the model estimation apparatus according to the present invention includes behavior time series data representing a series of times at which the individual has acted, which is observed for each of a plurality of individuals, and action selection contents when the individual has acted Action data including selected series data representing a series of the above and the observation period of the individual, and a series of times when the individual contacts the stimulus, observed for each of the plurality of individuals and observed for each action option An input unit that accepts stimulus data representing the degree to which the individual causes a behavior by contact with the stimulus when the individual comes into contact with a stimulus greater than or equal to a predetermined first amount for each of the plurality of individuals When the individual touches a stimulus greater than or equal to a predetermined second amount, the stimulus contact effect decreases and the contact with the individual's stimulus is increased. A model relating to the occurrence of an individual's action, in which a rate λ (t) at which the individual takes action per unit time at time t is modeled so that the stimulation contact effect attenuates according to the elapsed time of A selection probability p _l (t) for selecting each option z _l when the individual takes action in the model for selection when an individual action occurs, and for each of the plurality of individuals An individual parameter that models that the parameter related to the model related to the occurrence of the behavior of the individual and the parameter related to the model related to the selection when the behavior of the individual occurs is generated according to the distribution represented by the overall parameter On the basis of the model related to the generation process and the action data and the stimulus data received by the input unit. Accordingly, the parameter estimation unit is configured to estimate the overall parameter and the individual parameter for each of the plurality of individuals.

  In the model estimation method according to the present invention, the model related to the individual parameter generation process is modeled based on a one-level hierarchical Bayesian model, and the step of the parameter estimation unit estimating the parameter is accepted by the input unit. Based on the behavior data and the stimulus data, the overall parameter is estimated, and based on the behavior data and the stimulus data received by the input unit and the estimated overall parameter, the plurality of individuals The individual parameters may be estimated for each.

  In the model estimation method according to the present invention, the model related to the individual parameter generation process is modeled based on a two-level hierarchical Bayesian model, and the step of estimating the parameter by the parameter estimation unit is accepted by the input unit. Further, based on the behavior data and the stimulus data, the overall parameter and the individual parameter for each of the plurality of individuals may be estimated.

  Further, in the model estimation method according to the present invention, the step of accepting the input unit further accepts attribute data representing an attribute for each of the plurality of individuals, and the model relating to the process of generating the individual parameters includes the plurality of individuals. The individual parameter for each is modeled that the individual parameter is generated according to the distribution represented by the attribute of the individual and the global parameter, and the step of estimating the parameter by the parameter estimation unit includes the behavior of the individual Based on the model related to the selection when generated and the model related to the generation process of the individual parameter, and the behavior data, the stimulus data, and the attribute data received by the input unit, each of the overall parameter and the plurality of individuals The individual parameters for may be estimated .

In addition, the optimization method according to the present invention includes an input unit and an optimization unit, and based on the individual parameters of the individual estimated by the model estimation method, the stimulation z _{1 to} be given to the individual An optimization method in an optimization device for optimizing a time series, wherein the input unit is observed with respect to a constraint condition related to a stimulus given to the individual, the behavior data of the individual, and the option z _l Receiving the stimulus data of the individual, and the stimulus data of the individual observed for the constraint condition, the behavior data of the individual, and the option z _l received by the input unit by the optimization unit And the individual parameters of the individual satisfy the constraint condition and cause the individual to take action during a predetermined period. And said to maximize the number of times to select the option z _l, it is configured to include the steps of: optimizing the choice z _l regarding sequence of time stimulation scheduled to be given to the individual.

Further, the optimization device according to the present invention optimizes a sequence of stimulation times related to the option z _{l to} be given to the individual based on the individual parameters of the individual estimated by the model estimation device. An apparatus for receiving a constraint condition relating to a stimulus to be given to the individual, the behavior data of the individual, and the stimulus data of the individual observed with respect to the option z _l , and an input unit received by the input unit , Satisfying the constraint condition based on the individual condition parameters of the individual and the stimulus data observed for the individual, the behavior data of the individual, and the choice z _l of the individual, and a predetermined period Until the individual takes action and maximizes the number of times the option z _l is selected. And an optimizing unit that optimizes a time series of stimuli related to the predetermined option z ₁ .

  The program according to the present invention is a program for causing a computer to execute each step of the model estimation method or the optimization method.

  According to the model estimation method, apparatus, and program of the present invention, the stimulus contact effect is enhanced when the individual contacts a stimulus of a predetermined first amount or more, and the individual is determined in the second A model related to the occurrence of individual behavior that is modeled so that the stimulus contact effect is low when contacted with a stimulus greater than or equal to the amount, and the stimulus contact effect is attenuated according to the elapsed time of contact with the individual stimulus. When the individual takes action, the selection probability of selecting each option is modeled. The model related to selection when the individual's action occurs, the parameter related to the model related to the occurrence of the individual action, and the action of the individual occur. The generation of individual parameters that modeled that individual parameters that represent parameters related to the selection of models are generated according to the distribution represented by the overall parameters. And the individual parameters for each of the plurality of individuals based on the behavior data and the stimulation data observed for each of the plurality of individuals, thereby determining the threshold characteristics of the stimulation contact effect and the stimulus contact effect. An effect is obtained that it is possible to obtain a parameter for estimating the stimulus contact effect on the selected action in consideration of the wearout and forgetting property of the stimulus contact effect.

Further, according to the optimization method, apparatus, and program of the present invention, the constraint condition related to the stimulus given to the individual, the behavior data of the individual, and the individual stimulation data observed for the option z _l are estimated by the model estimation device. Based on the individual parameters of the individual, the individual is satisfied so that the number of times that the individual takes action and selects the choice z _l during a predetermined period is maximized. By optimizing the sequence of stimuli time for the scheduled option z _l , the selection behavior specific to the individual is taken into account in consideration of the threshold value of the stimulus contact effect, the wear out of the stimulus contact effect, and the forgetting property of the stimulus contact effect It is possible to optimize the stimulus for causing the problem.

It is a block diagram which shows the main structures of the model estimation apparatus which concerns on embodiment of this invention. It is a figure which shows an example of the model regarding generation | occurrence | production of an individual's action. It is a figure which shows an example of the model regarding generation | occurrence | production of an individual's action. It is a figure which shows an example of the model regarding selection when an individual's action generate | occur | produces. It is a figure which shows an example of the individual parameter estimated by the model estimation apparatus. It is a block diagram which shows the main structures of the optimization apparatus which concerns on embodiment of this invention. It is a figure which shows an example of the series of the time of the stimulus regarding the predetermined option output by the optimization apparatus. It is a flowchart which shows the content of the model estimation process routine in embodiment of this invention. It is a flowchart which shows the content of the optimization process routine in embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

<Outline of Embodiment of the Present Invention>

  First, an outline of an embodiment of the present invention will be described.

  In the embodiment of the present invention, various situations in which stimulation is given are assumed for the purpose of causing a certain decision (action) to an individual such as a human being or an animal. For example, contact with direct mail, contact with a TV / web advertisement for a product, purchase the product, contact with a travel advertisement for a region, and decide to travel to the region. To click on the homepage address of a specific company.

  In the embodiment of the present invention, both the generation of decision making and the selection of decision making contents are incorporated into the model, and the high-precision stimulation contact effect considering the threshold property, wearout, and forgetting property of the stimulation contact effect at the same time. An object of the present invention is to provide a technique that makes it possible to realize estimation on an individual basis.

  In the embodiment of the present invention, a case where the present invention is applied to a model estimation device and an optimization device will be described as an example. First, an individual parameter is estimated from data in a model estimation device. The individual parameter is an evaluation value of the advertisement contact effect for each individual. In the next optimizing device, the stimulation contact that maximizes the advertising effect is determined based on the estimated individual parameters.

<Configuration of Model Estimation Device According to Embodiment of the Present Invention>
The configuration of model estimation apparatus 100 according to the embodiment of the present invention will be described.

  As shown in FIG. 1, a model estimation apparatus 100 according to the present embodiment is a computer that includes a CPU, a RAM, and a ROM that stores a program and various data for executing a model estimation processing routine described later. Can be configured. Functionally, the model estimation apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 50 as shown in FIG.

  The input unit 10 receives behavior data, stimulus data, and attribute data.

  Behavior data is observed for each of a plurality of individuals, behavior time series data representing a series of times when an individual took action, selection series data representing a series of action selection contents when an individual acts, Including the observation period. The action data represents time-series data of actions of a plurality of individuals to be analyzed (for example, humans or animals).

Specifically, the action data is action time series data ({t _j ^u } = (t ₀ ^u ) representing a series of the individual ID u and the time t _j ^u at which the action of the individual u occurred for each of a plurality of individuals. ^{_{, t 1 u, t 2 u}} , ...)), selection of actions when the individual u acted _v ^j selected sequence data representing a sequence of ^{_{u ({v j u} =}} (v 0 u, v 1 u, v ₂ ^u, ...)), the observation period (start time _{T s,} constituted the end time _[T s, _{T e]} as _{T e} the drawing) and contain. However, the action options are v∈ {z ₁ , z ₂ , z ₃ ,. J is an index representing the order of actions.

Stimulation data is observed for each of a plurality of individuals u and observed for each action option z _{l, the} time when the individual u contacts the stimulus z _l

This data represents a series of In this embodiment, the stimulus data is

It expresses. For example, if an individual is a user and a stimulus is a web advertisement, a sequence of times when each user views the advertisement is input as stimulus data.

The attribute data represents an attribute for each of a plurality of individuals u. In this embodiment, it represents the attribute data and d ^u. As the attribute data, for example, the gender, age, income, etc. of the user are used. However, attribute information is not essential in the model estimation apparatus according to the present embodiment.

  The input unit 10 also receives information related to selection of a hierarchical Bayesian model used in the selection unit 32 described later.

  The calculation unit 20 includes a storage unit 22 and an estimation unit 30.

  The storage unit 22 stores a model related to the occurrence of individual behavior, a model related to selection when an individual behavior occurs, and a model related to the generation process of individual parameters. As a model relating to the occurrence of individual behavior, a model in which at least one of [Example 1-1] to [Example 1-5] described later is combined is stored. In addition, as a model related to selection when an individual's action occurs, a model in which at least one of [Example 2-1] to [Example 2-4] described later is combined is stored. Note that the model related to the individual parameter generation process stores a model modeled by a one-level Bayesian model, which will be described later, and a model modeled by a two-layer Bayesian model.

  Here, the principle of modeling in this embodiment will be described.

  The mathematical model assumed in the embodiment of the present invention is a model in which a model relating to the occurrence of an individual's behavior is integrated with a model relating to selection when the behavior of the individual occurs. Hereinafter, a model relating to the occurrence of individual behavior, a model relating to selection when an individual behavior occurs, and a model relating to the process of generating individual parameters will be described in detail.

[Model of behavior of individuals]

First, a model relating to the occurrence of individual behavior will be described.
In the present embodiment, a model relating to the occurrence of an individual's behavior is obtained by selecting the behavior of the individual by contact with the stimulus when the individual contacts a predetermined amount or more of the stimulus for each of the plurality of individuals. Stimulus contact effect indicating the degree of occurrence of the stimulation is increased, and when the individual contacts a predetermined amount or more of the stimulus, the stimulation contact effect is decreased, and the elapsed time of contact with the individual stimulus The probability λ (t) that the individual takes an action per unit time at time t is modeled so that the stimulus contact effect is attenuated according to.

In the present embodiment, a stimulus contact effect representing a degree of an individual's behavior when contacted with a stimulus when the individual contacts a stimulus of a predetermined first amount or more as a model related to the occurrence of the behavior of the individual. Is modeled so that the threshold value of the stimulus contact effect is expressed.
In addition, a model relating to the occurrence of the behavior of the individual is modeled so that the stimulus contact effect is lowered when the individual contacts a predetermined amount or more of the stimulus, thereby expressing the wear-out of the stimulus contact effect.
In addition, a model relating to the occurrence of the individual's behavior is modeled so that the stimulus contact effect is attenuated according to the elapsed time of contact with the individual's stimulus, thereby expressing the forgetting property of the stimulus contact effect.

  In addition, a model relating to the occurrence of an individual's behavior is expressed by a probability λ (t) of the individual's behavior per unit time under a probability theory called “point process”. Here, t represents time. λ (t) is called a rate. Modeling of the threshold property, the wearout, and the forgetting property of the stimulus contact effect is realized through this rate. Here are some examples of modeling. However, the modeling of the threshold value, the wearout, and the forgetting property is not limited to the following examples.

  In addition, in the stimulus data used in the present embodiment, the stimulus contact time of each individual is given for each action content option (

), A stimulus for any option can be a stimulus for the occurrence of behavior itself. Therefore, in the following modeling example, the stimulus {s _j ^u } for the occurrence of the action is

It is defined as That is, a stimulus for any option is equally regarded as a stimulus for the occurrence of behavior. Of course, the stimulus for each option may be distinguished.

Further, the following equation is discussion of probability for each individual u, easy for _{^{{t j u}, {v}} j u}, {s j u} simply _{{t j}, {v j} }, {s _j }.

[Example 1-1: Modeling wearout as intensity attenuation]
First, assuming that a stimulus effect is accumulated every time a stimulus is touched, and that the effect is exponentially forgotten over time, the accumulation of stimulus effect (hereinafter referred to as stimulus stock) n (t) is expressed by the following equation: It is expressed by (1).

However, a _s is the intensity of the stimulation contact effect of per once in the above formula (1),

Represents the duration of the stimulation contact effect, and s _i represents the i-th stimulation contact time. Next, assuming that the effect of stimulation contact appears at the rate λ (t) only during a period when the stimulation stock exceeds a certain threshold value n _th , the rate λ (t) can be expressed as shown in the following equation (2). it can.

In the above formula (2), λ ₀ represents a basal rate, λ ₁ represents an excitation rate, n _th represents a threshold value of a stimulation contact effect, and a function G (y) represents a nonlinear function. The nonlinear function G models the threshold value of the stimulation contact. For example, a sigmoid function as shown in the following formula (3) may be used.

Furthermore, it is assumed that the intensity a _s of the above formula (1) has dynamics as shown in the following formula (4).

However, _{a 0} is basic strength of the above formula (4), _{s i} is the i-th stimulation contact time,

Is the strength of wear-out due to a single stimulus contact, and

Is the wearout duration. An example of rate behavior when the first function of the above equation (3) is employed is shown in FIG. As shown in FIG. 2, it can be confirmed that the effect of individual stimulation is attenuated (forgetting), and the effect on the rate does not appear (thresholding) unless the effect exceeds the threshold. Also, too frequent stimulation contact leads to decline in stimulating contact strength a _s, a result of a decline in stimulating contact strength a _s are invited, cause decline of the rate. The decline in the rate expresses a situation in which the willingness to purchase is reduced due to, for example, excessive web advertisement.

  In addition, as shown in the following formula (5), forgetting is not only exponential attenuation but also power attenuation.

Can also be used to model.

[Example 1-2: Modeling wearout independently of stimulus stock]
In the example 1-1, but wear-out was expressed as the attenuation of the intensity a _s, here, as shown in the following equation (6) and (7), apart from wear-out and stimulus stock n (t) Consider state m (t).

However, _aw is the increase in wearout due to a single stimulus contact,

Is the wearout duration and mth is the _wearout threshold. In the above formula (6), stimulation stock n (t) is the threshold value _{n th} or more and wear out the state m (t) is the threshold value _{m th} following time rate is excited lambda _1. In the above equation (7), both the stimulus stock n (t) and the wear-out state m (t) increase every time they come into contact with the stimulus, and gradually approach zero with time if there is no contact. For this reason, the stimulation stock does not increase below the threshold when the stimulation is too low, and the rate does not increase when the wearout state exceeds the threshold even when the stimulation is excessively frequent. FIG. 3 shows an example of behavior when wearout is modeled independently of the stimulus stock.

[Example 1-3: When stimulus data is given by period]
In the example 1-1 and the example 1-2, only the information on the stimulation contact time is considered. However, for example, the impact given by a single contact may be different in the web CM of 1 minute and 10 minutes. As one method for incorporating the difference into the model, a method shown in the following formula (8) is conceivable.

In the above equation (8), w _k ^start and w _k ^end are the contact start time and the contact end time of the k-th stimulus, respectively. The longer the contact time, the greater the impact. g (t−t ′) is a convolution function, and an exponential function, a power function, or the like can be applied in the same manner as in Example 1-1 and Example 1-2. In the case of Example 1-2, a model similar to the above equation (7) may be considered for the wear-out state m (t).

[Example 1-4: Considering influence from past action history]
In Example 1-1 to Example 1-3 described above, only the effect of stimulating contact was considered, but a situation in which the current behavior is affected by the past own behavior is also conceivable. For example, in the case of a luxury item such as coffee or tobacco, the purchase of the user may prompt the next purchase. In that case, the rate can be modeled in the form of the following equation (9) using the Hawkes process (see, for example, Non-Patent Document 10 below).

(Non-Patent Document 10)
A. Hawkes, "Spectra of some self-exciting and mutually exciting point processes", Biometrika, Vol. 58, No. 1, pp. 83-90, 1971.

Where t _j in the above equation (9) is the j-th action time of the individual,

Is the strength of impact,

Represents the duration of the effect. Some individuals may behave based on their own behavioral rhythm rather than stimulating contact. It is expected that the effect of the stimulus can be estimated more correctly by simultaneously considering the effect of the stimulus and the effect from the action history. However, the behavior history modeling is not limited to the above equation (9).

[Example 1-5: Considering the influence of covariates other than stimuli]
A situation where the rate fluctuates under the influence of a covariate Y (t) other than the stimulus can also be considered. For example, in-house inventory in consumer goods purchasing behavior. The situation in which the purchase probability rises with a decrease in domestic stock, the stock recovers after purchase and the purchase probability declines. The rate λ (t) defined in the previous examples is

It is realized by correcting. However, the modeling of covariate effects is not limited to the above.

[Model for selection when individual behavior occurs]
Next, a model related to selection when an individual's action occurs will be described.
In the present embodiment, the selection probability p _l (t) for selecting each option z _l when the individual takes action at time t is modeled, and the model is related to selection when the individual action occurs.

Specifically, when the occurrence time of an individual's action is determined based on the model regarding the occurrence of the action of the individual constructed as described above, the selection content at the time t when the action occurs is determined by the discrete distribution _pchoice (z | t). However, the action options are z∈ {z ₁ , z ₂ , z ₃ ,. Hereinafter, p _choice (z | t) is expressed as a selection probability.

The selection probability p _choice (z | t) can be expressed by the following equation (10).

Here, p _l (t) represents the probability of selecting z _l when the individual takes action at time t, and takes a value between 0 and 1. For example, z _l represents the l-th brand of a certain product category (such as a bag). By integrating the rate λ (t) constructed above and the selection probability expressed by the above equation (10), the probability λ _z (t) that the individual takes action per unit time and selects z _l is And can be expressed by the following equation (11).

Note that λ _z (t) in the above equation (11) can be interpreted as a rate for the selection z _l .

  When modeling selection probabilities, a model that does not include stimulus contact effects at all, a model that only considers forgetting of stimulus contact effects, a model that considers forgetting and thresholding, and threshold, wearout, and forgetting Any model may be adopted that takes into account simultaneously. Hereinafter, examples of each modeling will be described, but the modeling of the selection probability is not limited to the following.

[Example 2-1: Model not including stimulus contact effect]
When the selection of the action content of the individual is not affected by any external factor, the selection probability _pchoice (z) can express the above equation (10) as the following equation (12).

The probability p _l of selecting z _l in the above equation (12) is estimated from the behavior data for each individual.

If the selection of action content is affected by the accompanying information {X ₁ (t), X ₂ (t), X ₃ (t),...} Of each option {z ₁ , z ₂ , z ₃ ,. The probability p _choice (z) can be expressed as in the following equation (13) using a multinomial logit model.

In the above equation (13), ξ is a weighting coefficient (response coefficient) of the accompanying information, and U _l (t) is a function (hereinafter referred to as utility function) that determines the probability that the individual selects the selection z _l . The accompanying information is given as data for each individual, and q _l and ξ are estimated from the behavior data for each individual.

For example, in the case of brand selection for a certain product category, the accompanying information includes the price and discount rate of each brand, (brand) loyalty, and the like. When the accompanying information is not available, X ₁ (t) = 0 and exp (q ₁ ) = p ₁ are used, resulting in the above equation (12).

[Example 2-2: Model that considers only forgettingness of stimulus contact effect]

  The selection probability of the above equation (10) can be expressed by the following equation (14).

However, n _l (t) in the above formula (14) is the amount of stimulation (stimulation stock) accumulated for the choice z _l ,

When

Are the intensity and duration of the stimulus contact effect for each option z _l (forgetting time constant). An example of a model that considers only the forgettingness of the stimulus contact effect is shown in FIG.

[Example 3: Model considering forgetting property and threshold value of stimulus contact effect]
The selection probability of the above equation (10) can be expressed by the following equation (14-2).

However, q _l ′ in the above formula (14-2) represents an increase in the utility function when the stimulus stock of the option z _l exceeds the threshold value n _th . G (y) is the same as defined in the above formula (3).

  Or the model which replaced the utility function in the said Formula (14-2) by the following formula | equation (15) can also be considered.

  When the formula (15) is replaced, the probability that an option whose stimulation stock does not exceed the threshold is selected is zero. Note that a model equivalent to the above equation (15) is proposed in Non-Patent Document 1.

[Example 2-4: Model considering the threshold value, wearout, and forgetting property of the stimulation contact effect]
The selection probability of the above equation (10) can be expressed by the following equation (16).

Unlike the above equation (14-2), only when the stimulus stock n _l (t) exceeds the threshold and the wear-out state m _l (t) falls below the threshold, the effect of the stimulation contact q _l ′ appears in the utility function. .

It may be considered that the effect also appears in the reaction coefficient ξ. For example, if the price sensitivity is weakened while the stimulus contact effect appears in the utility function, the price component ξ _price of the response coefficient can be expressed by the following equation (17).

  However, the method of defining the reaction coefficient is not limited to the above equation (17). The same applies to the above formula (14-2).

[Model for individual parameter generation process]
Next, a model relating to an individual parameter generation process will be described.
In the present embodiment, for a model relating to an individual parameter generation process, an individual representing a parameter relating to a model relating to generation of an individual behavior and a parameter relating to a model relating to selection when the behavior of the individual occurs for each of a plurality of individuals. Model that the parameters are generated according to the distribution represented by the global parameters.

In modeling a model relating to the occurrence of an individual behavior and a model relating to selection when an individual behavior occurs, a parameter group relating to modeling (in the above example, a _s , b _s , a ₀ , a ₁ , λ ₀ , λ ₁ , ξ, q _1, etc.) are defined. A group of parameters related to modeling is collectively expressed as an individual parameter θ≡ (a _s , b _s , a ₀ , a ₁ , λ ₀ , λ ₁ , ξ, q ₁ ...).

Since the individual parameter θ can be different for each individual, the parameter of the individual ^u is expressed as θ ^u in particular. In this processing block, the individual parameter generation process is modeled based on a hierarchical Bayesian model in order to explain the difference in parameters between individuals. However, the subsequent processing differs depending on whether the number of layers is 1 or 2.

[One-level hierarchical Bayesian model]
In order to model the difference in individual parameter between individuals, it is assumed that the individual parameter θ ^u is generated from the normal distribution of the following equation (18).

However, d ^u in the formula (18) (representing intercept of the regression) 1 first component, the vertical vector is the second component after an attribute variable individual u, rank β is the number of rows is d ^u, column it is a matrix that number is equal to the rank of θ ^u. Β ′ represents a transpose matrix of β, and N (θ ^u | x, y) represents a normal distribution in which the mean and variance are x and y, respectively.

Since β and Λ are parameters that determine the distribution shape of θ ^{u in} the whole individual, the two types of parameters are referred to as global parameters here. The overall parameters are estimated from the data by the parameter estimation unit 34 described later.

[Two-level hierarchical Bayesian model]
As in the case of the one-level hierarchical Bayesian model, it is assumed that the individual parameter θ ^u is generated from the normal distribution of the following equation (19).

  Furthermore, it is assumed that global parameters Λ and β are generated from the probability distribution of the following equation (20).

Where Wi (θ ^u | x, y) in the above equation (20) is the degree of freedom x, the Wishart distribution of the scale parameter y,

Represents the Kronecker product. Parameters ν ₀ , Λ ₀ , β ₀ , and Ω ₀ that determine the distribution shape of the overall parameters are determined in advance, and are appropriately specified by, for example, the user of the model estimation apparatus 100. For an example, see the appendix of Non-Patent Document 1 above.

For two-tier hierarchical Bayesian model, so that the entire parameter Λ and β are estimated by overall and individual parameter estimation unit 40 to the individual parameter theta ^u simultaneously below.

  The estimation unit 30 estimates the parameters of each model stored in the storage unit 22 based on the behavior data, stimulus data, and attribute data received by the input unit 10. The estimation unit 30 includes a selection unit 32 and a parameter estimation unit 34.

  The selection unit 32 selects a hierarchical Bayes model to be used by the parameter estimation unit 34 described later based on the information related to the selection of the hierarchical Bayes model received by the input unit 10. Specifically, the selection unit 32 selects a hierarchical Bayes model of one hierarchy or a hierarchical Bayes model of two hierarchies based on information regarding selection of the hierarchical Bayes model received by the input unit 10.

  The parameter estimation unit 34, according to the type of the hierarchical Bayes model selected by the selection unit 32, a model related to the occurrence of individual behavior stored in the storage unit 22, a model related to selection when an individual behavior occurs, and Based on the model related to the generation process of the individual parameters and the behavior data, stimulus data, and attribute data received by the input unit 10, the overall parameters and the individual parameters for each of the plurality of individuals are estimated. The parameter estimation unit 34 includes an overall parameter estimation unit 36, an individual parameter estimation unit 38, and an overall and individual parameter estimation unit 40.

  When the type of the hierarchical Bayes model selected by the selector 32 is a one-level hierarchical Bayes model, the overall parameter estimation unit 36 is based on the behavior data, stimulus data, and attribute data received by the input unit 10. Estimate the overall parameters.

  Specifically, when assuming a one-layer Bayes model, the overall parameter estimation unit 36 is based on the experience data, stimulus data, and attribute data received from the input unit 10 based on the experience Bayes method. presume.

First, the calculation of the likelihood function p ({t _j ^u }, {v _j ^u } | θ ^u ) of the individual parameter θ ^u of each individual u is a model relating to the occurrence of the behavior of the individual stored in the storage unit 22, Using the rates λ (t | θ ^u ) and λ _z (t | θ ^u ) modeled as a function of the parameter θ ^{u in} the model related to selection when an individual's action occurs, the following equation (21) is used: Run as shown.

Here, λ _z (t) = p _choice (z | t) · λ (t). The above equation (21) is derived from a probability theory called a point process (for example, see Non-Patent Document 11). From the probability distribution p (θ ^u | β, Λ) of θ ^u selected by this likelihood function and the model relating to the generation process of individual parameters, the marginal likelihood function for (β, Λ) based on Bayes' theorem is It is calculated as shown in Equation (22).

(Non-Patent Document 11)
DL Snyder, "Random Point Processes", Wiley New York, 1975.

  However, D in the above formula (22) represents data of all individuals. The global parameter (β, Λ) is estimated to maximize this marginal likelihood function p (D | β, λ). In this way, a method for estimating all parameters from data using a marginal likelihood function or the like is called an experience Bayesian method.

  Since maximization of the marginal likelihood function p (D | β, λ) is impossible analytically, in this embodiment, the overall parameter estimation unit 36 uses the EM method to calculate the marginal likelihood function p ( D│β, λ) is maximized. Under the EM method, (β, λ) that maximizes the marginal likelihood function is obtained by repeatedly executing the update rule of the following equation (23).

However,

It is. In the above equations (23) and (24), (β ^(p) , Λ ^(p) ) represents an updated value in the p-th iteration, and E [Z (θ ^u ) | {t _j ^u }, {v _j ^u }, Β ^(p) , Λ ^(p) ] represents the posterior average for θ ^u defined by the following equation (25). In addition, “′” in the above formula (24) represents transposition.

Here, Z (θ ^u ) in the above equation (25) is an arbitrary function of θ ^u . A posteriori averaging is performed using the Markov chain Monte Carlo method.

  The individual parameter estimation unit 38 estimates individual parameters for each of a plurality of individuals based on the behavior data, stimulus data, and attribute data received by the input unit 10 and the overall parameters estimated by the overall parameter estimation unit 36. To do.

Specifically, the individual parameter estimation unit 38 uses the overall parameters ^ β and ^ Λ estimated by the overall parameter estimation unit 36, and calculates the individual parameter θ ^u of each individual according to the following equation (26). Estimate as

  When the model related to the generation process of the individual parameters is modeled based on the two-level hierarchical Bayesian model, the whole and individual parameter estimation unit 40 determines the whole parameter based on the behavior data and the stimulus data received by the input unit 10. And individual parameters for each of the plurality of individuals.

Specifically, when assuming that the model relating to the generation process of the individual parameters is a two-layer Bayesian model, the entire and individual parameter estimation unit 40 not only determines the individual parameter θ ^u but also the entire parameter β according to the following equation (27). , Λ are also estimated as posterior averages at the same time.

  In addition, the posterior average of the above formula (27) is defined by the following formula.

The output unit 50 outputs the individual parameter {circumflex over (θ) ^{} u} for each of a plurality of individuals estimated by the individual parameter estimation unit 38 or the whole and the individual parameter estimation unit 40 as a result. The individual parameter is a numerical evaluation of the stimulus contact effect.

  FIG. 11 is an example of output of individual parameters when [Example 1-2] is used as a model related to the occurrence of the individual's behavior and [Example 2-2] is used as a model related to selection when the behavior of the individual occurs. As shown in FIG. However, it is assumed that there are three options (three types of brands, etc.) and two accompanying information (product price and royalty, etc.) in FIG.

<Configuration of Optimization Device According to Embodiment of the Present Invention>

  Next, an optimization apparatus according to an embodiment of the present invention will be described. The optimization apparatus according to the embodiment of the present invention optimizes a series of stimulation times related to options to be given to an individual based on the individual parameters of each individual estimated by the model estimation apparatus 100. As shown in FIG. 6, the optimization apparatus 200 according to the present embodiment is a computer that includes a CPU, a RAM, and a ROM that stores a program for executing an optimization processing routine described later and various data. Can be configured. Functionally, the optimization apparatus 200 includes an input unit 210, a calculation unit 220, and an output unit 250 as shown in FIG.

  The input unit 210 receives constraint conditions related to the stimulus given to the individual, individual behavior data, and individual stimulus data observed for the options. The constraint condition related to the stimulus is input as a constraint condition when the stimulus contact is optimized. For example, in the case of an advertisement stimulus, the budget (or the number of contacts) that can be allocated to the advertisement, the minimum interval of the stimulus that can be contacted, the period of the advertisement, and the like.

  The calculation unit 220 includes a storage unit 222 and an optimization unit 224.

  In the storage unit 222, individual parameters for each of a plurality of individuals estimated by the model estimation apparatus 100, a model relating to the occurrence of individual behavior used when estimating each individual parameter, and the behavior of the individual have occurred. And a model related to the selection.

For each of the plurality of individuals, the optimization unit 224 receives the constraint conditions relating to the stimulus, the behavior data of the individual, and the stimulation data of the individual observed for the action option z _l and the individual Based on the individual parameters of the individual, so that the constraint on the stimulus is satisfied, the individual takes action during a predetermined period, and the number of times the option z _l is selected is maximized. Optimize the stimulus time series for the option z _{l to} be given to.

Specifically, the optimization unit 224 performs the individual behavior under the constraint condition related to the individual's past behavior data, the individual's past stimulus data, the individual parameter of the individual estimated by the model estimation apparatus 100, and the stimulus. The stimulus I _z ^u (t) to be contacted for each u is optimized. Here, “optimization” means maximizing the number of occurrences of a specific selection action by stimulus contact.

First, the optimization unit 224 performs the past behavior data {t _j ^u } {v _j ^u }, the past stimulus data I _z ^u (T _s <t <T _e ), and the estimated individual for the individual ^u. Using the parameter ^ θ ^u and the stimulus I _z u (t> T _e ) to be contacted, the predicted rate of the selected z ^ λ _z (t | ^ θ ^u , {t _j ^u }, {v _j ^u }, I _z ^u (t)). Next, the optimization unit 224 calculates an integrated value of the predicted rate according to the following equation (28).

However, T in the above equation (28) represents a period for which stimulation is to be applied. Since the rate is the probability that the individual will cause the selected action z _l per unit time, the integral value Q (I _z ^u (t)) calculated by the above equation (28) is the expectation of the number of actions caused by the stimulus contact. Value. Specifically, according to the following formula, by determining a stimulus ^to I _z ^u (t> T _e ) that maximizes the expected value Q (I _z ^u (t)) under the constraint condition related to the stimulus. Optimization of stimulation contact is realized.

The output unit 250 outputs, for each of the plurality of individuals optimized by the optimization unit 224, a series of stimulation times related to the option z _{l to} be given to the individual. In the output unit 250, the optimized stimulation contact is output for each individual. An output example is shown in FIG. However, FIG. 7 shows an example in which the number of stimulation contacts is 10.

<Operation of Model Estimation Device According to Embodiment of the Present Invention>

  Next, the operation of the model estimation apparatus 100 according to the embodiment of the present invention will be described. When behavior data, stimulus data, and attribute data for each of a plurality of individuals and information related to selection of a hierarchical Bayes model are input, the model estimation device 100 executes a model estimation processing routine shown in FIG.

  First, in step S100, the input unit 10 receives behavior data, stimulus data, and attribute data for each of a plurality of individuals, and information related to selection of a hierarchical Bayesian model.

  Next, in step S102, the selection unit 32 selects a hierarchical Bayes model to be used by the parameter estimation unit 34 described later based on the information regarding the selection of the hierarchical Bayes model received in step S100. Specifically, the selection unit 32 proceeds to step S106 when the information regarding the selection of the hierarchical Bayes model accepted in Step S100 represents a hierarchical Bayes model of one hierarchy. On the other hand, if the information related to the selection of the hierarchical Bayes model received in Step S100 represents a hierarchical Bayes model of the second hierarchy, the process proceeds to Step S110.

  In step S106, the overall parameter estimation unit 36 repeatedly executes the update rule of the formula (23) based on the behavior data, stimulus data, and attribute data for each of the plurality of individuals received in step S100. Estimate the overall parameters ^ β, ^ Λ.

Then, in S108, the individual parameter estimation unit 38, based on the behavior data and stimulus data for each of the plurality of individuals received in Step S100, and the overall parameters ^ β and ^ Λ estimated in Step S106, According to the above equation (26), the individual parameter ^ θ ^u is estimated for each of the plurality of individuals.

In step S110, the whole and individual parameter estimation unit 40, based on the behavior data and stimulus data for each of the plurality of individuals received in step S100, according to the above equation (27), the whole parameters ^ β, ^ Λ, An individual parameter {circumflex over (θ) ^{} u} for each of a plurality of individuals is estimated.

Then, in step S112, the output unit 50 outputs the individual parameters ^ theta ^u for each of a plurality of individuals estimated in step S108 or step S110 as a result, and ends the model estimation process routine.

<Operation of the optimization device according to the embodiment of the present invention>

Next, the operation of the optimization apparatus 200 according to the embodiment of the present invention will be described. First, when an individual parameter {circumflex over (θ)} ^u for each of a plurality of individuals output by the model estimation apparatus 100 is input to the optimization apparatus 200, it is stored in the storage unit 222. Then, when the behavior data of the individual to be optimized, the stimulus data of the individual observed for a specific option, and the constraint conditions related to the stimulus are input, the optimization apparatus 200 performs the optimization processing routine shown in FIG. Execute. The optimization processing routine is repeatedly executed with each individual as an optimization target.

  First, in step S200, the input unit 210 receives constraint conditions related to stimulation given to an individual, behavior data of an optimization target individual, and stimulation data of the individual observed for a specific option.

Next, in step S202, the optimization unit 224, with respect to the individual u to be optimized, the individual observed for the constraint condition related to the stimulus, the behavior data of the individual, and the specific option z _l received in step S100. On the basis of the stimulation data and the individual parameter {circumflex over (θ) ^u } of the individual stored in the storage unit 222, satisfying the constraint condition regarding stimulation according to the above formula (28) and formula (29), and up to a predetermined period during, individuals take action, and to maximize the number of times to select the option z _l, optimizing the sequence of time of stimulation related choices z _l scheduled to be given to the individual.

Next, in step S204, the output unit 250 outputs the stimulus time series related to the option z _{1 to} be given to the optimization target individual optimized in step S202, and ends the optimization processing routine. To do.

  As described above, according to the model estimation device according to the present embodiment, the stimulus contact effect is enhanced when an individual contacts a stimulus of a predetermined first amount or more, and the individual is predetermined. Of the behavior of the individual modeled so that the stimulus contact effect is reduced when contacted with a stimulus of the second amount or more, and the stimulus contact effect is attenuated according to the elapsed time of contact with the individual stimulus. A model related to occurrence, a model related to selection when an individual's behavior occurs modeling the selection probability of selecting each option when the individual takes action, a parameter related to the model related to occurrence of the individual's behavior, and the individual's behavior An individual parameter that models that an individual parameter that represents a parameter related to a model related to selection when an error occurs is generated according to the distribution represented by the overall parameter Based on the model related to the generation process and the behavior data and stimulus data observed for each of the plurality of individuals, by estimating the individual parameters for each of the plurality of individuals, the threshold property of the stimulus contact effect, the stimulus contact It is possible to obtain a parameter for estimating the stimulation contact effect on the selected action in consideration of the effect wearout and the forgetting property of the stimulation contact effect.

In addition, according to the behavior prediction device according to the present embodiment, the constraint conditions related to the stimulus given to the individual, the behavior data of the individual, the individual stimulation data observed for the option z _l , and the individual estimated by the model estimation device Based on the individual parameters of the individual to be given to the individual so as to satisfy the constraints and to maximize the number of times that the individual takes action and selects the choice z _l during a predetermined period of time. By optimizing the time series of stimuli with respect to option z _l , a specific selection action is caused to an individual in consideration of the threshold property of the stimulus contact effect, the wear out of the stimulus contact effect, and the forgetting property of the stimulus contact effect. Can be optimized.

  In addition, according to the model estimation device and the optimization device according to the present embodiment, high accuracy in consideration of threshold generation, wearout, and forgetting, incorporating decision generation and selection of decision content, and both Provided is a technique that makes it possible to realize a simple stimulus contact effect estimation for each individual. It is also possible to derive the optimal method (quantity and timing) for each individual.

  Further, for example, the business operator can determine whether or not the advertisement contact is effective for each individual based on the information on how to give the optimum stimulus to each individual. Alternatively, the maximum advertising effect can be achieved with the minimum budget. In addition, the advertising agency can calculate an appropriate advertising fee based on the correct advertising effect.

  Note that the present invention is not limited to the above-described embodiment, and various modifications and applications are possible without departing from the gist of the present invention.

For example, in the above embodiment, when estimating the overall parameters and individual parameters, a case of using the attribute data d ^u has been described as an example, but the invention is not limited to this, without using the attribute data d ^u Global parameters and individual parameters may be estimated. When estimating the overall parameters and individual parameters without using the attribute data d ^u sets the attribute data d ^u as a vector of elements 1, and may be set to the value of the element 1.
Moreover, although the case where the one-level hierarchical Bayes model or the two-level hierarchical Bayes model is selected has been described as an example, the present invention is not limited to this, and any one of the one-level hierarchical Bayes model and the two-level hierarchical Bayes model is used. You may comprise only one of them. When a one-level hierarchical Bayes model is used, the selection unit 32 and the entire and individual parameter estimation unit 40 are not necessary. When a two-level hierarchical Bayes model is used, the selection unit 32 and the overall parameter estimation unit 36 are used. , And the individual parameter estimation unit 38 is unnecessary.

  Moreover, although the above-mentioned model estimation apparatus demonstrated the case where the memory | storage part 22 was provided, the memory | storage part 22 is provided in the external apparatus of the model estimation apparatus, for example, and a model estimation apparatus uses an external apparatus and a communication means. You may make it refer to the memory | storage part 22 by communicating.

  Moreover, although the above-mentioned optimization apparatus demonstrated the case where the memory | storage part 222 was provided, the memory | storage part 222 is provided in the external apparatus of the optimization apparatus, for example, and an optimization apparatus uses an external apparatus and a communication means. You may make it refer to the memory | storage part 222 by communicating.

  Moreover, although the case where the model estimation apparatus and the optimization apparatus are configured as separate apparatuses has been described as an example in the above embodiment, the model estimation apparatus and the optimization apparatus may be configured as one apparatus.

  In addition, the model estimation device and the optimization device described above have a computer system inside, but if the computer system uses a WWW system, the homepage providing environment (or display environment) is also included. Shall be.

  In the present specification, the embodiment has been described in which the program is installed in advance. However, the program can be provided by being stored in a computer-readable recording medium.

DESCRIPTION OF SYMBOLS 10 Input part 20 Operation part 22 Storage part 30 Estimation part 32 Selection part 34 Parameter estimation part 36 Overall parameter estimation part 38 Individual parameter estimation part 40 Whole and individual parameter estimation part 100 Model estimation apparatus 200 Optimization apparatus 210 Input part 220 Operation part 222 Storage unit 224 Optimization unit 250 Output unit

Claims (8)

A model estimation method in a model estimation device including an input unit and a parameter estimation unit,
Action time series data representing a time series when the individual took action observed by each of the plurality of individuals, and a selection series representing a series of action selection contents when the individual acted Receiving behavior data including data, and stimulating data that is observed for each of a plurality of individuals and that is observed for each action option, and that represents a sequence of times when the individual contacts the stimulus;
The parameter estimation unit,
For each of multiple individuals,
When the individual comes into contact with a stimulus of a predetermined first amount or more, a stimulus contact effect representing a degree of the individual to take action by contact with the stimulus becomes high, and the individual is predetermined. A unit time at time t so that the stimulus contact effect is reduced when contacted with a stimulus of a second amount or more, and the stimulus contact effect is attenuated according to the elapsed time of contact with the individual's stimulus. A model relating to the occurrence of an individual's behavior that models the rate λ (t) at which the individual takes action, and a selection probability p _l for selecting each option z _l when the individual takes action at time t A model for selecting when an individual's behavior occurs, modeling (t);
For each of the plurality of individuals, an individual parameter that represents a parameter related to the model related to the occurrence of the behavior of the individual and a parameter related to the model related to the selection when the behavior of the individual occurs is generated according to the distribution represented by the overall parameter. Based on the model related to the generation process of the individual parameters and the behavior data and the stimulus data received by the input unit,
Estimating the global parameters and the individual parameters for each of the plurality of individuals;
A model estimation method including: The model related to the generation process of the individual parameters is modeled based on a one-level hierarchical Bayesian model,
The step of estimating the parameter by the parameter estimating unit estimates the overall parameter based on the behavior data and the stimulus data received by the input unit, and the behavior data and the stimulus data received by the input unit; The model estimation method according to claim 1, wherein the individual parameter is estimated for each of the plurality of individuals based on the estimated overall parameter. The model related to the generation process of the individual parameters is modeled based on a two-level hierarchical Bayesian model,
The step of estimating a parameter by the parameter estimation unit estimates the overall parameter and the individual parameter for each of the plurality of individuals based on the behavior data and the stimulus data received by the input unit. 2. The model estimation method according to 1. The step of receiving by the input unit further receives attribute data representing an attribute for each of a plurality of individuals,
The model related to the generation process of the individual parameter is a model in which the individual parameter for each of the plurality of individuals is generated according to a distribution represented by the attribute of the individual and the overall parameter,
The step of estimating the parameter by the parameter estimation unit includes a model relating to selection when the behavior of the individual occurs and a model relating to the generation process of the individual parameter, the behavior data received by the input unit, the stimulation data, and The model estimation method according to claim 1, wherein the overall parameter and the individual parameter for each of a plurality of individuals are estimated based on the attribute data. The option z _{l to} be given to the individual based on the individual parameters of the individual estimated by the model estimation method according to any one of claims 1 to 4 including an input unit and an optimization unit An optimization method in an optimization device for optimizing a sequence of stimulation times,
Receiving the constraint condition relating to the stimulus given to the individual by the input unit, the behavior data of the individual, and the stimulus data of the individual observed for the option z _l ;
Based on the constraint condition, the behavior data of the individual, the stimulation data of the individual observed for the option z _l , and the individual parameters of the individual, which the optimization unit has received by the input unit The option z to be given to the individual so as to maximize the number of times that the individual takes action and selects the option z _l during a predetermined period of time, satisfying the constraint conditions optimizing the sequence of stimulus times for _l ;
Optimization method including. Observed for each of a plurality of individuals, behavior time series data representing a series of times when the individual took action, selection series data representing a series of action selection contents when the individual acted, and the individual And an input unit for receiving stimulus data representing a series of times when the individual contacts the stimulus, which is observed for each of the plurality of individuals and observed for each action option,
For each of multiple individuals,
When the individual comes into contact with a stimulus of a predetermined first amount or more, a stimulus contact effect representing a degree of the individual to take action by contact with the stimulus becomes high, and the individual is predetermined. A unit time at time t so that the stimulus contact effect is reduced when contacted with a stimulus of a second amount or more, and the stimulus contact effect is attenuated according to the elapsed time of contact with the individual's stimulus. A model relating to the occurrence of an individual's behavior that models the rate λ (t) at which the individual takes action, and a selection probability p _l for selecting each option z _l when the individual takes action at time t A model for selecting when an individual's behavior occurs, modeling (t);
For each of the plurality of individuals, an individual parameter that represents a parameter related to the model related to the occurrence of the behavior of the individual and a parameter related to the model related to the selection when the behavior of the individual occurs is generated according to the distribution represented by the overall parameter. Based on the model related to the generation process of the individual parameters and the behavior data and the stimulus data received by the input unit,
A parameter estimator that estimates the overall parameters and the individual parameters for each of the plurality of individuals;
Model estimation apparatus including An optimization device for optimizing a sequence of stimulation times related to the option z _{l to} be given to the individual based on the individual parameters of the individual estimated by the model estimation device according to claim 6,
An input unit for receiving a constraint condition relating to a stimulus given to the individual, the behavior data of the individual, and the stimulus data of the individual observed with respect to the option z _l ;
The constraint condition is satisfied based on the constraint condition, the behavior data of the individual, the stimulus data of the individual observed for the option z _l , and the individual parameter of the individual, which is received by the input unit. The time of stimulation for the option z _{l to} be given to the individual so as to maximize the number of times that the individual takes action and selects the option z _l during a predetermined period of time An optimization unit for optimizing the series;
Including an optimization device.   The program for making a computer perform each step of the model estimation method of any one of Claims 1-4, or the optimization method of Claim 5.