JP4839358B2 - Purchase prediction method, purchase prediction apparatus, purchase prediction program, and recording medium - Google Patents

Description

  The present invention relates to a technique for predicting a subsequent purchase situation based on time-series purchase data for a plurality of products of a plurality of users.

  In recent years, with the development of online technology and database technology, a huge amount of purchase data can be collected every day. By predicting the subsequent purchase status based on the purchase data, it is possible to teach the recommended product to the user and analyze the purchase tendency.

As a conventional method for predicting a purchase situation, there is a method of extracting a purchase order pattern frequently appearing from purchase data and predicting based on the pattern (see Non-Patent Document 1). This method does not take into account purchase time information (month, date, etc.). There is also a method for predicting a purchase situation in consideration of purchase time information (Non-patent Document 2).
Tomoharu Iwata, Takeshi Yamada, Nobuyoshi Ueda, “Collaborative Filtering Using Purchase Order Efficiently”, IPSJ Transactions: Mathematical Modeling and Applications, Vol. 49, no. SIG4 (TOM20), p. 125-134, 2008 Tomoharu Iwata, Toshiyuki Tanaka, Takeshi Yamada, Nobuyoshi Ueda, “Model learning method for data with varying distributions”, Information theory learning theory workshop (IBIS2007), p. 170-175, 2007

  However, the technique of Non-Patent Document 1 has a problem in that it cannot cope with a change in fashion or a change in interest because purchase time information is not taken into consideration. Further, in the technique of Non-Patent Document 2, since it is necessary to read all data and perform calculation every time data is added, there is a problem that it is difficult to sequentially cope with a huge amount of data accumulated every day. is there.

  Therefore, the present invention has been made in view of the above problems, and it is an object to predict a purchase situation with a small amount of calculation while dealing with changes in purchase data over time in consideration of purchase time information. To do.

In order to solve the above-described problem, the present invention is based on purchase data in which purchase data for a plurality of products of a plurality of users is pre-collected in time series, and subsequent purchases for any product of any user. When predicting the probability of purchase, purchase prediction is performed using a probability model that divides multiple users into multiple classes and assumes that users belonging to the same class will purchase any product with the same probability. The class probability of a user, which is a device, having as parameters a purchase probability, a class probability set that is a set of probabilities belonging to each class for each user, and a class probability invariance indicating the degree to which the probability that the user belongs to a class does not change prior probability, each item of each class purchase probability set is a set of probability to be purchased by the user of the class, and, click With purchase probability not change degree indicating a degree that does not change probability of purchase items by a user belonging to the scan as a parameter, a storage unit for storing the prior probability, the purchase probability of class, the class probability immutabilization degree likelihood And the probability of purchase probability unchanged so that the likelihood of purchase probability unchanged is maximized, and the class probability unchanged and purchase probability unchanged are repeatedly calculated, and the calculated class probability unchanged and purchase probability unchanged are calculated. used, and the model estimation unit you update the class probability set and purchase probability set, using the updated class probability set and purchase probability set, and the purchase prediction unit that to calculate the probability that a user purchases the goods It is characterized by providing. Moreover, a purchase prediction method can also be executed using this purchase prediction apparatus.

According to the invention, the model estimator assuming that a plurality of users are divided into a plurality of classes class probabilities set and purchase probability set estimated (updated), purchased prediction unit within that class probabilities set and purchase probability set By predicting the purchase situation (probability of purchase) based on this, it is possible to predict the purchase situation with a small amount of calculation while responding to changes over time in purchase data in time series.

Further, in the present invention, the storage unit stores a class probability set , a user class probability prior probability, a purchase probability set , and a class purchase probability prior probability for a predetermined time before the latest time of purchase data. The class estimation unit has a class probability for a predetermined time so that the likelihood of the class probability unchanged for a predetermined time and the likelihood of the purchase probability unchanged for a predetermined time are maximized. The degree of change and the purchase probability unchanged degree for a predetermined time are repeatedly calculated, and the calculated class probability unchanged degree for the predetermined time and the purchase probability unchanged degree for the predetermined time are used. The class probability set for a predetermined time and the purchase probability set for a predetermined time are updated, and the purchase predicting unit uses the updated class probability set for the predetermined time and the purchase probability set for the predetermined time. There possible to calculate the probability to purchase goods Preferred.

  According to this invention, when the class probability set and the purchase probability set are not only for the latest time of the purchase data but also for a predetermined time before that, only when the latest time of the purchase data is Compared with this, the prediction accuracy can be increased.

  Moreover, this invention is a purchase prediction program for functioning a computer as each part of a purchase prediction apparatus. Thereby, the computer installed with this program can realize each function based on this program.

  The present invention is a computer-readable recording medium in which the purchase prediction program is recorded. Thereby, the computer equipped with this recording medium can realize each function based on the program recorded on this recording medium.

  According to the present invention, it is possible to predict a purchase situation with a small amount of calculation while dealing with changes in purchase data over time in consideration of purchase time information.

  Hereinafter, the best mode for carrying out the present invention (hereinafter referred to as “embodiment”) will be described in detail. Note that in this embodiment, the possibility of subsequent purchases for any product by any user is predicted based on purchase data in which purchase data for a plurality of products by a plurality of users is collected in time series. In this case, it is assumed that a plurality of users are divided into a plurality of classes, and a probability model that assumes that users belonging to the same class purchase arbitrary products with the same probability is used.

  In the following, expressions such as “prediction of purchase possibility”, “estimation (calculation) of purchase probability”, “prediction of purchase status”, and “prediction of interest” are synonymous. Furthermore, in each of the following mathematical formulas, a bold character (such as θ) indicates that it has a plurality of components. Also, these bold characters are not shown in bold in the text, but are assumed to be consistent with each mathematical expression.

  FIG. 1 is a block diagram showing the configuration of the interest prediction apparatus of this embodiment. As shown in FIG. 1, the interest prediction device 1 (purchase prediction device) includes a calculation means 2, an input means 3, a storage means 4, and an output means 5, which are connected to a bus line 11. ing.

  The calculation means 2 includes a model estimation unit 21, an interest prediction unit 22 (purchase prediction unit), and a memory 23. The calculation means 2 is composed of, for example, a CPU (Central Processing Unit) and a RAM (Random Access Memory), and the CPU reads the model estimation program 41 and the interest prediction program 42 from the storage means 4 and stores them in the memory 23 which is a RAM. And by executing, the model estimation part 21 and the interest prediction part 22 are each implement | achieved.

  The input means 3 includes a keyboard and a disk drive device. The input data is input by the administrator of the interest prediction device 1 via the input unit 3 and stored in the storage unit 4.

  The storage unit 4 includes a hard disk device and the like, and includes a program storage unit 40a and a data storage unit 40b. The program storage unit 40a stores a model estimation program 41 and an interest prediction program 42. The data storage unit 40b stores input data 43, a class set 44, a class probability set 45, a purchase probability set 46, a class probability invariance set 47, and a purchase probability invariance set 48.

  The input data 43 is purchase data in which purchase data for a plurality of products of a plurality of users is collected in advance in time series. The class set 44 is set data of a plurality of classes that divide a plurality of users in the input data 43.

  The class probability set 45 is a set of probabilities belonging to each class for each user. The purchase probability set 46 is a set of probabilities that each product is purchased by a user of the class for each class.

  The class probability invariance degree set 47 is a set to which the probability of belonging to each class for each user does not change. The purchase probability invariance degree set 48 is a set for each class to the extent that the probability that each product is purchased by a user of the class does not change.

  The output means 5 is, for example, a graphic board and a monitor connected to the graphic board, and displays the result of interest prediction.

  In the present embodiment, the probability P (i | u, t) that the user u purchases the product i at time t is estimated (calculated). That is, the probability P (i | u, t) represents the degree of interest in the product i at the time t of the user u. The time t is a discrete value, and an arbitrary period such as one day or one week can be used as a unit time.

  When estimating the probability P (i | u, t), if the total number of users is U and the total number of products is I, U (I-1) parameters are required at each time. In “U (I-1)”, “I-1” instead of “I” means that if “I-1” parameters are determined, the remaining one parameter is the parameter This is because it is automatically determined by subtracting the total value of “I−1” parameters from the total total value. Usually, U (I-1) is much larger than U and I and is difficult to estimate. Therefore, a class z that is a hidden variable is introduced to model the probability P (i | u, t) as shown in Equation (1).

If Z is the total number of classes, the total number of parameters at each time is U (Z-1) + Z (I-1). Since Z << U and Z << I, the total number of parameters is greatly increased. Can be reduced to a robust estimate. Here, P ( z | u , t) is a probability that the user u belongs to the class z at the time t, and P (i | z, t) is a probability that the product i is purchased at the class z at the time t. To express.

  P (z | u, t) and P (i | z, t) are expressed by the following formulas (2) and (3) in order to cope with changes in interest and popularity of products. It is assumed that the time evolves with a function F that takes the state one time ago as an argument.

For example, the time evolution can be estimated by a Kalman filter using a state space model. Further, φ _tuz = P (z | t, u) (= P (z | u, t)) and θ _tzi = P (i | z, t) are assumed, and the following time development is also conceivable.

Here, the prior probability of the class u φ _tu of the user u at time t is the class probability φ _t−1u of the user u one time before (“t−1u” means “(t−1) u”. The same applies to other variables) and the Dirichlet distribution as in the following expression (4) having the class u invariance α _tu of the user u as a parameter.

The average value E of this distribution coincides with the class probability one time ago (E (φ _tu | φ _t−1u , α _tu ) = φ _t−1u ),
The variance var is inversely proportional to α _tu +1 (var (φ _tuz | φ _t−1u , α _tu ) =
([ _{Phi] t-1uz} (1- [phi] _t-1uz )) / [alpha] _tu + 1).

Similarly, the prior probability of the purchase probability θ _tz of the class z at the time t similarly has the purchase probability θ _t−1z of the class z one time ago and the purchase probability unchanged degree β _tz of the class z as parameters as follows: It is assumed that the Dirichlet distribution is as in Expression (5). Note that Γ () is a gamma function.

<Model estimation unit>
The model estimation unit 21 will be described with reference to FIGS. 2 and 3. FIG. 2 is an explanatory diagram including a block diagram of a model estimation unit of the interest prediction apparatus of the present embodiment. As shown in FIG. 2, the model estimation unit 21 includes an input data reading unit 211, a parameter reading unit 212, an initialization unit 213, a class estimation unit 214, a class probability invariance estimation unit 215, and a purchase probability. A non-change degree estimation unit 216 and a parameter writing unit 217 are provided.

  FIG. 3 is a flowchart showing a process flow of the model estimation unit. First, in step S1, the input data reading unit 211 reads the input data 43, and the parameter reading unit 212 estimates using the data one hour before (the processing in steps S1 to S7 is performed). Read probability set 46. When there is no class probability set 45 and purchase probability set 46 one time ago, that is, when t = 0, the class probability and purchase probability are uniformly distributed.

  Next, in step S2, the initialization unit 213 initializes the class set 44, the class probability unchanged degree set 47, and the purchase probability unchanged degree set 48. For example, the class set 44 is initialized to be a random value, and the class probability invariance set 47 and the purchase probability invariance set 48 are all initialized to “1”.

  Next, calculation of the class set 44 by the class estimation unit 214 (step S3), calculation of the class probability invariance set 47 by the class probability invariance estimation unit 215 (step S4), and by the purchase probability invariance estimation unit 216 By repeating the calculation (step S5) of the purchase probability invariance set 48 (step S6 (determining whether or not the end condition is satisfied) → step S3), the class set 44, the class probability invariance set 47 and The likelihood that the current estimated value of the purchase probability unchanged set 48 can explain the input data 43 is maximized. For example, purchases of users who have the same interest in products (purchase data; the same applies hereinafter) belong to the same class, or purchases of products that are easily purchased by common users (users with the same class) belong to the same class. If it belongs, the likelihood is high. The likelihood calculation can be realized by using the input data 43, the class probability set 45 and the purchase probability set 46 one time before. For example, the following equation (6) can be used as the likelihood.

Here, x _tuj is a product purchased by user u at time t at _j time, and x _tu = {x _tuj } _j is a set of products purchased by user u at time t, X _t = {x _tu } _u is a set of purchased products of all users at time t. Also, φ _tuz = P (z | t, u) is the probability that user u at time t belongs to class z (see equation (4)), and φ _tu = {φ _tuz } _z is user u at time t. Φ _t = {φ _tu } _u is a set of class probabilities at time t, and θ _tzi = P (i | z, t) is a probability that a product i is purchased with class z at time t (formula ( 5), θ _tz = {θ _tzi } _i is a purchase probability of class z at time t, and Θ _t = {θ _tz } _z is a purchase probability set at time t. Also, α _t = {α _u } _u represents a class probability invariance set, and β _t = {β _z } _z represents a purchase probability invariance set.

In step S3, the class estimation unit 214 calculates which class each purchase m belongs to. The class calculation by the class estimator 214 is as follows: the number n _{tuk \} m that the purchase of the user u is class k at the time t excluding the purchase m, and the number of purchases n of the user u at the time t excluding the purchase m. take _tu\m, number _{n tik\m} purchasing of goods i at time t, except for the purchase m is a class k, the number _{n tk\m} purchase is a class k at time t, except for the purchase m, for example The following equation (7) based on Gibbs sampling is used. Here, Z _{t \ m} = {z _tn } _{n ≠ m} represents a class set at time t excluding purchase m.

In step S4, the class probability unchanged degree estimation unit 215 calculates the class probability unchanged degree α _tu of each user u so as to increase the likelihood. For example, α _tu with a high likelihood can be calculated by repeating the calculation of the following equation (8). Here, “←” represents substitution, and Ψ (•) represents a digamma function (the first derivative of the logarithm of the gamma function).

In step S5, the purchase probability unchanged degree estimation unit 216 calculates the purchase probability unchanged degree _βtz of each class z so that the likelihood becomes high. For example, β _tz having a high likelihood can be calculated by repeating the calculation of the following equation (9).

  As the repetition end condition (step S6), the class set 44, the class probability invariance set 47, and the purchase probability invariance set 48 converge, or the number of repetitions is more than a certain value. In the present embodiment, for example, the convergence is set as an end condition.

  After the end condition is satisfied (Yes in step S6), the parameter writing unit 217 stores the probability belonging to the class z of the user u at time t calculated by the following equation (10) in the class probability set 45, and The purchase probability of the product i of the class z at the time t calculated by the equation (11) is stored in the purchase probability set 46 (step S7).

<Interest Prediction Department>
The interest prediction unit 22 will be described with reference to FIG. FIG. 4 is an explanatory diagram including a block diagram of an interest prediction unit of the interest prediction apparatus of the present embodiment. As shown in FIG. 4, the interest prediction unit 22 includes a parameter reading unit 221, an interest calculation unit 222, and an interest output unit 223.

  In the interest prediction unit 22, first, the parameter reading unit 221 reads the latest class probability set 45 and purchase probability set 46 calculated by the model estimation unit 21. Next, the interest calculation unit 222 uses the class probability set 45 and the purchase probability set 46, based on the following equation (12), interest of the user u at the time t, that is, the user selects the product. Calculate the probability of buying.

  Finally, the interest output unit 223 outputs the predicted interest result to the output unit 5.

(Modification)
In the interest prediction device 1, as described above, not only the parameters one class before (class probability set 45 and purchase probability set 46) are used, but the parameters from L time to one time before (parameters for a predetermined time) are used. It can also be used to predict interest. In other words, φ _tu has the class probability φ _t−1u of user u before l (el) time and the class probability invariance α _tu of user u from before l (el) time as parameters (13 ).

Similarly, θ _tz has the following parameters as parameters: purchase probability θ _t−1u of class z before l (el) time and purchase probability unchanged degree β _tzl of class z from l (el) time before Suppose that it follows a Dirichlet distribution as in equation (14).

  By using parameters from time L to one hour before, it can be expected that model estimation is stabilized and prediction accuracy is increased as compared to the case of using only the parameters one time before. In this modified example, in the processing by the model estimation unit 21, Expression (7), Expression (8), Expression (9), Expression (10), and Expression (11) are changed into the following expressions (15), It changes into Formula (16), Formula (17), Formula (18), and Formula (19). In this modification, the content of the processing by the interest prediction unit 22 is not changed.

  Thus, according to the interest prediction apparatus 1 of the present embodiment, the model estimation unit 21 estimates the probability model on the assumption that a plurality of users are divided into a plurality of classes, and the interest prediction unit 22 is based on the probability model. By predicting the user's interest (subsequent purchase status (purchase probability)), the user's interest can be predicted with a small amount of calculation while responding to changes in the input data 43 (time-series purchase data) over time. be able to. In other words, this prediction can be used to teach recommended products suitable for each user, and to analyze purchasing trends such as which products are likely to be purchased by the same user and which products were popular when. Is possible.

  Further, since the class probability set 45 and the purchase probability set 46 consider not only the latest time of the input data 43 but also a predetermined time before that, the prediction accuracy can be increased.

  Furthermore, the likelihood model is estimated by calculating the likelihood (see Expression (6)) for the input data 43 expressed using the class probability set 45 and the purchase probability set 46, and maximizing the likelihood. The probability model and thus the accuracy of prediction can be increased.

  In addition, the interest prediction device 1 can be realized by causing a general computer to execute the above-described processing programs. This program can be provided through a communication line, or can be written and distributed on a recording medium such as a CD-ROM (Compact Disc-Read Only Memory).

  Although description of this embodiment is finished above, the aspect of the present invention is not limited to these. For example, the present invention can be applied to any probability model or likelihood calculation formula. In this embodiment, u is a user and i is a product. However, u and i may be arbitrary information as long as they are discrete variables that develop over time. For example, u is a document, i is a word, and it can be applied to modeling of time evolution of which word is likely to be used in each document. In addition, specific configurations such as hardware and flowcharts can be appropriately changed without departing from the spirit of the present invention.

  Next, an example of the interest prediction device 1 of the present embodiment will be described. In order to evaluate the interest prediction apparatus 1 of the present embodiment, a purchase data prediction experiment was performed. The unit time was 1 day. Using the data up to the previous day as learning data, we evaluated the correct answer rate of the problem of predicting the purchase of each user on each day.

  As purchase data, we used videos and logs from the online store for manga distribution. The video data is a log for 110 days from May 14, 2007 to August 31, 2007. The number of users is 70,122, the number of products is 7,469, and the total number of purchases is 11,243,935. It was. The comic data is a log for 151 days from January 1, 2006 to May 31, 2006. The number of users was 143,212, the number of products was 206, and the total number of purchases was 12,642,505. For each data, products with a purchase quantity of less than 10 were omitted. Also, for each data, new products are released every week.

  As comparative methods, Comparative Example 1 (LDAall), Comparative Example 2 (LDAonline), and Comparative Example 3 (LDAone) were used. LDA is a method in which the time evolution of the class probability set 45 and the purchase probability set 46 is removed from the processing contents of the interest prediction device 1 of the present embodiment. In Comparative Example 1 (LDAall), LDA is learned using all data from the log start date to the previous day, and in Comparative Example 2 (LDAonline), LDA is learned using the class set estimated from the previous day's data and previous data. In Comparative Example 3 (LDAone), LDA is learned using only the previous day's data.

  FIG. 5 is a graph showing the three best answer rates per day for (a) a moving image and (b) a comic, where the vertical axis shows the correct answer rate (%) and the horizontal axis shows the day. The 3-best correct answer rate is a ratio (%) when any of the top three correct answer candidates obtained by prediction is actually correct. In addition, Example 1 (OurMethod 7) shows a prediction result by the interest prediction device 1 when parameters from 7 days ago to the previous day are used, and Example 2 (OurMethod 1) shows a case where only the parameters of the previous day are used. The prediction result by the interest prediction apparatus 1 is shown.

  In FIG. 5A, it can be seen that the 3 best correct answer rates of Example 1 (OurMethod 7) and Example 2 (Our Method 1) are generally higher than the 3 best correct answer rates of Comparative Examples 1-3. Moreover, in FIG.5 (b), it turns out that the 3 best correct answer rate of Example 1 (OurMethod7) is generally high compared with the 3 best correct answer rate of Comparative Examples 1-3. Further, in FIGS. 5A and 5B, in particular, in Example 1 (OurMethod 7), Example 2 (OurMethod 1), and Comparative Example 3 (LDAone), a new product is shown in the valley portion for each week. It shows that the correct answer rate is low due to the release.

  In addition, Table 1 shows the correct answer rate (%) averaged over the entire time. In Table 1, (a) is a moving image, and (b) is a result of a comic. A number in parentheses (such as “0.9”) accompanying the correct answer rate represents a standard deviation. In the tables of (a) and (b), “1” to “5” in the leftmost column represent “1 best correct answer rate” to “5 best correct answer rate”. In the tables of (a) and (b), it can be confirmed that the correct answer rate of Example 1 (OurMethod 7) is the highest and the user's interest can be accurately predicted. The correct answer rate of Example 2 (OurMethod 1) is also higher than any of the comparative examples in the moving image, and is equal to that of the comparative example 1 in the comic, but higher than those of the comparative examples 2 and 3.

  Table 2 shows the average calculation time (seconds) per time of each method in a PC (Personal Computer) of a CPU of Xeon (registered trademark) 2.93 GHz in this case. In Table 2, (a) is the result for a moving image, and (b) is the result for a comic. The numbers in parentheses (such as “40.4”) attached to the average calculation time value represent standard deviation. In Comparative Example 1, the correct answer rate in comic data (see (b) of Table 1) was almost equal to that in Example 1 and Example 2. Since this comparative example 1 uses all data, it can be seen that a large amount of calculation is required for both moving images and comics compared to other methods. On the other hand, in both the case of moving images and comics, the calculation in Example 1 and Example 2 was completed in 1/10 or less time compared to Comparative Example 1, and it can be seen that high-speed calculation was possible even for large-scale data. .

  Thus, from this example, the calculation by the interest prediction device 1 of the present embodiment is superior to the calculations of Comparative Examples 1 to 3 when viewed from two viewpoints of calculation accuracy and calculation time. Recognize.

It is a block diagram which shows the structure of the interest prediction apparatus of this embodiment. It is explanatory drawing including the block diagram of the model estimation part of the interest prediction apparatus of this embodiment. It is a flowchart which shows the flow of a process of a model estimation part. It is explanatory drawing containing the block diagram of the interest prediction part of the interest prediction apparatus of this embodiment. It is a graph which shows the 3-best correct answer rate for every method of each method including the interest prediction method of this embodiment.

Explanation of symbols

1 Interest prediction device (purchase prediction device)
2 Calculation means 3 Input means 4 Storage means 5 Output means 11 Bus line 21 Model estimation part 22 Interest prediction part (purchase prediction part)
23 memory 40a program storage unit 40b data storage unit 41 model estimation program 42 interest prediction program 43 input data 44 class set 45 class probability set 46 purchase probability set 47 class probability invariant set 48 purchase probability invariant set

Claims (8)

When predicting the possibility of subsequent purchase for any of the products of any user based on purchase data collected in advance in time series for purchase data for a plurality of products of a plurality of users, A purchase prediction method by a purchase prediction device that predicts the purchase possibility using a probability model that divides a plurality of users into a plurality of classes and assumes that the users belonging to the same class purchase any of the products with the same probability Because
The purchase prediction device
The purchase data,
A class probability set that is a set of probabilities belonging to each of the classes for each user;
A prior probability of the class probability of the user, having as a parameter a class probability invariance indicating the degree to which the probability that the user belongs to the class does not change,
A purchase probability set that is a set of probabilities that each of the products for each class is purchased by a user of that class; and
A storage unit that stores , as a parameter, a purchase probability invariance indicating a degree that the probability of purchasing a product by the user belonging to the class does not change, and a prior probability of the purchase probability of the class ;
A model estimation unit and a purchase prediction unit,
The model estimation unit repeatedly calculates the class probability unchanged degree and the purchase probability unchanged degree so that the likelihood of the class probability unchanged degree and the likelihood of the purchase probability unchanged degree are maximized. and, using said purchase probability not change degree and the class probability invariable degree that the calculation, further new the class probability set and the purchase probability set,
The purchase prediction unit, the updated using the class probability set and the purchase probability set, you calculate the probability that before Symbol user purchases the merchandise
Purchase prediction method wherein a call. The prior probability of the user class probability is defined as a Dirichlet distribution,
Prior probability of purchase probability of the class is defined as Dirichlet distribution
The purchase prediction method according to claim 1, wherein: The storage unit, of the purchase latest time before the predetermined period of time data, the class probability set, the prior probability of class probability of the user, the purchase probability set, and store the prior probability, the probability purchase of the class And
The model estimation unit is configured to increase the likelihood of the class probability unchanged for the predetermined time and the likelihood of the purchase probability unchanged for the predetermined time to the maximum. The class probability unchanged degree and the purchase probability unchanged degree for the predetermined time are repeatedly calculated, the class probability unchanged degree for the calculated predetermined time and the purchase probability for the predetermined time are calculated. Update the class probability set for the predetermined time and the purchase probability set for the predetermined time using the degree of invariance,
The purchase prediction unit calculates the probability that the user purchases the product using the updated class probability set for the predetermined time and the purchase probability set for the predetermined time. The purchase prediction method according to claim 1 or 2 . When predicting the possibility of subsequent purchase for any of the products of any user based on purchase data collected in advance in time series for purchase data for a plurality of products of a plurality of users, A purchase prediction apparatus that divides a plurality of users into a plurality of classes and predicts the possibility of purchase using a probability model that assumes that the users belonging to the same class purchase any of the products with the same probability,
The purchase data,
A class probability set that is a set of probabilities belonging to each of the classes for each user;
A prior probability of the class probability of the user, having as a parameter a class probability invariance indicating the degree to which the probability that the user belongs to the class does not change,
A purchase probability set that is a set of probabilities that each of the products for each class is purchased by a user of that class; and
A storage unit that stores , as a parameter, a purchase probability invariance indicating a degree that the probability of purchasing a product by the user belonging to the class does not change, and a prior probability of the purchase probability of the class ;
The class probability unchanged and the purchase probability unchanged are repeatedly calculated so that the likelihood of the class probability unchanged and the purchase probability unchanged are maximized, and the calculated using class probability not change degree and the said purchase probability immutable degree, a model estimation unit you update the class probability set and the purchase probability set,
Using the class probability set and the purchase probability set was the update, and the purchase prediction unit that to calculate the probability that before Symbol user purchases the merchandise,
A purchase prediction apparatus comprising: The prior probability of the user class probability is defined as a Dirichlet distribution,
  Prior probability of purchase probability of the class is defined as Dirichlet distribution
  The purchase prediction apparatus according to claim 4, wherein: The storage unit, of the purchase latest time before the predetermined period of time data, the class probability set, the prior probability of class probability of the user, the purchase probability set, and stores the prior probability, the probability purchase of the class And
The model estimation unit is configured to increase the likelihood of the class probability unchanged for the predetermined time and the likelihood of the purchase probability unchanged for the predetermined time to the maximum. The class probability unchanged degree and the purchase probability unchanged degree for the predetermined time are repeatedly calculated, the class probability unchanged degree for the calculated predetermined time and the purchase probability for the predetermined time are calculated. Update the class probability set for the predetermined time and the purchase probability set for the predetermined time using the degree of invariance,
The purchase prediction unit calculates the probability that the user purchases the product using the updated class probability set for the predetermined time and the purchase probability set for the predetermined time. The purchase prediction device according to claim 4 or 5 . The purchase prediction program for functioning a computer as each part of the purchase prediction apparatus as described in any one of Claims 4-6 . A computer-readable recording medium on which the purchase prediction program according to claim 7 is recorded.

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