JP6285846B2 - Individual behavior model estimation device, purchasing behavior model estimation device, external stimulus timing optimization device, individual behavior model estimation method, and program - Google Patents

Description

  The present invention relates to a technique for calculating a stimulus timing that maximizes a stimulus contact effect by modeling the probability that an individual who has touched an external stimulus will act.

  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 TV / web advertisement of a product, purchase the product, contact with travel advertisement to a region, and decide to travel to the region. To click on the homepage address of a specific company. In addition, there is an example in which a human being is guided to a desirable behavior such as awakening from sleep by an alarm alarm or taking in a desired food by a proposal of a software agent.

  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, decreasing property, 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. Moreover, the decreasing property of the stimulation contact effect is a property in which the increase in the effect becomes smaller as the stimulation contact amount is increased. In advertising research (stimulus = advertisement, effect = sales or market share), the existence of these two properties has been pointed out (Non-Patent Documents 1 and 2). Non-Patent Documents 1 and 2 propose a method for estimating the effect of advertisement on sales in consideration of the threshold value. However, only the macro advertising effect per customer and per month is considered.

  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 for the advertising effect (Non-Patent Documents 3 and 4), the influence of others on the purchasing behavior and mail transmission behavior (Non-Patent Documents 5 and 6), and the like. It is often assumed even in animal selection behavior (Non-patent Document 7). It has also been confirmed by psychological experiments (Non-Patent Document 8).

A. C. Bemmaor, "Testing Alternative Econometric Models on the Existence of Advertising Threshold Effect", Journal of Marketing Research, Vol. 21, No. 3, pp. 298-308, 1984. J. L. Simon, J. Arndt, "The Shape of the Advertising Response Function", Journal of Advertising Research, Vol. 20, No. 4, pp.11-28, 1980. 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. 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. 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. 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. A. Hawkes, "Spectra of some self-exciting and mutually exciting point processes", Biometrika, Vol. 58, No. 1, pp. 83-90, 1971. E. N. Brown, R. Barbieri, et al., "The Time-Rescaling Theorem and Its Application to Neural Spike Train Data Analysis", Neural Computation, Vol. 14, No. 2, pp. 325-346, 2002.

  In recent years, with the development of ICT technology, there is an increasing need to control stimuli such as advertisements on an individual basis, but Non-patent Documents 1, 2, and 3 can only handle macro stimulus effects and measure stimulus contact effects on an individual basis. Because it is not possible, the above-mentioned needs cannot be satisfied.

  In Non-Patent Documents 5, 6, and 9, which can measure the stimulus contact effect in individual units, the threshold value, diminishing property, and forgetting property of the stimulus contact effect are not considered at the same time, so the stimulus contact effect is accurately measured. Or it cannot be optimized. For example, if gradual decrease is ignored, the greater the number of stimulation contacts, the greater the expected effect, leading to useless stimulation contact.

  Non-patent document 4 regarding advertising effectiveness considers all of threshold, diminishing, and forgetting, but the effect on the selection behavior of the product brand (the problem of which brand to buy when given the purchase time) It is only discussed and the effect on the occurrence of purchasing behavior cannot be measured. In this case, the advertising effect cannot be optimized unless the target user's next purchase time is known. In order to measure the effect on the occurrence of purchasing behavior, as in Non-Patent Document 9, it is necessary to calculate the “rate” based on the point process described later. However, all of threshold, diminishing, and forgetting are considered. In addition, a technique for calculating the rate has not been proposed yet. In an era where web advertisements and other stimuli can be controlled in seconds, a technology is needed to calculate when and how much the stimuli cause decision making (such as purchasing) and optimize the timing of the stimuli. ing.

  Whether threshold value, diminishing property, and forgetting property are all considered or not, the conclusion is that the effect of prompting the action increases as the contact amount to the stimulus increases. However, there are situations where too many stimuli actually have a negative effect. For example, there is a phenomenon in which web advertisements that appear frequently feel uncomfortable and reduce the willingness to purchase. In the present specification and claims, this phenomenon is included in “decreasing”.

  That is, in addition to the original meaning that the increased amount of the effect decreases as the stimulation contact amount is increased, the “decreasing property” has a meaning that the increased amount of the effect falls negatively. In recent years, advertising expenses have become a large expense for businesses, and therefore a technology that takes this point into consideration is also required in order to calculate budget allocation without waste. However, there is no prior art that takes this into consideration.

  The present invention has been made in view of the above points, and provides a technique capable of realizing highly accurate stimulation contact effect estimation in consideration of threshold value, diminishing property, and forgetting property on an individual basis. With the goal.

According to an embodiment of the present invention, an individual behavior model estimation apparatus for estimating an individual behavior model with respect to an external stimulus,
Input means for inputting, as input data, stimulus data that is time-series data of external stimuli that cause the individual to behave, and action data that is time-series data of the action event of the individual;
Based on the function indicating the forgetting property of the stimulating contact effect and the function indicating the threshold property and decreasing property of the stimulating contact effect, an action probability function indicating the probability that the individual takes action per unit time is defined. Parameter estimation means for estimating a parameter of an action probability function,
The parameter estimation means determines the parameter based on the behavior probability function, the probability distribution of the parameter, and the input data so that the marginal likelihood related to the inter-individual distribution of the parameter is maximized. An individual behavior model estimation device is provided.

According to an embodiment of the present invention, means for calculating a predicted value of the action probability based on the stimulus data, the action data, the action probability function, and the parameter estimated by the parameter estimation means;
Means for calculating the timing of an external stimulus that maximizes the expected value of the number of actions of each individual caused by the external stimulus by calculating the timing of the external stimulus that maximizes the integral value of the predicted value of the action probability; An external stimulus timing optimizing device is provided.

Further, according to the embodiment of the present invention, a purchasing behavior model estimation device for estimating a purchasing behavior model of an individual with respect to an advertisement stimulus,
Input means for inputting, as input data, stimulus data that is time-series data of advertising stimuli that cause the individual to make a purchase behavior, and purchase behavior data that is time-series data of the purchase behavior event of the individual, and forgetting the stimulus contact effect Based on the function indicating sex and the function indicating the threshold value and decreasing property of the stimulation contact effect, an action probability function indicating the probability that the individual takes a purchase action per unit time is determined. Parameter estimation means for estimating parameters,
The parameter estimation means determines the parameter based on the behavior probability function, the probability distribution of the parameter, and the input data so that the marginal likelihood related to the inter-individual distribution of the parameter is maximized. A purchase behavior model estimation device is provided.

In addition, according to the embodiment of the present invention, an individual behavior model estimation method executed by an individual behavior model estimation device that estimates an individual behavior model with respect to an external stimulus,
An input step for inputting stimulus data, which is time-series data of external stimuli that cause the individual to behave, and action data, which is time-series data of behavior events of the individual, as input data, and shows forgetability of the stimulus contact effect Based on the function and the function indicating the threshold value and the decreasing property of the stimulus contact effect, an action probability function indicating the probability that the individual takes action per unit time is determined, and the parameter of the action probability function is estimated. A parameter estimation step,
In the parameter estimation step, the individual behavior model estimation device is configured so that, based on the behavior probability function, the probability distribution of the parameter, and the input data, the marginal likelihood related to the inter-individual distribution of the parameter is maximized. An individual behavior model estimation method characterized by determining a parameter is provided.

  According to the embodiment of the present invention, there is provided a technique capable of realizing highly accurate stimulation contact effect estimation in consideration of threshold value, diminishing property and forgetting property. It is also possible to derive the optimum way (amount and timing) of giving stimulus to each individual.

  With such information, for example, the business operator can achieve the maximum advertising effect with the minimum budget. Further, the advertising agency can calculate an appropriate advertising fee based on the correct advertising effect.

It is a functional block diagram of the stimulation contact effect management apparatus 300 which concerns on embodiment of this invention. It is a figure which shows the process sequence regarding the stimulus contact effect estimation part. It is a figure which shows the example of a model of a rate. It is a figure which shows the example of a model of the rate at the time of imposing diminishing property on intensity | strength. It is a figure which shows the example of an output of the stimulation contact effect estimation part 100. FIG. It is a figure which shows the process sequence regarding the stimulus contact effect optimization part. It is a figure which shows the example of the optimal stimulation contact. It is a figure which shows the output example of the stimulation contact effect optimization part.

  Embodiments of the present invention will be described below with reference to the drawings. The embodiment described below is only an example, and the embodiment to which the present invention is applied is not limited to the following embodiment. For example, in the following description, the subject that makes a decision on a stimulus is assumed to be a human, but the subject that makes a decision on a stimulus is not limited to a human, and may be another organism. These may be collectively referred to as “individuals”.

  In the embodiment of the present invention, the individual behavior model is estimated by modeling the relationship between the probability of making a decision (behavior) and the stimulus contact using a probability theory called “point process”. At that time, a model is constructed that simultaneously considers the threshold value, decreasing property, and forgetting property of the stimulus contact effect. Hereinafter, the detailed contents of the present embodiment will be described.

(Apparatus configuration, function overview)
In FIG. 1, the functional block diagram of the stimulation contact effect management apparatus 300 which concerns on embodiment of this invention is shown. As illustrated in FIG. 1, the stimulation contact effect management device 300 includes a stimulation contact effect estimation unit 100 and a stimulation contact effect optimization unit 200.

  The stimulation contact effect estimation unit 100 is a functional unit that models the probability of human decision making as a function of the input stimulus and estimates the stimulation contact effect (eg, advertisement stimulation contact effect) from the observation data. In the present embodiment, “modeling” is to define a function that is a basis of a model and to estimate an optimum parameter for the function. A model in which the parameter is estimated may be referred to as an “individual behavior model”. The stimulating contact effect estimation unit 100 estimates the individual behavior model in units of individuals and considers the stimulating contact effect by considering the three properties of the stimulating contact effect: 1) threshold value, 2) decreasing property, and 3) forgetting property. It is possible to estimate.

  Further, the stimulus contact effect optimization unit 200 calculates a stimulus (timing timing or the like) that maximizes the stimulus contact effect based on the estimation result obtained by the stimulus contact effect estimation unit 100.

  The stimulus contact effect estimation unit 100 receives each person's decision making time series, observation period, and stimulus information as input, estimates a model, estimates the stimulus contact effect for each person, and outputs the result. it can. Further, the stimulus contact effect optimization unit 200 receives each person's decision making time series and the estimated stimulus contact effect, etc. as input, and calculates a stimulus that maximizes the probability of making a decision on an individual basis, The result can be output.

  As shown in FIG. 1, the stimulation contact effect estimation unit 100 includes an input unit 101 that inputs data, an overall parameter estimation unit 102, a stimulation contact effect parameter estimation unit 103, and an output unit 104 that outputs data. The stimulation contact effect optimization unit 200 includes an input unit 201 that inputs data, a stimulation optimization processing unit 202, and an output unit 203 that outputs data. Details of the operation will be described later.

  The stimulation contact effect management apparatus 300 according to the present embodiment can be realized by causing one or a plurality of computers to execute a program describing the processing content described in the present embodiment. That is, the function of the stimulation contact effect management device 300 executes a program corresponding to the process executed by the stimulation contact effect management device 300 using hardware resources such as a CPU, memory, and hard disk built in the computer. This can be realized by doing so. Further, the program can be recorded on a computer-readable recording medium (portable memory or the like), stored, or distributed. It is also possible to provide the program through a network such as the Internet or electronic mail.

  Further, the stimulation contact effect estimation unit 100 and the stimulation contact effect optimization unit 200 may be devices realized by separate computers. In this case, the stimulation contact effect estimation unit 100 is referred to as a stimulation contact effect estimation device, The stimulation contact effect optimization unit 200 can be called a stimulation contact effect optimization device. In addition, the stimulation contact effect estimation device may be called an individual behavior model estimation device, and the stimulation contact effect optimization device may be called an external stimulation timing optimization device.

  Both the stimulation contact effect estimation device and the stimulation contact effect optimization device can be realized by causing one or a plurality of computers to execute a program describing the processing contents described in the present embodiment. That is, the function of the device can be realized by executing a program corresponding to the process executed by the device using hardware resources such as a CPU, a memory, and a hard disk built in the computer. It is. Further, the program can be recorded on a computer-readable recording medium (portable memory or the like), stored, or distributed. It is also possible to provide the program through a network such as the Internet or electronic mail.

  The program in the stimulation contact effect management apparatus 300 includes both a program in the stimulation contact effect estimation apparatus and a program in the stimulation contact effect optimization apparatus. That is, the program in the stimulus contact effect management device 300 corresponds to a program for causing a computer to function as each unit of the individual behavior modeling device and each unit of the external stimulus timing optimization device.

  Hereinafter, the processing content regarding the stimulation contact effect estimation part 100 and the stimulation contact effect optimization part 200 is demonstrated in detail.

(Processing in stimulation contact effect estimation unit 100)
First, processing in the stimulation contact effect estimation unit 100 will be described. FIG. 2 is a diagram illustrating a processing procedure related to the stimulation contact effect estimation unit 100.

  As shown in FIG. 2, in step 101, thresholding, decreasing, and forgetting are modeled (in this case, a function or constant that is a basis of the model is determined), and in step 102, the probability of the stimulation contact effect parameter Select the distribution type. In step 103, the result of step 101 (function information, etc.), the result of 102 (information of the selected probability distribution type, etc.), action data 10 and stimulus data 20 are input, and the overall parameter estimation unit 102 performs global parameter estimation based on the experience Bayesian method. In step 104, the stimulation contact effect parameter estimation unit 103 estimates the stimulation contact effect parameter and outputs the stimulation contact effect parameter and the stimulation contact effect (30). The input / output data is held in a storage means such as a memory and used for subsequent calculations.

  Of the above steps, steps 101 and 102 are performed in advance by a user of the stimulation contact effect management apparatus 300 or the like. Further, regarding the input data, separately observed data may be input, or the input unit 101 has a function of observing the behavior data 10 and the stimulus data 20, and the input unit 101 inputs the observed data. It is good as well. In any case, there is no substitute for inputting data. The same applies to the input unit 201.

  Hereinafter, an example of input data and the contents of each step will be described in detail.

<About input data>
First, input data will be described. The action data 10 is action time series data of a user (individual) to be analyzed. The action data 10 includes a user ID (denoted as u) and a series of times ({t _j ^u } = (t ₀ ^u , t ₁ ^u , t ₂ ^u ) when the action of the user u (a user whose ID is u) is caused. ,...)), And an observation period (indicated as [T _s , T _e ] with a start time of T _s and an end time of T _e ).

  The stimulus data 20 is time-series data of the stimulus that has been touched by each user. For example, in the case of a TVCF advertisement, a sequence of times when the user views the advertisement is given as data. The action time-series data in this advertisement example is given as, for example, time-series data of an event in which a product is purchased.

<Step 101: Modeling of threshold, decreasing, and forgetting>
Next, modeling of threshold value, decreasing property, and forgetting property will be described. In the present embodiment, the user's behavior is expressed by a probability λ (t) that the user takes action per unit time under a probability theory called “point process”. Here, t represents time. λ (t) is called the rate. Modeling of the threshold property, the diminishing property, and the forgetting property of the stimulation contact effect is realized through this rate. Here are some examples of modeling. However, the following equation is discussion of probability for each user u, simply shall be denoted as t _j a t _j ^u for simplicity.

Example 1: When the stimulus data is given by the stimulus contact time. When the rate is excited and the effect is forgotten exponentially at each stimulus contact, the rate λ (t) is

で表現することができる。ただし、λ_０は基礎レート、ｓ_ｉはｉ番目の刺激接触時刻、ａ_ｓ（≧０）は一度当りの刺激接触効果の強度、１／ｂ_ｓ（≧０）は刺激接触効果の持続時間、ｎ_ｔｈは刺激接触効果の閾値、関数Ｇ（ｙ）は非線形関数を表す。ｎ（ｔ）の指数関数は刺激接触効果の忘却性をモデル化している。非線形関数Ｇは刺激接触の閾値性と逓減性をモデル化するものであり、例えば以下のようなシグモイド型の関数を用いれば良い。

Can be expressed as Where λ ₀ is the basal rate, s _i is the i th stimulation contact time, a _s (≧ 0) is the intensity of the stimulation contact effect per time, 1 / b _s (≧ 0) is the duration of the stimulation contact effect, n _th represents the threshold value of the stimulation contact effect, and the function G (y) represents a nonlinear function. The exponential function of n (t) models the forgetting nature of the stimulus contact effect. The nonlinear function G models the threshold characteristics and decreasing characteristics of the stimulation contact. For example, the following sigmoid function may be used.

式（２）の二つ目の関数を採用したときのレートの挙動例を図３に示す。図３において、刺激接触時刻のグラフは刺激データ２０から与えられた刺激接触回数の情報であり、ｎ（ｔ）のグラフは値が大きいほど刺激接触の効果が高いことを意味している。なお、ｎ（ｔ）は実質的な累積刺激接触量だと解釈することもできる。図３より、個々の刺激接触の効果が減衰する（忘却性）、その効果が閾値を超えない限りレートへの影響がほぼ現れない（閾値性）、閾値以上の刺激量を増やしてもレートの増加が鈍る（逓減性）様子が確認できる。

An example of rate behavior when the second function of equation (2) is employed is shown in FIG. In FIG. 3, the graph of the stimulation contact time is information on the number of stimulation contacts given from the stimulation data 20, and the graph of n (t) means that the effect of stimulation contact is higher as the value is larger. Note that n (t) can be interpreted as a substantial cumulative stimulus contact amount. From FIG. 3, the effect of individual stimulus contact is attenuated (forgetfulness), and the effect on the rate hardly appears unless the effect exceeds the threshold (threshold property). It can be seen that the increase is slow (decreasing).

  Forgetability may be modeled using an exponential attenuation function as shown in the following equation (3) in addition to exponential attenuation.

また、忘却性は、レイリー分布などの時間遅れを伴う減衰関数を用いてモデル化することもできる。

Forgetability can also be modeled using an attenuation function with a time delay such as a Rayleigh distribution.

Example 2: In Example 1, stimulation contact strength a _s if imposed diminution of the strength of Example 1 was constant, assumed here intensity with dynamics as follows.

ただし、ａ_０は基礎強度、ｓ_ｉはｉ番目の刺激接触時刻、ａ_１（≧０）は一度の刺激接触による逓減の強さ、そして１／β（≧０）は逓減の持続時間である。式（４）において、刺激接触強度は刺激への接触の度に減少し、接触が無ければ時間とともにａ_０の値に回復する。そのため、過度に頻繁な刺激接触は刺激接触強度ａ_ｓの減退を招き、その結果、式（１）で表されるレートの減退を生じさせる。これは例えば過度なウェブ広告により購買意欲が減退する状況を表現している。図４に、強度に逓減性を課した場合のレートのモデル例を示す。刺激接触の効果を示すｎ（ｔ）のグラフの最も右側において、過度に頻繁な刺激接触を与えたことによって減衰を生じていることが見て取れる。ｎ（ｔ）を閾値以上に保つためには中間的な頻度で刺激を与える必要があることが分かる。

Where a ₀ is the basic intensity, s _i is the i-th stimulus contact time, a ₁ (≧ 0) is the strength of diminution by one stimulus contact, and 1 / β (≧ 0) is the duration of the diminution . In the formula (4), stimulation contact strength decreases every time the contact to the stimulus, to recover if there is no contact with time to a value of a _0. Therefore, excessively frequent stimulation contact leads to decline in stimulating contact strength a _s, as a result, causes a decline in the rate represented by the formula (1). This expresses a situation in which the willingness to purchase declines due to excessive web advertisements, for example. FIG. 4 shows an example of a rate model in the case where a decreasing property is imposed on the strength. It can be seen on the far right side of the graph of n (t) that shows the effect of stimulating contact that attenuation is caused by applying too frequent stimulating contact. It can be seen that stimuli need to be applied at an intermediate frequency in order to keep n (t) above the threshold.

Example 3: Case where stimulation data is given by period In Example 1, only information on the stimulation contact time was considered, but the impact given by one contact may differ, for example, in a 1-minute and 10-minute TV CM. The following method can be considered as one of the methods for incorporating the difference into the model.

ここで、式（５）におけるｗ_ｋ ^{ｓｔａｒｔ}、ｗ_ｋ ^ｅｎｄはそれぞれｋ番目の刺激の接触開始時刻と接触終了時刻である。接触時間が長いとそれだけ受ける影響が大きくなる。ｇ（ｔ−ｔ´）は忘却性を表す畳み込み関数であり、例１と同様に指数関数（指数的減衰）、ベキ関数（べき的減衰）、あるいはレイリー分布などの時間遅れを伴う減衰関数を当てはめることができる。

Here, w _k ^start and w _k ^end in Equation (5) 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 representing forgetting property, and in the same manner as in Example 1, an exponential function (exponential decay), a power function (exponential decay), or a decay function with a time delay such as a Rayleigh distribution is represented. Can be applied.

Example 4: Considering influence from past action history In Examples 1 to 3, only the effect of stimulating contact was considered, but there may be situations where the current action is influenced by the past action. 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, by using the Hawkes process (Non-Patent Document 10), the rate is

の形でモデル化することができる。ただし、式（６）において、ｔ_ｊはユーザのｊ番目の行動時刻、ａ_ｈ（≧０）はインパクトの強さ、１／ｂ_ｈ（≧０）は効果の持続時間を表す。ユーザによっては刺激接触ではなく自身の行動リズムに基づいて行動を起こしている場合もある。刺激の影響と行動履歴からの影響を同時に考慮することで、刺激の効果をより正しく推定することができると期待される。ただし、行動履歴のモデル化は式（６）に限るものではない。

Can be modeled. In equation (6), t _j represents the j-th action time of the user, a _h (≧ 0) represents the strength of impact, and 1 / b _h (≧ 0) represents the duration of the effect. Some users may act based on their own behavioral rhythm instead of 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 equation (6).

<Step 102: Select probability distribution type of stimulation contact effect parameter>
Next, the probability distribution type selection of the stimulation contact effect parameter will be described. Threshold of the step 101, decreasing resistance, in the modeling of forgetfulness, _(a s in the above _example, b _s, such as _a 0, a ₁₎ stimulating exposure effect parameter group is defined. The parameter group is collectively expressed as θ≡ (a _s , b _s , a ₀ , a ₁ ,...), And hereinafter referred to as a stimulation contact effect parameter. Since the stimulation contact effect parameter θ may be different for each user, the parameter of the user u is particularly expressed as θ ^u .

In order to model the difference in parameters between users (individuals), between users of each component θ _l ^u of stimulation contact effect parameters θ ^u = (θ ₁ ^u , θ ₂ ^u , θ ₃ ^u ,...) Distribution is a bivariate exponential family

でモデル化することを考える。ただし、Ｓ_１（θ_ｌ ^ｕ）とＳ_２（θ_ｌ ^ｕ）は２変数指数分布族を特徴付ける十分統計量、μ_ｌとν_ｌは分布の形状を決める２つのパラメータである。このときパラメータθ^ｕの従う確率分布は

Think about modeling with. However, S ₁ (θ _l ^u ) and S ₂ (θ _l ^u ) are sufficient statistics that characterize the two-variable exponential distribution family, and μ _l and ν _l are two parameters that determine the shape of the distribution. At this time, the probability distribution according to the parameter θ ^u is

と表現される。ただし、μ＝（μ_１，μ_２，μ_３，・・・）とν＝（ν_１，ν_２，ν_３，・・・）はユーザ全体におけるθ^ｕの分布形状を決めるパラメータであるので、ここではその２種類のパラメータを全体パラメータと呼ぶこととする。どの指数分布族を用いるかは刺激接触効果管理装置３００の使用者が決める。指数分布族には代表的なものに正規分布（Ｓ_１（ｘ）＝ｘ，Ｓ_２（ｘ）＝ｘ^２）、ガンマ分布（Ｓ_１（ｘ）＝ｘ，Ｓ_２（ｘ）＝ｌｏｇ（ｘ））、逆正規分布（Ｓ_１（ｘ）＝ｘ，Ｓ_２（ｘ）＝ｘ^−１）などがある。激接触効果管理装置３００の使用者は、これらのうちから１つ選択する。なお、２種類のパラメータμとνは入力データから推定されることになる。その処理を次に説明する。

It is expressed. However, μ = (μ ₁ , μ ₂ , μ ₃ ,...) And ν = (ν ₁ , ν ₂ , ν ₃ ,...) Are parameters that determine the distribution shape of θ ^{u in} the entire user. Here, these two types of parameters are referred to as overall parameters. Which index distribution family is used is determined by the user of the stimulus contact effect management apparatus 300. Typical examples of the exponential distribution family include normal distribution (S ₁ (x) = x, S ₂ (x) = x ² ), gamma distribution (S ₁ (x) = x, S ₂ (x) = log ( x)), and an inverse normal distribution (S ₁ (x) = x, S ₂ (x) = x ⁻¹ ). The user of the intense contact effect management device 300 selects one of these. Note that the two types of parameters μ and ν are estimated from the input data. The process will be described next.

<Step 103: Overall Parameter Estimation Based on Experience Bayes Method>
Next, the overall parameter estimation process based on the experience Bayes method executed by the overall parameter estimation unit 102 will be described.

The overall parameter estimation unit 102 estimates the overall parameters μ and ν from the input data based on the experience Bayes method. First, the likelihood function p stimulation exposure effect parameters for each user _{^{({t j u} │θ u}} ) , the rate λ being modeled as a function of a parameter theta ^u at step 101 | using (t θ ^u) And

と計算される。これは点過程と呼ばれる確率理論（非特許文献１１）から導かれる。式（８）で表される尤度関数は、ステップ１０１での例１〜４で例示したモデルの関数の全てに成り立つものであり、以後の計算は例１〜４全てに適用できる。

Is calculated. This is derived from a probability theory called a point process (Non-Patent Document 11). The likelihood function represented by Expression (8) is established for all the functions of the model exemplified in Examples 1 to 4 in Step 101, and the subsequent calculations can be applied to all of Examples 1 to 4.

Based on this likelihood function and the probability distribution p (θ ^u | μ, ν) of θ ^u selected in step 102, the marginal likelihood function for (μ, ν) is calculated as follows based on Bayes' theorem. Is done.

ただし、式（９）におけるＤは全ユーザのデータを表す。つまり、Ｄは、全ユーザに関する刺激データと行動データを表す。（μ，ν）はこの周辺尤度関数ｐ（Ｄ│μ，ν）を最大化するように推定する。このように、周辺尤度関数などを用いてモデルパラメータを全てのデータから推定する方法を経験ベイズ法と呼ぶ。

However, D in Formula (9) represents the data of all the users. That is, D represents stimulus data and action data regarding all users. (Μ, ν) is estimated so as to maximize this marginal likelihood function p (D | μ, ν). In this way, a method for estimating model parameters from all data using a marginal likelihood function or the like is called an experience Bayes method.

  Since (μ, ν) that maximizes the marginal likelihood function p (D | μ, ν) cannot be obtained analytically, it is executed using the EM method (expected value maximization method). Under the EM method, (μ, ν) that maximizes the marginal likelihood is obtained by repeatedly executing the following update rule.

ただし、（μ^（ｐ），ν^（ｐ））はｐ番目の更新値を表し、Ｅ［Ｓ（θ^ｕ）｜｛ｔ_ｊ ^ｕ｝，μ^（ｐ），ν^（ｐ）］は以下の式で定義されるθ^ｕについての事後平均を表す。

However, (μ ^(p) , ν ^(p) ) represents the p-th updated value, and E [S (θ ^u ) | {t _j ^u }, μ ^(p) , ν ^(p) ] represents the following equation: Represents the posterior average for θ ^u defined by.

ただし、Ｚ（θ^ｕ）は任意のθ^ｕの関数である。

However, Z (θ ^u ) is an arbitrary function of θ ^u .

<Step 104: Estimation of stimulation contact effect parameter>
Next, the stimulation contact effect parameter estimation process executed by the stimulation contact effect parameter estimation unit 103 will be described. In the following, for convenience of description, a hat (^) indicating an estimated amount may be described before a variable instead of the head of the variable, for example, “^ μ”.

The stimulation contact effect parameter estimation unit 103 estimates the stimulation contact effect parameter θ ^u of each user as a posterior average using the overall parameters (^ μ, ^ ν) estimated in step 103 as follows.

そして、刺激接触効果パラメータ推定部１０３は、推定された各ユーザの刺激接触効果パラメータを出力部１０４から出力する。また、推定されたパラメータ＾θ^ｕを用いてレートの推定値＾λ（ｔ｜＾θ^ｕ，｛ｔ_ｊ ^ｕ｝）を計算し、その積分値

Then, the stimulation contact effect parameter estimation unit 103 outputs the estimated stimulation contact effect parameter of each user from the output unit 104. Further, an estimated value ^ λ (t | ^ θ ^u , {t _j ^u }) is calculated using the estimated parameter ^ θ ^u and the integrated value thereof is calculated.

を計算し、出力することができる。レートは単位時間当りにユーザが行動を起こす確率であるので、式（１４）で計算されるレートの積分値Ｚは観測期間［Ｔ_ｓ，Ｔ_ｅ］の刺激接触によって引き起こされる行動の回数の期待値である。よってＺは与えられた刺激の効果を表す。ステップ１０１での例１、例２の場合における出力例を図５に示す。

Can be calculated and output. Since the rate is the probability that the user will take action per unit time, the integral value Z of the rate calculated by the equation (14) is the expectation of the number of actions caused by the stimulus contact in the observation period [T _s , T _e ]. Value. Thus, Z represents the effect of the applied stimulus. An output example in the case of Example 1 and Example 2 in Step 101 is shown in FIG.

As described above, according to the present embodiment, an individual behavior model estimation device that estimates an individual's behavior model with respect to an external stimulus, the stimulation data being time-series data of the external stimulus that causes the individual to act, , Input means (for example, the input unit 101) for inputting behavior data that is time-series data of the behavior event of the individual as input data, a function indicating the forgetting property of the stimulation contact effect, and a threshold property of the stimulation contact effect An action probability function (eg, λ (t)) indicating the probability that an individual will take action per unit time is determined based on a function indicating a decreasing property, and a parameter (eg, θ ^u ) of the action probability function is determined. ) For estimating the parameter (for example, the overall parameter estimation unit 102, the stimulation contact effect estimation unit 103), and the parameter estimation unit includes the action probability function (for example, λ (t θ ^u)), the probability distribution (example of the ^{parameter: p (θ u | μ,} ν)), and the input data (e.g., based on D), marginal likelihood relates interindividual distribution of the parameters (e.g. There is provided an individual behavior model estimation device characterized by determining the parameters so that p (D | μ, ν)) is maximized.

  The function indicating the forgetting property includes, for example, the intensity of the stimulus contact effect, and the intensity decreases as a result of contact with the stimulus, and increases with time if there is no contact (eg, step 101). Example 2). The behavior probability function may be a function in which the output of the convolution function of the length of contact time with the external stimulus and the forgetting property is applied to the function representing the threshold value and the decreasing property (for example, in step 101) Example 3). A function representing the influence from the past behavior history of the individual was added to the function obtained based on the function indicating the forgetting property of the stimulation contact effect and the function indicating the threshold property and the decreasing property of the stimulation contact effect. A function may be used as the action probability function (Example: Example 4 in Step 101).

  Further, in particular, in order to estimate an individual purchase behavior model for an advertisement stimulus, a purchase behavior model estimation device comprising: stimulus data that is time-series data of an advertisement stimulus that causes the individual to make a purchase behavior; and Based on the input means for inputting purchase behavior data that is time-series data of purchase behavior events as input data, the function indicating the forgetting property of the stimulation contact effect, and the function indicating the threshold property and the decreasing property of the stimulation contact effect, An action probability function indicating a probability that an individual will cause a purchase action per unit time is defined, and parameter estimation means for estimating a parameter of the action probability function, the parameter estimation means includes the action probability function, Based on the probability distribution of the parameter and the input data, the parameter is set so that the marginal likelihood related to the inter-individual distribution of the parameter is maximized. It may be provided purchasing behavior model estimation apparatus and determines the meter.

(Processing in the stimulation contact effect optimization unit 200)
Next, processing in the stimulation contact effect optimization unit 200 will be described. FIG. 6 is a diagram illustrating a processing procedure related to the stimulation contact effect optimization unit 200.

  As shown in FIG. 6, in step 200, the stimulus optimization processing unit 202 in the stimulus contact effect optimization unit 200 receives the action data 10, the stimulus data 20, the stimulus contact effect parameter 30, and the constraint condition 40 related to the stimulus as inputs. Then, the stimulation contact optimization process is performed, and the result 50 is output. The input data is held in a storage means such as a memory and used for subsequent calculations.

<About input data>
Among the input data, the action data 10, the stimulus data 20, and the stimulus contact effect parameter 30 are as described above.

  The constraint 40 regarding the stimulus is a constraint when optimizing the stimulus contact. For example, in the case of an advertisement stimulus, the budget (or the number of times of contact) that can be allocated to the advertisement and the minimum number of stimuli that can be contacted Such as the interval and duration of the advertisement.

<Step 200: Optimization of stimulation contact>
The stimulus optimization processing unit 202 makes a contact for each user based on the past behavior data 10, the past stimulus data 20, the estimated stimulus contact effect parameter 30, and the constraint condition 40 related to the stimulus as follows. To optimize. Here, the optimization means calculating a stimulus that maximizes the probability that an action is caused by the stimulus contact.

First, the past action data {t _j ^u }, the past stimulus data I ^u (T _s <t <T _e ), the estimated stimulus contact effect parameter ^ θ ^u , and the user u are to be contacted. Using the stimulus I ^u (t> T _e ), the predicted value of the rate {circumflex over (λ)} (t | ^ θ ^u , {t _j ^u }, I ^u (t))) is calculated. Then, the integral of the predicted rate

を計算する。ただし、式（１５）において、Ｔは刺激を与える予定の期間を表す。式（１４）同様、式（１５）の積分値Ｚは刺激接触によって引き起こされる行動の回数の期待値である。そして、下記の式（１６）に示すように、この期待値Ｚを最大化するような刺激Ｉ^ｕ _{ｏｐｔｉｍａｌ}（ｔ＞Ｔ_ｅ）を求めることで刺激接触の最適化が実現される。

Calculate However, in Formula (15), T represents the period which gives a stimulus. Similar to equation (14), the integral value Z in equation (15) is the expected value of the number of actions caused by the stimulation contact. Then, as shown in the following equation (16), the stimulation contact is optimized by _{obtaining the} stimulation I ^u _optimal (t> T _e ) that maximizes the expected value Z.

ステップ１０１での例１、例２の場合における結果例を図７に示す。ユーザに２０回の刺激をある期間内に接触させる場合を想定すると、接触の間隔を疎に取りすぎても（図７Ａ）、密に取り過ぎても（図７Ｂ）、積分値Ｚ（図７Ａ〜Ｂの最上部の影部分の面積、矢印部分）は増えず、始めは密にその後ほど良い密度で接触させる時に積分値Ｚが最大になることが分かる（図７Ｃ矢印部分）。

FIG. 7 shows a result example in the case of Example 1 and Example 2 in Step 101. Assuming that the user is contacted with 20 stimuli within a certain period, even if the contact interval is too small (FIG. 7A) or too dense (FIG. 7B), the integrated value Z (FIG. 7A) It can be seen that the integrated value Z is maximized when contact is made densely at a good density at the beginning afterwards (the area of the shadow portion at the top of ~ B, the arrow portion).

  The output unit 203 of the stimulation contact effect optimization unit 200 outputs the optimized stimulation contact 50 for each user. An output example in the case of Example 1 and Example 2 in Step 101 is shown in FIG. The example shown here is an example when the number of stimulation contacts is 10. However, “optimum stimulation contact” in FIG. 8 represents the optimal stimulation contact time. For example, it can be seen that it is optimal for the user 1 to give a stimulus 0.1, 0.2, 0.3,... The stimulus contact effect Z represents an expected value of the number of actions that the user who has received the optimum stimulus takes.

  As described above, the stimulus optimization processing unit 202 calculates the predicted value of the action probability (rate) based on the stimulus data, the action data, the action probability function, and the parameters estimated by the stimulus contact effect estimation unit 100. And calculating the timing of the external stimulus that maximizes the expected value of the number of actions of each individual caused by the external stimulus by calculating the timing of the external stimulus that maximizes the integrated value of the predicted value of the action probability Means.

  In addition, although the example of the purchase action with respect to an advertisement stimulus was demonstrated as an example of application of this invention, this is only an example. The present invention is an individual behavior other than purchasing behavior, such as determining food and drink by advertisement, telling the market of finance (stocks, trust investment and foreign currency), making a trading transaction, and evacuating by warning in the event of a disaster, etc. Anything can be applied to various situations as long as it stimulates (user) and causes an action.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims.

DESCRIPTION OF SYMBOLS 100 Stimulus contact effect estimation part 101 Input part 102 Whole parameter estimation part 103 Stimulus contact effect parameter estimation part 104 Output part 200 Stimulus contact effect optimization part 201 Input part 202 Stimulus optimization process part 203 Output part 300 Stimulus contact effect management apparatus

Claims (8)

An individual behavior model estimation device that estimates an individual behavior model for an external stimulus,
Input means for inputting, as input data, stimulus data that is time-series data of external stimuli that cause the individual to behave, and action data that is time-series data of the action event of the individual;
Based on the function indicating the forgetting property of the stimulating contact effect and the function indicating the threshold property and decreasing property of the stimulating contact effect, an action probability function indicating the probability that the individual takes action per unit time is defined. Parameter estimation means for estimating a parameter of an action probability function,
The parameter estimation means determines the parameter based on the behavior probability function, the probability distribution of the parameter, and the input data so that the marginal likelihood related to the inter-individual distribution of the parameter is maximized. An individual behavior model estimation device. The function indicating the forgetting property includes a strength of a stimulation contact effect, and the strength decreases as a result of contact with the stimulus, and increases with time when there is no contact. 2. The individual behavior model estimation apparatus according to 1. 2. The function according to claim 1, wherein the behavior probability function is a function obtained by applying an output of a convolution function of a length of contact time with an external stimulus and a forgetting property to a function representing a threshold property and a decreasing property. Individual behavior model estimation device. A function representing the influence from the past behavior history of the individual was added to the function obtained based on the function indicating the forgetting property of the stimulation contact effect and the function indicating the threshold property and the decreasing property of the stimulation contact effect. The function is used as the behavior probability function. The individual behavior model estimation device according to claim 1, wherein: 5. A means for calculating a predicted value of an action probability based on the stimulus data according to claim 1, the action data, the action probability function, and the parameter estimated by the parameter estimation means. When,
Means for calculating the timing of an external stimulus that maximizes the expected value of the number of actions of each individual caused by the external stimulus by calculating the timing of the external stimulus that maximizes the integral value of the predicted value of the action probability; An external stimulus timing optimization device comprising: A purchase behavior model estimation device that estimates an individual purchase behavior model for advertising stimulation,
Input means for inputting, as input data, stimulus data that is time-series data of advertising stimuli that cause the individual to make a purchase behavior, and purchase behavior data that is time-series data of the purchase behavior event of the individual, and forgetting the stimulus contact effect Based on the function indicating sex and the function indicating the threshold value and decreasing property of the stimulation contact effect, an action probability function indicating the probability that the individual takes a purchase action per unit time is determined. Parameter estimation means for estimating parameters,
The parameter estimation means determines the parameter based on the behavior probability function, the probability distribution of the parameter, and the input data so that the marginal likelihood related to the inter-individual distribution of the parameter is maximized. Purchasing behavior model estimation device. An individual behavior model estimation method executed by an individual behavior model estimation device that estimates an individual behavior model with respect to an external stimulus,
An input step for inputting stimulus data, which is time-series data of external stimuli that cause the individual to behave, and action data, which is time-series data of behavior events of the individual, as input data, and shows forgetability of the stimulus contact effect Based on the function and the function indicating the threshold value and the decreasing property of the stimulus contact effect, an action probability function indicating the probability that the individual takes action per unit time is determined, and the parameter of the action probability function is estimated. A parameter estimation step,
In the parameter estimation step, the individual behavior model estimation device is configured so that, based on the behavior probability function, the probability distribution of the parameter, and the input data, the marginal likelihood related to the inter-individual distribution of the parameter is maximized. An individual behavior model estimation method characterized by determining a parameter. A program for causing a computer to function as each unit of the individual behavior modeling device according to any one of claims 1 to 4 and each unit of the external stimulus timing optimization device according to claim 5.

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