JP6558860B2 - Estimation device, prediction device, method, and program - Google Patents

Description

  The present invention relates to an estimation device, a prediction device, a method, and a program.

  As a conventional technique, there is a technique using a topic model (Non-Patent Document 1). In the topic model, a finite characteristic behavior pattern is extracted from the behavior history data of an individual group, and the behavior of each individual is expressed by a combination of the characteristic behavior patterns and prediction is performed. More specifically, the process in which an individual selects an action from a plurality of options is modeled stochastically with a multinomial distribution, and the selection behavior of each individual is expressed as a linear sum of a finite multinomial distribution. The parameter value and the weight coefficient of the linear sum of each individual are estimated from the behavior history data of the individual group. The prediction of the behavior of each individual is executed based on the linear sum of the estimated multinomial distributions. Further, since the weighting factor estimated for each individual is a numerical value of the behavior pattern or behavior tendency of each individual, the individual can be classified or segmented based on the weighting factor.

  In addition, there is a technique that allows an individual's selection behavior to depend on the previous selection (Non-patent Document 2). In this case, the process in which an individual selects an action from a plurality of options is expressed by a conditional multinomial distribution.

T. Iwata et al., “Topic Tracking Model for Analyzing Consumer Purchase Behavior”, IJCAI, pp.1427-1432, 2009. H. M. Wallach, “Topic modeling: beyond bag-of-words”, Proceedings of the 23rd international conference on Machine learning, pp.977-984, 2006.

  In the prior art (Non-Patent Documents 1 and 2), the prediction of the individual's selection behavior is prediction of only the content of selection, and the selection timing is outside the target of prediction. In the behavior history data of an individual, only the history of options taken by the individual in the past is used, and the history of the timing or time when the selected behavior occurs is not used. Here, the timing means an elapsed time from the immediately preceding selection action. At this time, the following problems occur.

(1) The timing at which each individual performs a selection action cannot be predicted.

(2) As a result of (1), the content recommended or navigated for each individual cannot be changed depending on the timing. For example, in the next purchase, the probability of purchasing T-shirts and socks is 0.6 and 0.4 respectively, and this customer actually purchased T-shirts yesterday, and this customer purchased T-shirts for two consecutive days. If the probability of purchase is very low, it is considered that the product to be recommended today is not a T-shirt but a sock, but in the prior art, a T-shirt is selected regardless of timing.

(3) It is not possible to extract the behavior pattern characteristics in consideration of the both sides of the content and timing of the selected behavior from the behavior history data of the individual group.

  The present invention has been made to solve the above-described problems, and provides an estimation device, method, and program capable of estimating parameters for accurately predicting the selection content and selection timing of an individual. For the purpose.

  It is another object of the present invention to provide a prediction apparatus, method, and program capable of accurately predicting the selection content and selection timing of an individual.

  In order to achieve the above object, the estimation device according to the first aspect of the present invention provides a selection that represents a selection content of the selection behavior of the individual and a selection timing that is an interval from the previous selection behavior, which are observed in a plurality of individuals. A set of action data as an input, and for each selected action data included in the set of selected action data, a conditional multinomial distribution representing the probability of selection content with respect to each topic for each topic, and the topic as a condition The topic to which the selected action data belongs is calculated according to the selection content and the simultaneous probability distribution of the selection timing, with the topic as a condition, for each topic, expressed using the probability density distribution of the selected timing, A topic representing the weight for each individual and each topic based on the calculation result of the topic for each selected behavior data A topic estimation unit that repeatedly updates a hyper parameter that represents a distribution of a rate and a hyper parameter that represents a distribution of a topic distribution parameter that characterizes the selection content and the selection timing in the topic, and is updated by the topic estimation unit Hyperparameters representing the distribution of the topic distribution parameters and the posterior probabilities of the topic distribution parameters based on the calculation results of the topics for each selection behavior data obtained for each iteration. A topic distribution parameter estimator for estimating a parameter, a hyperparameter representing the distribution of the topic ratio updated by the topic estimator, and a calculation result of the topic for each selection behavior data obtained for each iteration. Z According posterior probability of the topic proportions, for each individual, and is configured to include a topic proportions estimator for estimating the topic proportions.

  In addition, the estimation method according to the second aspect of the present invention is directed to a selection behavior in which the topic estimation unit indicates a selection content of the selection behavior of the individual and a selection timing that is an interval from the previous selection behavior, observed by a plurality of individuals. With a set of data as input, for each selected action data included in the set of selected action data, a conditional multinomial distribution representing the probability of selection content on the topic for each topic, and the topic as a condition The topic to which the selected behavior data belongs is calculated according to the selection content and the simultaneous probability distribution of the selection timing, with the topic as a condition, for each topic, expressed using the probability density distribution of the selection timing, A topic ratio representing the weight for each individual and each topic based on the calculation result of the topic for the selected behavior data Repeatedly updating the hyperparameter representing the distribution of the topic and the hyperparameter representing the distribution of the parameter of the topic distribution that characterizes the selection content and the selection timing in the topic, and the topic distribution parameter estimation unit includes the topic estimation unit The topic according to the posterior probabilities of the parameter of the topic distribution based on the hyperparameter representing the distribution of the parameter of the topic distribution updated by the method and the calculation result of the topic for each selection behavior data obtained for each iteration. The parameter of the distribution is estimated, and the topic ratio estimation unit is a hyperparameter representing the distribution of the topic ratio updated by the topic estimation unit, and the calculation result of the topic for each selection behavior data obtained for each iteration In Brute according posterior probability of the topic proportions, for each individual, estimates the topic proportions.

  Further, in the estimation device according to the first invention and the estimation method according to the second invention, the probability density distribution of the selection timing with the topic as a condition is such that the selection timing is generated independently of the selection content. It may be determined as follows.

  In the estimation apparatus according to the first invention and the estimation method according to the second invention, the probability density distribution of the selection timing on the condition of the topic is generated depending on the selection content immediately before the selection timing. It may be determined to be as follows.

  Further, in the estimation device according to the first invention and the estimation method according to the second invention, the probability density distribution of the selection timing based on the topic is generated depending on the selection content immediately after the selection timing. It may be determined to be as follows.

  A prediction device according to a third aspect of the invention is a prediction device that predicts a selection behavior of an individual to be predicted, a topic ratio that represents a weight for each topic, which is obtained in advance for the individual to be predicted. The topic for each topic based on a topic distribution parameter that characterizes the selection content of the individual's selection behavior and a selection timing that is an interval from the individual's previous selection behavior in the topic determined in advance. A conditional multinomial distribution that represents the probability of selection content as a condition, and a probability density distribution at the selection timing that is conditional on the topic. The selection of the individual to be predicted according to the selection content of the selection action and the simultaneous probability distribution of the selection timing It includes prediction unit for predicting at least one of volume and the selected timing is constructed.

  A prediction method according to a fourth aspect of the invention is a prediction method for predicting a selection behavior of an individual to be predicted, in which a prediction unit represents a weight for each topic, which is obtained in advance for the individual to be predicted. For each topic, based on the ratio and the topic distribution parameters characterizing the selection timing of the individual's selection behavior and the interval from the previous selection behavior of the individual in the topic determined in advance A conditional multinomial distribution representing the probability of selection content subject to a topic, and a probability density distribution of the selection timing, conditional on the topic, for each topic, subject to the topic, According to the selection content of the selection action of the individual, and the simultaneous probability distribution of the selection timing, for the individual to be predicted, Predicting at least one of-option content and the selected timing.

  A program according to a fifth aspect of the invention is a program for causing a computer to function as each unit constituting the estimation device or the prediction device.

  According to the estimation apparatus, method, and program of the present invention, for each selected action data, a conditional multinomial distribution representing the probability of selection content on the topic for each topic, and the probability of selection timing on the topic The topic to which the selected action data belongs is calculated according to the simultaneous probability distribution of the selection contents and the selection timing represented by the density distribution, and the distribution of the topic ratio is calculated based on the calculation result of the topic for each selected action data. The hyperparameter representing the distribution of the topic parameter and the hyperparameter representing the distribution of the parameter of the topic distribution, and the hyperparameter representing the parameter distribution of the updated topic distribution and each selection behavior data obtained for each iteration. Topic distribution parameters based on topic calculation results Estimating topic distribution parameters according to posterior probabilities, posterior probabilities of topic ratios based on hyperparameters representing updated topic ratio distributions, and topic calculation results for each selected behavior data obtained for each iteration Thus, by estimating the topic ratio for each individual, it is possible to estimate the parameters for accurately predicting the selection content and selection timing of the individual.

  Further, according to the prediction apparatus, method, and program of the present invention, based on the topic ratio and the topic distribution parameter representing the weight for each topic, which are obtained in advance for the individual to be predicted, for each topic, Individual selection behavior for each topic, expressed using a conditional multinomial distribution that represents the probability of selection content on the condition of the topic, and a probability density distribution of the selection timing on the topic. According to the simultaneous probability distribution of the selection content and the selection timing, it is possible to accurately predict the selection content and the selection timing of the individual by predicting at least one of the selection content and the selection timing for the individual to be predicted. An effect is obtained.

It is explanatory drawing for demonstrating the outline | summary of embodiment of this invention. It is a block diagram which shows the structure of the estimation apparatus which concerns on embodiment of this invention. It is a figure showing the graphical model of the model type I of embodiment of this invention. It is a figure showing the graphical model of model type II of embodiment of this invention. It is a figure showing the graphical model of model type III of embodiment of this invention. It is a figure showing the graphical model of model type IV of embodiment of this invention. It is a block diagram which shows the structure of the prediction apparatus which concerns on embodiment of this invention. It is a flowchart which shows the estimation process routine in the estimation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the prediction process routine in the prediction apparatus which concerns on embodiment of this invention.

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

<Outline according to Embodiment of the Present Invention>

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

  In the embodiment of the present invention, in the topic model, the feature of the behavior pattern is defined by two pieces of information, that is, the content and timing of the selected behavior of the individual. The behavior of each individual is expressed by a characteristic behavior pattern, that is, a combination of “what to select” and “when to select”, and prediction is performed.

  In this embodiment, a human behavior pattern is described by a mathematical model, each user's behavior pattern is learned from each user's behavior history data, and the future behavior of each user is predicted based on the learned mathematical model. . For example, when this embodiment is applied to a theme park visitor, the behavior pattern of each visitor is learned from the behavior history data, and the behavior of each visitor after entering the park is predicted.

  Then, based on the obtained prediction result, navigation suitable for each user's behavior pattern (including hobbies and preferences) is performed. In the theme park, navigation suitable for each visitor's behavior pattern (including hobbies and preferences) is performed through a smartphone or the like based on the prediction result.

  Since each user's action history data is small (in many cases), the model of each user cannot be learned correctly. For example, since there is little or no action history data for each visitor in the theme park (when no data is stored as a member), the action pattern of each visitor cannot be learned correctly and cannot be predicted.

  Therefore, in the present embodiment, the action pattern of each user is expressed in a low dimension using a topic model. Finding some kind of commonality in the user's pattern can compensate for the lack of data (the principle is almost the same as NMTF: Nonnegative Multiple Tensor Factorization). For example, in the case of a theme park, 10 types of behavior patterns that are seen by visitors are extracted using a topic model. Then, by identifying which behavior pattern each visitor applies to, the behavior pattern of each visitor can be predicted and appropriate navigation can be performed.

  In the prior art, the timing of an individual's action has not been considered so far. Therefore, in this embodiment, the “content” and “timing” of the user's selection action are predicted simultaneously, and the navigation content and timing are determined based on the prediction result. In the present embodiment, the user is expressed in a low-dimensional manner using the topic model.

  In the conventional topic model, the user's next action content can be predicted by the multinomial distribution, but the timing at which the action occurs (= elapsed time from the immediately preceding action occurrence time) cannot be predicted. Therefore, (i) the timing for transmitting information cannot be determined, and (ii) the content of information transmitted according to the timing cannot be changed.

  Therefore, in the present embodiment, the elapsed time from the action occurrence time immediately before the user is expressed by a probability density function. FIG. 1 is a diagram for explaining the present embodiment. In the present embodiment, for example, as shown in FIG. 1, the user's behavior is modeled based on the transition matrix of the user's selection contents (A, B, C) and the change over time of the selection contents. Further, by using a marginal exponential distribution family for the probability density function, the ease of implementation and the calculation cost equivalent to those of the conventional topic model are realized.

  More specifically, the process in which an individual chooses one of the options is a conditional multinomial distribution (or simply a multinomial distribution if the selection action is not affected by the previous selection action), and the selection action is The elapsed time from the immediately preceding selected action at the time of occurrence is modeled by a probability density distribution, and the characteristics of the action pattern are expressed by the parameters of the simultaneous distribution of the conditional multinomial distribution and the probability density distribution. The selection behavior of each individual, that is, when to select what is expressed by a linear sum of a finite number of simultaneous distributions, and the parameter value and the weight coefficient of the linear sum of each individual are estimated from the behavior history data of the individual group. The present embodiment solves three problems in the prior art.

  The embodiment of the present invention predicts the behavior that an individual will select in the future when at least two or more behavior options are given. According to the present embodiment, it is possible to predict what action an individual will take in the future, and based on the prediction result, appropriately select content recommended for the individual or content for navigating the individual. Can do. Moreover, it is possible to classify individual groups by analyzing how individual individuals tend to select. Table 1 shows examples of individuals, action types, and options. Table 2 shows an example of recommendation / navigation for an individual. However, individuals, types of actions and options are not limited to the following.

  In the embodiment of the present invention, an example will be described in which the present invention is applied to an estimation device that estimates each parameter from a set of selection behavior data of each individual and a prediction device. Specifically, first, in the estimation device, parameters representing characteristic behavior patterns and behavior trends of each individual are estimated from the data, and the simultaneous probability distribution of the selection contents and selection timing of each individual is determined. In the next prediction device, a selection behavior to be observed in the future is predicted based on the estimated joint probability distribution for each individual. Details of each device will be described below.

<Configuration of estimation apparatus according to embodiment of the present invention>

  Next, the configuration of the estimation apparatus according to the embodiment of the present invention will be described. As shown in FIG. 2, the estimation apparatus 100 according to the embodiment of the present invention is a computer that includes a CPU, a RAM, and a ROM that stores a program and various data for executing an estimation processing routine described later. Can be configured. Functionally, the estimation apparatus 100 includes an input unit 10, a calculation unit 20, and an output unit 40 as shown in FIG.

  The input unit 10 accepts input of a selection content of a selection action of the individual observed by a plurality of individuals and a set of selection action data representing a selection timing that is an interval from the previous selection action.

The selection behavior data is generated from an individual to be analyzed. The selection behavior data includes an individual ID (hereinafter referred to as u), a total number of individuals (hereinafter referred to as U), the number of selection behaviors observed in the individual u (hereinafter referred to as _Nu ), Subtracting the number of individuals from the total number of selection behavior data observed for all individuals (hereinafter referred to as N), a set of selection content data observed for all individuals ({y ^j } ≡ (y ¹ , y ² ,..., Y ^N )), a set of selection timing data observed in all individuals (represented as {t ^j } ≡ (t ¹ , t ² ,... T ^N )), and the individual that generated each selection action data A set of IDs (represented as {u _j } ≡ (u ₁ , u ₂ ,... U _N )).

However, the selection content data y ^j is composed of a pair (y ₁ ^j , y ₂ ^j ) of the selection content immediately before and immediately after, and the selection timing data t ^j represents the interval between the selection time immediately before and immediately after. In addition, the options are expressed by natural numbers starting from 1 (the number of options is expressed as _Nc ), and a pair of selection contents is expressed as (immediate purchase, immediate purchase). For example, considering purchase selection behavior by a consumer, when products ₁ , ₂ , ₃ , and ₁ are purchased at times s ₀ , s ₁ , s ₂ , and s ₃ , respectively, y ¹ = (1,2,), y ² = ^(2,3), a y 3 = (3, ^1), a _{^{t 1 = s 1 -s 0,}} t 2 = s 2 -s 1, t 3 = s 3 -s 2.

  In addition, the input unit 10 receives the number K of topics representing a characteristic behavior pattern of an individual as an input. Hereinafter, characteristic behavior patterns are referred to as topics. A topic is expressed by a simultaneous distribution of conditional multinomial distribution and probability density distribution (hereinafter referred to as topic distribution), and the parameters of the simultaneous distribution differ for each topic. Here, K topics are denoted by k = 1, 2, 3,..., K, respectively.

  Further, the input unit 10 receives input of the model type and the selection timing distribution. As will be described later, the model type has a selection timing determined independently of the selection content (type I), depends only on the immediately preceding selection content (type II), and depends only on the immediately following selection content (type) III) There are four types (type IV) that depend on both immediately before and after (type IV), and the selection timing distribution is specified from an arbitrary exponential distribution family. Examples of the exponential distribution family include a normal distribution, a log normal distribution, and a gamma distribution.

  Here, the principle of the generation model used in this embodiment will be described.

First, it is assumed that selection content and selection timing data are generated from each individual based on the following generation model. The individual u _{j that} has generated the j-th data (y ^j , t ^j ) is derived from the probability distribution p (y, t | {φ ^k }, {Υ ^k }) expressed by a linear sum of K topic distributions. Data (y ^j , t ^j ) is generated.

However, z _j is a latent variable representing the topic (1-K) to which the j-th data belongs,

Is the weight of the individual u _{j to} the topic k (represented as topic ratio), p (y ^j , t ^j | z _j = k, φ ^k , ^{ｋ k} ) is the topic distribution of topic k, ({φ ^k }, {Υ ^k }) is a topic distribution parameter (tensor parameter) that characterizes the topic. Here, the topic distribution is expressed by multiplication of the conditional multinomial distribution that generates the selection contents and the probability density distribution that generates the selection timing. In this embodiment, the definition of the probability density distribution that generates the selection timing is There are four ways to do this:

(1) Type I: Selection timing is generated independently of selection contents. Specifically, as shown in the following equation (2), the probability density distribution p (t ^j | z _j = k, Υ ^k ) of the selection timing on the condition of the topic indicates that the selection timing t ^j is the selection content y. ^j is generated independently.

(2) Type II: The selection timing depends only on the immediately preceding selection content y ₂ ^j−1 . Specifically, as shown in the following formula (3), the probability density distribution p (t ^j | y ₂ ^j−1 , z _j = k, Υ ^k ) of the selection timing on the condition of the topic is the selection timing. It is determined that t ^j is generated depending on the immediately preceding selection content y ₂ ^j−1 .

(3) Type III: The selection timing depends only on the immediately selected content y ₂ ^j . Specifically, as shown in the following formula (4), the probability density distribution p (t ^j | y ₂ ^j , z _j = k, ^{ｋ k} ) of the selection timing on the condition of the topic is the selection timing t ^j Is generated depending on the selection content y ₂ ^j immediately after.

(4) Type IV: The selection timing depends on the selection contents (y ₂ ^j−1 , y ₂ ^j ) both immediately before and after. Specifically, as shown in the following formula (5), the probability density distribution p (t ^j | y ₂ ^j−1 , y ₂ ^j , z _j = k, Υ ^k ) of the selection timing with the topic as a condition. Is determined such that the selection timing t ^j is generated depending on the selection contents (y ₂ ^j−1 , y ₂ ^j ) immediately before and after.

Where p (y ^j | z _j = k, φ ^k ) is a conditional multinomial distribution and φ ^k is a transition matrix

P (t ^j | z _j = k, Υ ^k ), p (t ^j | y ₂ ^j−1 , z _j = k, Υ ^k ), p (t ^j | y ₂ ^j , z _j = k , ^{Ｋ k} ) or p (t ^j | y ₂ ^j−1 , y ₂ ^j , z _j = k, Υ ^k ) is an arbitrary exponential family. Which model type and exponential distribution family is used is determined according to the model type and exponential distribution family received by the input unit 10.

Next, the topic ratio θ and the tensor parameters φ ^k and Υ ^k characterizing the topic appearing in the above formulas (1) to (5) are conjugate prior distributions p (θ | α) and p (φ ^k | β), respectively. , P (Υ ^k | γ), and the assigned topic z≡ (z ₁ , z ₂ ,... Z _N ) for each data point and observed as shown in the following equation (7): The simultaneous probability of the selection content y≡ (y ¹ , y ² ,... Y ^N ) and the selection timing t≡ (t ¹ , t ² ,... T ^N ) is obtained.

However, α, β, and γ in the above equation (7) are hyperparameters estimated from the data. For reference, the graphical models of each of the four model types are shown in FIGS. 3 to 6, θ _u represents the topic ratio of the individual u, and the index i represents the i-th generated data point in the selection behavior data of the individual u.

  The generation model in the present embodiment can be calculated by the above equations (1) to (5). The above is the principle of the generation model in the present embodiment.

  The calculation unit 20 includes a selection behavior data storage unit 22, a topic estimation unit 24, a topic distribution parameter estimation unit 26, a topic ratio estimation unit 28, a parameter storage unit 30, and a topic ratio storage unit 32. Has been.

  The selection behavior data storage unit 22 stores a set of selection behavior data received by the input unit 10.

The topic estimation unit 24 is a conditional multinomial distribution that represents the probability of selection content for each topic with respect to the topic k for each selection behavior data included in the set of selection behavior data stored in the selection behavior data storage unit 22. p (y ^j | z _j = k, φ ^k ) and a selection density y ^j and a topic k as a condition for each topic, expressed using a probability density distribution at a selection timing with the topic k as a condition. The topic k to which the selected action data belongs is calculated according to the joint probability distribution p (y ^j , t ^j | z _j = k, φ ^k ) at the selection timing t ^j . Further, the topic estimation unit 24, based on the calculation result of the topic k for each selected action data, the hyper parameter α representing the distribution of the topic ratio θ _u representing the weight for each individual u and each topic k, and the topic k The hyperparameters β and γ representing the distribution of topic distribution parameters φ ^k and Υ ^k that characterize the selection contents and selection timing are updated. The topic estimation unit 24 repeatedly performs the above topic calculation and hyperparameter update.

A specific calculation method performed by the topic estimation unit 24 will be described in detail below. The topic estimation unit 24 estimates the belonging topic z≡ (z ₁ , z ₂ ,... Z _N ) for each selected action data from the posterior probability. In the present embodiment, the topic estimation unit 24 estimates the affiliated topic based on the Gibbs sampling formula shown in the following formula (8), and P samples (z≡ (z ₁ , z ₂ ,... Z _N )) ( z ⁽¹⁾ , z ⁽²⁾ ,..., z ^(P) ).

However, -j appearing in the above equation (8) represents a subset obtained by excluding the jth data from the total number N of data sets. The topic k calculation results (z ⁽¹⁾ , z ⁽²⁾ ,..., Z ^(P) ) calculated by the topic estimation unit 24 for each selected action data are the topic distribution parameter estimation unit 26 described later. And stored in a memory (not shown) for processing in the topic ratio estimation unit 28.

Further, the topic estimation unit 24 generates P samples at the same time, and based on the probabilistic EM method (see, for example, Non-Patent Document 3), according to the following equation (9), the unknown hyperparameter α, Update the values of β and γ P times. Then, the topic estimation unit 24 sets the parameter values α ^(P) , β ^(P) , and γ ^(P) after updating P times as estimated values.

Non-Patent Document 3: C. Bishop. “Pattern Recognition and Machine Learning”, Springer, New York, 2006.

The topic distribution parameter estimation unit 26 performs hyperparameters β and γ representing the distribution of the parameters {φ ^k } and {Υ ^k } updated by the topic estimation unit 24, and each selection action data obtained for each iteration. Estimate topic distribution parameters {φ ^k }, {Υ ^k } according to the posterior probabilities of the topic distribution parameters based on the topic calculation results (z ⁽¹⁾ , z ⁽²⁾ ,..., Z ^(P) ). .

Specifically, the topic distribution parameter estimation unit 26 uses the following formula using β, γ, (z ⁽¹⁾ , z ⁽²⁾ ,..., Z ^(P) ) obtained by the topic estimation unit 24. According to (10) and (11), the topic distribution parameters {φ ^k }, {Υ ^k ) are estimated. In the present embodiment, the average of the posterior probabilities is adopted as the estimated value of the topic distribution parameter.

  However, k = 1, 2, 3,..., K, and the posterior probabilities are respectively given by the following formula (11).

The topic ratio estimation unit 28 calculates the hyperparameter α representing the distribution of the topic ratio updated by the topic estimation unit 24 and the topic calculation results (z ⁽¹⁾ , z ⁾ obtained for each selection behavior data obtained for each iteration. ^{(2), ...,} based on the ^{z (P)),} according to the posterior probability of the topic proportions, for each individual u, to estimate the topic ratio θ _u.

Specifically, the topic ratio estimation unit 28 uses the hyperparameter α obtained by the topic estimation unit 24 and the topic calculation results (z ⁽¹⁾ , z ⁽²⁾ ,..., Z ^(P) ), The topic ratio θ _u for each individual (u = 1, 2,..., U) is estimated according to the following equations (12) and (13). In the present embodiment, the average of the posterior probabilities is adopted as the estimated value of the topic ratio.

  However, the posterior probability is given by the following equation (13).

The parameter storage unit 30 stores topic distribution parameter values estimated by the topic distribution parameter estimation unit 26. Table 3 shows examples of topic distribution parameters. The example shown in Table 3 below is a case where the model type is type IV, the number of topics K = 2, the number of options N _c = 3, and the number of parameters of the selection timing distribution is 2.

  The topic ratio storage unit 32 stores the topic ratio value for each individual estimated by the topic ratio estimation unit 28. Table 4 shows an example of the topic ratio. The example shown in Table 4 below is a case where the number of topics K = 2.

  The output unit 40 outputs the topic distribution parameters stored in the parameter storage unit 30 and the topic ratios for each individual stored in the topic ratio storage unit 32 as a result.

<Configuration of prediction apparatus according to embodiment of the present invention>

  Next, the configuration of the prediction device according to the embodiment of the present invention will be described. As shown in FIG. 7, a prediction device 200 according to an embodiment of the present invention is a computer including a CPU, a RAM, and a ROM that stores a program for executing a prediction processing routine described later and various data. Can be configured. The prediction device 200 functionally includes an input unit 50, a calculation unit 60, and an output unit 70 as shown in FIG. The prediction device 200 predicts the selection behavior of the individual to be predicted.

  The input unit 50 includes a topic ratio representing a weight for each topic, which is estimated in advance by the estimation device 100 with respect to an individual to be predicted, and a topic distribution parameter that characterizes selection content and selection timing in a previously obtained topic. Accept.

  The calculation unit 60 includes a prediction unit 62.

Based on the topic ratio {θ _u } and the topic distribution parameters {φ ^k }, {Υ ^k } received by the input unit 50, the prediction unit 62 represents the probability of selection content on the topic as a condition for each topic. Selection of individual selection behavior by topic for each topic expressed using conditional multinomial distribution and probability density distribution of selection timing, which is the interval from the previous selection behavior, with topic as a condition According to the simultaneous probability distribution of the content and the selection timing, the selection content y ^* and the selection timing t ^* of the individual selection behavior for the individual to be predicted are predicted.

Specifically, the prediction unit 62 uses the topic distribution parameter values {φ ^k }, {Υ ^k } and the topic ratio {θ _u } estimated by the estimation apparatus 100, and past selection behavior data (y , T) is used to predict the next (future) selection action (y ^* , t ^* ) of the individual u (u = 1, 2,..., U).

The target of prediction is (a) selection content y ^* when selection timing t ^* is given, (b) selection timing t ^* when selection content y ^* is given, (c) selection content y ^* and selection timing t ^*. There are three types of both. The prediction unit 62 performs each estimation in the following procedure.

(A) When the selection content y ^* is predicted when the selection timing t ^* is given The prediction unit 62 uses the selection timing t ^* as a condition for each selection content y ^* according to the following equation (14). The probability distribution p (y ^* | t ^* ) of the selection content y ^* is calculated, and the top R selection content is selected at the probability level and set as the predicted value.

At this time, since the prediction result may vary depending on the timing t ^* , that is, the elapsed time from the immediately preceding selected action occurrence time, the content to be recommended or navigated can be changed depending on the timing. The number R can take a value from 1 to _Nc , and is arbitrarily determined by the user of the prediction device 200 according to the usage pattern.

(B) When predicting the selection timing t ^* when the selection content y ^* is given The prediction unit 62 selects each of the selection timings t ^{* based on} the selection content y ^* according to the following equation (15). The probability distribution p (t ^* | y ^* ) at timing t ^* is calculated, and the maximum value (mode) of p (t ^* | y ^* ) or the average value of t ^* is calculated as a predicted value.

  By selecting according to the above formula (15), the selected content

A prediction value of the selection timing is obtained for each time.

(C) When predicting both selections ^{y *} and the selected timing ^{t *} prediction unit 62, selection ^{y *} both for each combination of the selection timing ^{t *,} choice ^{y *} and the timing ^{t *} joint probability of The distribution p (t ^* , y ^* | {φ ^k }, {Υ ^k }) is calculated, and the maximum value (mode) of p (t ^* , y ^* | {φ ^k }, {Υ ^k }), or t ^* a calculated average value and maximum value of y ^*, and predicted values.

Then, the predicting unit 62 predicts the predicted value y ^* of the selected content calculated in (a), the predicted value t ^* of the selected timing calculated in (b), or the selected content calculated in (c). And the predicted value (t ^* , y ^* ) of the selection timing are output.

The output unit 70 outputs the predicted value y ^* of the selected content, the predicted value t ^{* of} the selected timing, or the predicted value (t ^* , y ^* ) of the selected content and the selected timing as a result.

<Operation of Estimation Device according to Embodiment of the Present Invention>

  Next, the operation of the estimation apparatus 100 according to the embodiment of the present invention will be described. When receiving the set of selected behavior data to which the individual ID of the individual is assigned, the number of topics K, the model type, and the selection timing distribution in the input unit 10, the estimation apparatus 100 executes an estimation processing routine shown in FIG. To do.

  First, in step S100, a set of selected action data received by the input unit 10, the number of topics K, a model type, and a selection timing distribution are acquired. A set of selected action data is stored in the selected action data storage unit 22.

  Next, in step S102, the topic estimation unit 24 sets initial values of α, β, and γ for each selection behavior data included in the set of selection behavior data stored in the selection behavior data storage unit 22 or the previous step S104. The topic k to which the selected action data belongs is calculated according to the above equation (8) based on α, β, and γ estimated in step (1).

In step S104, the topic estimation unit 24 calculates the distribution of the topic ratio θ _u representing the weight for each individual u and each topic k based on the calculation result of the topic k for each selection behavior data obtained in step S102. The hyperparameters α and the hyperparameters β and γ representing the distribution of topic distribution parameters φ ^k and Υ ^k that characterize the selection content and selection timing in the topic ^k are updated according to the above equation (9).

  In step S106, it is determined whether the process of steps S102 to S104 has been repeated P times. If the process has not been repeated a predetermined number of times, the process returns to step S102 and the processes of steps S102 to S104 are repeated. If it has been repeated a number of times, the process proceeds to step S108.

In step S108, the topic distribution parameter estimation unit 26 calculates the hyperparameters β and γ updated in step S104 and the topic calculation result for each selected behavior data calculated in step S102 obtained for each iteration. Based on (z ⁽¹⁾ , z ⁽²⁾ ,..., Z ^(P) ), the topic distribution parameters φ ^k and Υ ^k are estimated according to the posterior probabilities of the topic distribution parameters shown in the above equation (11). The topic distribution parameter estimation unit 26 stores the topic distribution parameters φ ^k and Υ ^k in the parameter storage unit 30.

In step S110, the topic ratio estimation unit 28 performs the hyper parameter α representing the distribution of the topic ratio updated in step S104 and the topic for each selected behavior data calculated in step S102 obtained for each iteration. The topic ratio θ _u is estimated for each individual according to the posterior probabilities of the topic ratio shown in the above equation (13) based on the calculation results (z ⁽¹⁾ , z ⁽²⁾ ,..., Z ^(P) ). The topic ratio estimation unit 28 stores the topic ratio θ _u for each individual in the topic ratio storage unit 32.

  In step S112, the output unit 40 outputs the topic distribution parameter stored in the parameter storage unit 30 and the topic ratio for each individual stored in the topic ratio storage unit 32 as a result, and ends the estimation processing routine. To do.

<Operation of Prediction Device according to Embodiment of the Present Invention>

Next, the operation of the prediction device 200 according to the embodiment of the present invention will be described. When the input unit 50 receives the topic ratio θ _u estimated by the estimation device 100 for the individual u to be predicted and the topic distribution parameters φ ^k and Υ ^k , the prediction device 200 performs the prediction processing routine shown in FIG. Execute.

In step S200, the topic ratio θ _u and the topic distribution parameters φ ^k and Υ ^k are acquired.

In step S202, when the selection content y ^* is predicted when the selection timing t ^* is given, the prediction unit 62 determines the topic ratio θ _u received by the input unit 50 and the topic distribution parameters φ ^k and Υ ^k . Based on the above, the probability distribution p (y ^* | t ^* ) of the selection content y ^* is calculated according to the above equation (14) with the selection timing t ^* as a condition. Select and use as predicted value.
When predicting the selection timing t ^* when the selection content y ^* is given, the prediction unit 62 uses the topic ratio θ _u received by the input unit 50 and the topic distribution parameters (φ ^k , ^{ｋ k} ). Based on the above, the probability distribution p (t ^* | y ^* ) of the selection timing t ^* on the condition of the selection content y ^* is calculated according to the above equation (15), and the maximum value of p (t ^* | y ^* ) Mode) or an average value of t ^* is calculated as a predicted value.
Further, in the case of predicting both selections ^{y *} as selection timing ^{t *,} the prediction unit 62, selection ^{y *} and the timing ^{t *} joint probability distribution ^{p (t *, y * |} {φ k}, {Υ ^k }) and calculate the maximum value (mode) of p (t ^* , y ^* | {φ ^k }, {Υ ^k }), or the average value of t ^* and the maximum value of y ^* , Estimated value.

In step S204, the output unit 70 calculates the predicted value y ^* of the selection content, the predicted value t ^{* of} the selection timing, or the predicted value of the selection content and the selection timing (t ^* , y) obtained in step S202. ^* ) Is output as a result, and the prediction processing routine is terminated.

  As described above, according to the estimation apparatus according to the present embodiment, for each selected action data, a conditional multinomial distribution that represents the probability of selection content on a topic for each topic, and a topic on a condition The topic to which the selected behavior data belongs is calculated according to the selection content and the simultaneous probability distribution of the selection timing expressed using the probability density distribution of the selection timing, and the topic is calculated based on the calculation result of the topic for each selected behavior data. Repeating the update of the hyperparameter representing the distribution of the ratio and the hyperparameter representing the distribution of the parameter of the topic distribution, the hyperparameter representing the parameter distribution of the updated topic distribution, and each selection obtained at each iteration The topic distribution parameters based on the topic calculation results for behavioral data. Estimate the topic distribution parameters according to the posterior probability of the meter, and update the topic ratios based on the hyperparameters that represent the updated topic ratio distribution and the topic calculation results for each selected behavior data obtained for each iteration. By estimating the topic ratio for each individual according to the posterior probability, it is possible to estimate parameters for accurately predicting the selection content and selection timing of the individual.

  Further, according to the prediction device according to the present embodiment, the topic for each topic is calculated based on the topic ratio and the parameter of the topic distribution representing the weight for each topic, which is obtained in advance for the individual to be predicted. Selection of individual selection behavior based on topic for each topic, expressed using conditional multinomial distribution representing the probability of selection content as a condition, and probability density distribution of selection timing based on topic By predicting the selection content and the selection timing for the individual to be predicted according to the simultaneous probability distribution of the content and the selection timing, it is possible to accurately predict the selection content and the selection timing of the individual.

  The present invention is not limited to the above-described embodiment, and various modifications and applications can be made without departing from the gist of the present invention.

  For example, in the prediction device according to the above-described embodiment, the case where the selection content and the selection timing of an individual are predicted has been described as an example. However, the present invention is not limited to this, and either the selection content or the selection timing is predicted. May be.

  Moreover, although the above-mentioned estimation apparatus 100 demonstrated the case where the selection action data storage part 22, the parameter storage part 30, and the topic ratio storage part 32 were provided, for example, the selection action data storage part 22, the parameter storage part 30, And at least one of the topic ratio storage unit 32 is provided in an external device of the estimation device 100, and the estimation device 100 communicates with the external device using a communication unit, whereby the selection behavior data storage unit 22, the parameter storage unit 30, Also, at least one of the topic ratio storage unit 32 may be referred to.

  Moreover, although the case where the estimation apparatus 100 and the prediction apparatus 200 are configured as separate apparatuses has been described as an example in the above embodiment, the estimation apparatus 100 and the prediction apparatus 200 may be configured as one apparatus.

  In addition, the estimation device and the prediction device described above have a computer system inside, but the “computer system” includes a homepage provision environment (or display environment) if a WWW system is used. 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 10,50 Input part 20,60 Operation part 22 Selection action data storage part 24 Topic estimation part 26 Topic distribution parameter estimation part 28 Topic ratio estimation part 30 Parameter storage part 32 Topic ratio storage part 40,70 Output part 62 Prediction part 100 Estimation Device 200 prediction device

Claims (8)

Each set included in the set of selected behavior data is input with a set of selection behavior data that represents the selection content of the selection behavior of the individual and a selection timing that is an interval from the previous selection behavior, observed in a plurality of individuals. For the selected behavior data, for each topic, expressed using a conditional multinomial distribution representing the probability of selection content with each topic as a condition for each topic, and a probability density distribution of selection timing with the topic as a condition, The topic to which the selected action data belongs is calculated according to the simultaneous probability distribution of the selection contents and the selection timing, with the topic as a condition,
Based on the calculation result of the topic for each selection behavior data, a hyper parameter representing a distribution of topic ratios representing weights for each individual and each topic, and a topic distribution characterizing the selection content and the selection timing in the topic A topic estimator that repeats updating hyperparameters representing the distribution of parameters;
A posterior probability of the parameter of the topic distribution based on the hyper parameter representing the distribution of the parameter of the topic distribution updated by the topic estimation unit and the calculation result of the topic for each selection behavior data obtained for each iteration A topic distribution parameter estimation unit for estimating a parameter of the topic distribution according to
Each individual according to the posterior probability of the topic ratio based on the hyperparameter representing the distribution of the topic ratio updated by the topic estimation unit and the calculation result of the topic for each selection behavior data obtained for each iteration. A topic ratio estimation unit for estimating the topic ratio;
Including the estimation device. The estimation apparatus according to claim 1, wherein the probability density distribution of the selection timing with the topic as a condition is determined such that the selection timing is generated independently of the selection content. The estimation apparatus according to claim 1, wherein the probability density distribution of the selection timing with the topic as a condition is determined such that the selection timing is generated depending on the selection content immediately before. The estimation apparatus according to claim 1, wherein the probability density distribution of the selection timing with the topic as a condition is determined so as to be generated depending on the selection content immediately after the selection timing. A prediction device for predicting the selection behavior of an individual to be predicted,
The topic ratio that represents the weight for each topic, obtained in advance for the individual to be predicted, the selection content of the individual's selection behavior and the interval from the previous selection behavior of the individual in the topic obtained in advance And a conditional multinomial distribution representing the probability of selection content on the basis of the topic and a probability density of the selection timing on the topic based on a topic distribution parameter characterizing the selection timing. The selection content for the individual to be predicted according to the selection content of the selection behavior of the individual and the simultaneous probability distribution of the selection timing for each topic represented by the distribution according to the topic. A prediction device including a prediction unit that predicts at least one of the selection timings. The topic estimation unit receives as input a selection content of the selection behavior of the individual observed in a plurality of individuals and a selection behavior data representing a selection timing that is an interval from the previous selection behavior. Each selection behavior data included in the set is expressed by using a conditional multinomial distribution representing the probability of selection contents with the topic as a condition and a probability density distribution of selection timing with the topic as a condition for each topic. , For each topic, calculate the topic to which the selected behavior data belongs, according to the simultaneous probability distribution of the selection content and the selection timing, with the topic as a condition,
Based on the calculation result of the topic for each selection behavior data, a hyper parameter representing a distribution of topic ratios representing weights for each individual and each topic, and a topic distribution characterizing the selection content and the selection timing in the topic Repeatedly updating the hyperparameters representing the distribution of parameters,
The topic distribution parameter estimation unit is based on the hyperparameter representing the distribution of the topic distribution parameter updated by the topic estimation unit, and the calculation result of the topic for each selection behavior data obtained for each iteration, Estimating the topic distribution parameters according to the posterior probabilities of the topic distribution parameters;
The topic ratio estimator is a hyperparameter representing the distribution of the topic ratio updated by the topic estimator and the calculation result of the topic for each selected behavior data obtained for each iteration. An estimation method for estimating the topic ratio for each individual according to a posteriori probability. A prediction method for predicting the selection behavior of an individual to be predicted,
The prediction unit is obtained in advance for the individual to be predicted, the topic ratio representing the weight for each topic, the selection content of the individual selection behavior in the topic obtained in advance, and the previous selection of the individual Based on the topic distribution parameters that characterize the selection timing, which is the interval from the action, a conditional multinomial distribution that represents the probability of selection content on the topic for each topic, and the selection on the topic According to the selection content of the selection action of the individual, with the topic as a condition, and the simultaneous probability distribution of the selection timing for each topic, expressed using a probability density distribution of timing, A prediction method for predicting at least one of the selection content and the selection timing.   The program for functioning a computer as each part which comprises the estimation apparatus of any one of Claims 1-4, or the prediction apparatus of Claim 5.

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