Event prediction device, method, and program

Abstract

An embodiment of the present invention is configured such that when estimating parameters of a prediction model for predicting the occurrence of an event to be predicted, a point process model, in which an intensity function of a point process representing the occurrence probability of the event is presented by using the derivative of a neural network, is defined, and relational expressions for parameter estimation, which are represented by an item representing likelihood in the point process model and restriction items formed from differential equations representing a predetermined theoretical model reflecting domain knowledge pertaining to the event, are defined. Next, parameters of the theoretical model and parameters of the point process model are estimated on the basis of information representing past event occurrence history and the relational expressions such that a likelihood value obtained by adding the restriction items to the item representing the likelihood in the point process model becomes the smallest.

Description

Technical Field

[0001] One aspect of the present invention relates to an event prediction apparatus, method, and program for predicting the occurrence of future events.

Background Art

[0002] In recent years, techniques for modeling event sequences and using this model to predict the occurrence of future events have attracted attention. For example, a technique for predicting the occurrence of infectious diseases is one of them. Using this technique, it is possible to grasp the signs of the spread of infectious diseases at an early stage and prevent the spread and expansion of infectious diseases. Also, for example, techniques for predicting the purchasing behavior of users on online shopping sites are being studied. Using this technique, it is possible to optimize product management. Other events to be predicted include, for example, the occurrence of crimes, the occurrence of disasters such as earthquakes and heavy rains, and the occurrence of taxi passengers.

[0003] For modeling event sequences, a theoretical model that reflects domain knowledge is generally used. For example, for modeling the occurrence of infectious diseases, a theoretical model called the Susceptible-Infected-Recovered (SIR) model is used. In the SIR model, the population is divided into three types: susceptible, infected, and recovered / removed according to the stage of infection, and the time change of the population belonging to each stage is modeled based on epidemiological knowledge. The simplest SIR model is described by the following ordinary differential equation.

[0004]

Equation

[0005] Here, S(t), I(t), and R(t) represent the number of susceptible individuals, infected individuals, and recovered / removed individuals (including those with acquired immunity or in quarantine) at time t, respectively. β represents the infection rate per unit time, and γ represents the recovery rate of infected individuals.

[0006] In addition, as theoretical models in the field of epidemiology, based on the SIR model of equations (1)-(3), the SEIR model considering the incubation period and extended models considering vaccination have also been proposed.

[0007] On the other hand, in the field of marketing, an approach has been proposed to model the competition for shares between competing services using the Lotka-Volterra equation. The Lotka-Volterra equation can be described as follows when considering, for example, two competing services.

[0008]

Equation

[0009] Here, x(t) represents the share of the first service at time t, and y(t) represents the share of the second service. a, b, c, and d are positive constants.

[0010] The Lotka-Volterra equation was originally proposed as a model to describe the growth relationship between predators and prey in the biological field. In recent years, it has been increasingly applied in the fields of marketing and economics, and its effectiveness has been confirmed.

[0011] By the way, these theoretical models have been analyzed using agent-based models or differential equation solvers so far. Theoretical models represented by the SIR model and the Lotka-Volterra equation have the advantage of high interpretability and can reflect domain knowledge when modeling the occurrence of events. However, since it is not easy to learn parameters from data, there are limitations in prediction accuracy.

[0012] In recent years, with respect to the occurrence of events such as infectious diseases and purchasing behavior, data with precise time information has become available. For example, due to the expansion of infectious disease surveillance systems and the increasing use of Social Network Service (SNS), large-scale data regarding the occurrence of infectious diseases is being accumulated. When calibrating theoretical models such as the SIR model and the Lotka-Volterra equation using these data, it is necessary to manually select the model and set the parameters, which is time-consuming and laborious.

[0013] Also, as an attempt to utilize data on large-scale event series, many approaches based on machine learning models have been proposed and have attracted attention. For example, a method using a probabilistic generative model called a point process has been proposed. In the framework of the point process, the probability of the occurrence of events such as the occurrence of infectious diseases and purchasing behavior is modeled by a function called an intensity function, and the parameters of the intensity function are estimated using the event occurrence history.

[0014] In the modeling of infectious diseases, a point process called the Hawkes process is particularly widely used. In the Hawkes process, when designing the intensity function, a functional form that decays with the jump-up time each time an event occurs is assumed. As a result, the mechanism by which the occurrence of an event induces the next occurrence can be explicitly modeled. Hawkes process-based methods are also widely used in the modeling of event series in the marketing field, such as purchase histories on online shopping sites.

[0015] Furthermore, in order to describe the competition for share among multiple services, models that extend the Hawkes process have also been proposed (see, for example, Non-Patent Document 1). This method can predict future purchasing behavior by considering not only the influence of past purchasing behavior but also the influence of the growth of other services. However, these methods based on the Hawkes process lack flexibility because they assume a simple functional form for the way of time decay.

[0016] Recently, many approaches using deep learning models have also been proposed. For example, in the prediction of infectious diseases, a method has been proposed to predict the number of occurrences of infectious diseases at future times based on the trend of the number of infected people observed up to the current time (see, for example, Non-Patent Document 2).

[0017] On the other hand, in the prediction of purchasing behavior, an approach using a deep learning model such as a Recurrent Neural Network (RNN) has been proposed. However, when using a deep learning model, while it enables flexible modeling of time series, there is another problem that domain knowledge in each field of epidemiology and marketing cannot be considered.

Prior Art Documents

Non-Patent Documents

[0018]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0019] As described above, various methods have been proposed for modeling and predicting event sequences, including theoretical models such as the SIR model and the Lotka-Volterra equations, and machine learning models such as point processes and deep learning. However, with these methods, it is difficult to fully utilize both large-scale data and domain knowledge.

[0020] This invention was made in view of the above circumstances, and aims to provide a technology that enables full utilization of both large-scale data and domain knowledge in modeling and predicting event sequences.

Means for Solving the Problem

[0021] One aspect of the event prediction apparatus or method according to this invention for solving the above problem comprises a processing unit or process for acquiring information representing the past occurrence history of an event to be predicted, and a processing unit or process for estimating parameters of a prediction model for predicting the occurrence of the event in a learning phase. When estimating the parameters, a process of defining a point process model that represents the intensity function of the point process representing the occurrence probability of the event using the derivative of a neural network, a term representing the likelihood of the point process model, and a constraint term consisting of a differential equation representing a predetermined theoretical model reflecting the domain knowledge related to the event are used to define a relational expression for parameter estimation. Based on the information representing the past occurrence history and the relational expression, a process is performed to estimate the parameters of the theoretical model and the parameters of the point process model such that the likelihood value obtained by adding the constraint term to the term representing the likelihood of the point process model is minimized.

[0022] According to one aspect of the present invention, when learning the parameters of a point process based on a neural network, by imposing a differential equation representing a theoretical model related to event occurrence as a constraint on the loss function, prior knowledge related to the field of events can be incorporated into the framework of the point process based on the neural network. At the same time, data on a large-scale past event occurrence history can be utilized, thereby making it possible to generate a prediction model capable of highly accurate event prediction.

Advantages of the Invention

[0023] That is, according to one aspect of the present invention, it is possible to provide a technique capable of fully utilizing both large-scale data and domain knowledge in modeling and predicting an event sequence.

Brief Description of the Drawings

[0024]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Mode for Carrying Out the Invention

[0025] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0026] [First Embodiment] (Configuration Example) FIGS. 1 and 2 are block diagrams showing an example of the hardware configuration and software configuration of the infectious disease occurrence prediction device SVA, which is the first embodiment of the event prediction device according to the present invention.

[0027] The infectious disease occurrence prediction device SVA is composed of, for example, a server computer arranged on the cloud or the Web, or a personal computer owned by a user. The infectious disease occurrence prediction device SVA includes a control unit 1A using a hardware processor such as a Central Processing Unit (CPU), and a storage unit having a program storage unit 2A and a data storage unit 3A is connected to the control unit 1A via a bus 5A, and an input / output interface (hereinafter, the interface is referred to as I / F) unit 4A is connected.

[0028] An input / output I / F unit 4A is connected to an input device IDA and an output device ODA. The input device IDA includes, for example, a keyboard and a mouse, and is used to input various operation information related to the infectious disease occurrence prediction process. The output device ODA has, for example, a display device, and is used to display prediction information and the like generated by the control unit 1A. In addition, as the output device ODA, a printer, an external storage device, or the like may be used.

[0029] The input / output I / F unit 4A has, for example, a communication interface function, receives operation information input by the input device IDA via a network or a signal cable, and outputs various information generated by the control unit 1A to the output device ODA via the network or the signal cable.

[0030] The program storage unit 2A is configured by, for example, combining a non-volatile memory such as an SSD (Solid State Drive) that can be written and read at any time as a storage medium and a non-volatile memory such as a ROM (Read Only Memory). In addition to middleware such as an OS (Operating System), it stores application programs necessary to execute various control processes according to one embodiment. Hereinafter, the OS and each application program are collectively referred to as a program.

[0031] The data storage unit 3A is, for example, a combination of a non-volatile memory such as an SSD that can be written and read at any time and a volatile memory such as a RAM (Random Access Memory) as a storage medium. In its storage area, as a storage unit used to implement the first embodiment, it includes an infectious disease occurrence history storage unit 31A and a parameter storage unit 32A.

[0032] The infectious disease occurrence history storage unit 31A is used to acquire information representing the past infectious disease occurrence history to be analyzed and store the acquired information representing the infectious disease occurrence history. The information representing the infectious disease occurrence history is represented as time-series data consisting of the occurrence time of the infectious disease and auxiliary information. For example, the information representing the infectious disease occurrence history observed up to time T is D = {(t i , m i )} I i=1 represented by

[0033] Here, t i is the observation time of the case, m i is the auxiliary information, and I is the number of data. As the auxiliary information, for example, the observation location of the infectious disease (country or region), the attributes of the affected person, etc. are given. In the first embodiment, a case is assumed in which the occurrence location m i ∈M of the infectious disease is given as the auxiliary information. Here, M represents a set of regions. FIG. 3 is a diagram showing an example of the infectious disease occurrence history.

[0034] Note that the infectious disease occurrence history storage unit 31A may be provided not in the infectious disease occurrence prediction device SVA but in another database server or the like arranged on the cloud or the web.

[0035] The parameter storage unit 32A is used to store the set of optimal parameters estimated by the parameter estimation process of the control unit 1A. Note that the parameter storage unit 32A may also be provided in another database server on the cloud or the web, or in another personal computer or the like, or may be provided in a part of the storage area of a storage device that stores other data such as a learning model.

[0036] The control unit 1A includes an operation information reception processing unit 11A, a parameter estimation processing unit 12A, an infectious disease occurrence prediction processing unit 13A, and a prediction information output processing unit 14A as the processing functions necessary for implementing the first embodiment. These processing units 11A to 14A are all realized by causing the hardware processor of the control unit 1A to execute an application program stored in the program storage unit 2A.

[0037] In addition to being pre-stored in the program storage unit 2A, the above application program may be downloaded from an external application server or the like when needed and stored in the program storage unit 2A. Also, some or all of the above processing units 11A to 14A may be realized using hardware such as LSI (Large Scale Integration) or ASIC (Application Specific Integrated Circuit).

[0038] The operation information reception processing unit 11A receives the operation information input in the input device IDA via the input / output I / F unit 4A. The operation information includes, for example, operation commands for registering the infectious disease occurrence history in the infectious disease occurrence history storage unit 31A, modifying and deleting the registered infectious disease occurrence history, and the like.

[0039] The parameter estimation processing unit 12A estimates the optimal parameters to be set in the infectious disease occurrence prediction model based on the information representing the infectious disease occurrence history stored in the infectious disease occurrence history storage unit 31A, and performs the process of storing the estimated optimal parameters in the parameter storage unit 32A. An example of this parameter estimation process will be described in the operation example.

[0040] The infectious disease occurrence prediction processing unit 13A uses the infectious disease occurrence prediction model in which the optimal parameters stored in the parameter storage unit 32A are reflected to predict the occurrence situation of infectious diseases in the future, and outputs the prediction result to the prediction information output processing unit 14A.

[0041] The prediction information output processing unit 14A generates information for outputting the prediction result of the above infectious disease occurrence situation, and outputs the generated prediction information from the input / output I / F unit 4A to the output device ODA.

[0042] (Operation example) Next, an operation example of the infectious disease occurrence prediction device SVA configured as described above will be described.

[0043] FIG. 4 is a flowchart showing an example of the processing procedure and processing content of the parameter estimation process of the infectious disease occurrence prediction model and the infectious disease occurrence prediction process using the learned prediction model, which are executed by the control unit 1A of the infectious disease occurrence prediction device SVA.

[0044] (1) Management of infectious disease occurrence history For example, assume that the administrator inputs the newly observed infectious disease occurrence history from the input device IDA together with the registration request. Then, the control unit 1A of the infectious disease occurrence prediction device SVA detects the above registration request in step S10 under the control of the operation information reception processing unit 11A and moves to step S11, where the newly observed infectious disease occurrence history is acquired. Then, in step S12, the operation information reception processing unit 11A registers the acquired infectious disease occurrence history in the infectious disease occurrence history storage unit 31A.

[0045] Note that the process of the administrator modifying or deleting the infectious disease occurrence history registered in the infectious disease occurrence history storage unit 31A is also performed in the same manner under the control of the operation information reception processing unit 11A.

[0046] (2) Estimation of parameters Assume that in a state where the learning phase of the infectious disease occurrence prediction model is set, the administrator inputs a parameter estimation request on the input device IDA. Then, when the control unit 1A of the infectious disease occurrence prediction device SVA receives the above parameter estimation request in step S13, it executes the parameter estimation process as follows in step S14 under the control of the parameter estimation processing unit 12A hereafter.

[0047] FIG. 5 is a flowchart showing an example of a processing procedure and processing content of parameter estimation processing executed by the parameter estimation processing unit 12A.

[0048] Based on the infectious disease occurrence history stored in the infectious disease occurrence history storage unit 31A, the parameter estimation processing unit 12A first introduces the intensity function λ m (t) of the point process representing the occurrence probability of infectious diseases in each region.

[0049] That is, the parameter estimation processing unit 12A designs the intensity function of region m using a black box function with time t as the input. At this time, in order to ensure the flexibility of the intensity function, the intensity function λ m (t) is described using a neural network. However, if the intensity function λ m (t) is directly modeled by a neural network, the calculation of the integral included in the log-likelihood of the point process may become difficult.

[0050] Therefore, in step S140, the parameter estimation processing unit 12A analytically calculates the integral of the intensity function included in the likelihood of the point process. For this purpose, instead of directly modeling λ m (t) with a neural network, the integral Λ m (t) is calculated by a neural network with time t and location m as inputs,

Equation

[0051] Under this formulation, the intensity function λ m (t) can be expressed as

Equation

[0052] Here, f ′(t, m; θ f) is the derivative of the neural network f(t, m; θ f ) and is defined as

Number

[0053] At this time, the intensity function λ m (t) corresponds to the variable I(t) in the SIR model defined by the above-mentioned equations (1)-(3). Therefore, in step S141, the parameter estimation processing unit 12A replaces I(t) included in equation (3) of the SIR model with λ m (t) and substitutes equation (7) to define the number of immune / acquired isolation individuals R m (t) in region m as

Number

[0054] Subsequently, in step S142, the parameter estimation processing unit 12A defines the population of uninfected individuals in region m as S m (t). That is, the population of uninfected individuals S m (t) in region m can be expressed as m using the population N m of region m, the infection probability λ m (t), and the number of immune / acquired isolation individuals R

Number

[0055] In this case, the population N m can be estimated as a parameter, but in the first embodiment, a given value obtained from a population census or the like is used. Similarly, equation (2) of the SIR model can be rewritten as

Number

[0056] Incidentally, when learning the prediction model, the parameter estimation processing unit 12A estimates the parameters {β, γ} of the SIR model and the parameters θ of the neural network that minimize the likelihood L defined by the following equation. f to estimate.

[0057]

Number

[0058] Here, L data is the likelihood representing the goodness of fit of the learning model to the data, and L ode is a term representing the constraint by the differential equation. α is a hyperparameter representing the importance of the second term.

[0059] In step S143, the parameter estimation processing unit 12A defines the likelihood of the point process shown in the first term on the right side of the above equation (12) as

Number

[0060] The black box function λ m (·) and its integral Λ m (·) can be expressed as

Number

[0061] Note that the derivative f′ of the neural network included in the first term of the above equation (14) m(t) can be easily calculated by using automatic differentiation implemented in a deep learning package such as PyTorch, for example.

[0062] Also, in step S144, the parameter estimation processing unit 12A uses the difference between the right side and the left side of the above equation (11) for the second term on the right side of the above equation (12).

Equation

[0063] Here, {τ1, …, τ J} are representative points on a predefined time axis. L ode represents the error of the differential equation at J representative points. In this example, the mean squared error is used as the error metric, but other error functions can also be used.

[0064] The above equation is obtained by taking the difference between the left side and the right side of the above equation (11), which is a differential equation, and substituting the time τ j of the representative point. By adding the constraint term of the above equation (15) to the likelihood L, the parameters of the intensity function λ(·) such that the output follows the differential equation defined by the above equation (2) can be learned.

[0065] In step S145, the parameter estimation processing unit 12A uses the first derivative f′(t, m) = df(t, m) / dt and the second derivative f′′(t, m) = d 2 f(t, m) / dt 2 of the neural network f(t, m) for the above equation (15).

Equation

[0066] In the first embodiment, the case of using the SIR model was described as an example, but any theoretical model such as the SEIR model can be applied. Also, any method can be used for parameter optimization, but in order to efficiently calculate the derivatives of the neural networks included in the above equations (14) and (16), it is advisable to use the backpropagation method.

[0067] In step S146, the parameter estimation processing unit 12A estimates the optimal parameters, that is, the parameters {β, γ} of the SIR model that minimize the likelihood L, and the parameters θ of the neural network. f The estimated parameters are stored in the parameter storage unit 32A in step S147.

[0068] (3) Prediction of the occurrence of infectious diseases and output of the prediction results When the estimation process of the optimal parameters for the infectious disease occurrence prediction model is completed as described above, the control unit 1A of the infectious disease occurrence prediction device SVA shifts to the prediction phase.

[0069] In the prediction phase, when a prediction request is input from the input device IDA, the control unit 1A of the infectious disease occurrence prediction device SVA detects the prediction request in step S15 under the control of the infectious disease occurrence prediction processing unit 13A and shifts to step S16, where the prediction conditions are first acquired. As the prediction conditions, for example, the future time period to be predicted is specified.

[0070] Subsequently, in step S17, the infectious disease occurrence prediction processing unit 13A inputs the prediction conditions as explanatory variables to the infectious disease occurrence prediction model with the optimal parameters set. Then, using the infectious disease occurrence prediction model, the occurrence time and occurrence location of the infectious disease in the time period are predicted, and the prediction result is obtained.

[0071] Finally, in step S18, the control unit 1A of the infectious disease outbreak prediction device SVA generates data for displaying the prediction results obtained by the infectious disease outbreak prediction processing unit 13A under the control of the prediction information output processing unit 14A, and outputs the generated display data from the input / output I / F unit 4A to the output device ODA. As a result, the output device ODA displays, for example, on a map, the location (country or region) of the infectious disease outbreak in the future time period specified as the prediction target and the time of outbreak. Note that any form can be adopted as the output form of the prediction results.

[0072] (Action and effect) As described above, in the first embodiment, the intensity function λ of the point process that represents the probability of an infectious disease outbreak in each region m is m (t) is defined as the differential of the neural network, and the above strength function λ m By replacing (t) with the number of infected people in the SIR model, the number of people who have acquired immunity and are in quarantine in region m, R m (t) and the uninfected population S m (t) is defined. Also, the likelihood L (θ f , β;D) as the likelihood of the point process Ldata (θ f ,;D) and αLode (θ f In the learning phase, the parameters of the intensity function are learned by applying the past history of infectious disease outbreaks to the above-defined relationship, and the likelihood L (θ f , β;D) and the parameters of the SIR model {β,γ} and the neural network parameters θ f In the prediction phase, the infectious disease outbreak prediction model in which the estimated parameters are set is used to predict the infectious disease outbreak status in a future time period, and the prediction result is output.

[0073] Therefore, according to the first embodiment, when learning the parameters of the point process based on the neural network, by imposing the differential equation representing the SIR model as a constraint on the loss function, prior knowledge in the field of infectious disease prediction can be incorporated into the framework of the point process based on the neural network. At the same time, data on past large-scale infectious disease occurrence histories can be utilized, enabling highly accurate prediction of infectious disease occurrences.

[0074] [Second Embodiment] (Configuration Example) FIG. 6 is a block diagram showing an example of the software configuration of a purchase behavior prediction device SVB, which is a second embodiment of the event prediction device according to the present invention. Note that the hardware configuration of the purchase behavior prediction device SVB is the same as that described with reference to FIG. 1 in the first embodiment, and thus a repeated description thereof will be omitted.

[0075] Similar to the infectious disease occurrence prediction device SVA described above, the purchase behavior prediction device SVB is composed of, for example, a server computer arranged on the cloud or the Web, or a personal computer owned by a user. The purchase behavior prediction device SVB includes a control unit 1B that uses a hardware processor such as a central processing unit (CPU). A storage unit having a program storage unit 2B and a data storage unit 3B, and an input / output I / F unit 4B are connected to the control unit 1B via a bus 5B.

[0076] An input device IDB and an output device ODB are connected to the input / output I / F unit 4B. The input device IDB includes, for example, a keyboard and a mouse, and is used to input various operation information related to the prediction process of purchase behavior. The output device ODB has, for example, a display device, and is used to display prediction information and the like generated by the control unit 1B. Note that other devices such as a printer and an external storage device may be used as the output device ODB.

[0077] The input / output I / F unit 4B has, for example, a communication interface function, receives operation information input in the input device IDB via a network or a signal cable, and outputs various information generated by the control unit 1B to the output device ODB via the network or the signal cable.

[0078] The program storage unit 2B is configured by combining, for example, a non-volatile memory such as an SSD that can be written to and read from at any time as a storage medium and a non-volatile memory such as a ROM. In addition to middleware such as an OS, it stores application programs necessary for executing various control processes according to one embodiment. Hereinafter, the OS and each application program are collectively referred to as a program.

[0079] The data storage unit 3B is, for example, a combination of a non-volatile memory such as an SSD that can be written to and read from at any time as a storage medium and a volatile memory such as a RAM. In its storage area, as a storage unit used for implementing the second embodiment, it includes a purchase behavior history storage unit 31B and a parameter storage unit 32B.

[0080] The purchase behavior history storage unit 31B is used to acquire information representing a past purchase behavior history to be analyzed and store the information representing the acquired purchase behavior history. The purchase behavior history information is represented as time-series data consisting of the time when the purchase behavior was performed and auxiliary information. For example, the purchase behavior observed up to time T is D ={(t i , m i )} I i=1 represented by.

[0081] Here, t i is the time when the purchase behavior was performed, m i is the auxiliary information, and I is the number of data. In the second embodiment, for example, the type m iAssume a case where ∈M is given as auxiliary information. Here, M represents a set of products or services. FIG. 7 is a diagram showing an example of a purchase behavior history.

[0082] Note that the purchase behavior history storage unit 31B may be provided not in the purchase behavior prediction device SVB but in another database server on the cloud or the Web, or a personal computer, etc.

[0083] The parameter storage unit 32B is used to store the set of optimal parameters estimated by the parameter estimation process of the control unit 1B. Note that the parameter storage unit 32B may also be provided in another database server on the cloud or the Web, or another personal computer, etc., or may be provided in a part of the storage area of a storage device that stores other data such as a learning model.

[0084] The control unit 1B includes an operation information reception processing unit 11B, a parameter estimation processing unit 12B, a purchase behavior prediction processing unit 13B, and a prediction information output processing unit 14B as processing functions necessary for implementing the second embodiment. These processing units 11B to 14B are all realized by causing the hardware processor of the control unit 1B to execute an application program stored in the program storage unit 2B.

[0085] Note that also in the second embodiment, the application program may be downloaded from an external application server, etc. to the program storage unit 2B and stored in the program storage unit 2B when necessary, in addition to being stored in the program storage unit 2B in advance. Also, a part or all of the above processing units 11B to 14B may be realized using hardware such as an LSI or an ASIC.

[0086] The operation information reception processing unit 11B receives the operation information input in the input device IDB via the input / output I / F unit 4B. The operation information includes, for example, operation commands for registering the purchase behavior history in the purchase behavior history storage unit 31B, modifying and deleting the registered purchase behavior history, etc.

[0087] Based on the information representing the purchase behavior history stored in the purchase behavior history storage unit 31B, the parameter estimation processing unit 12B estimates the optimal parameters to be set in the purchase behavior prediction model, and stores the estimated optimal parameters in the parameter storage unit 32B. An example of this parameter estimation process will be described in the operation example.

[0088] Using the purchase behavior prediction model in which the optimal parameters stored in the parameter storage unit 32B are reflected, the purchase behavior prediction processing unit 13B predicts the future purchase behavior of the user, and outputs the prediction result to the prediction information output processing unit 14B.

[0089] The prediction information output processing unit 14B generates information for displaying the prediction result of the future purchase behavior, and outputs the generated prediction information from the input / output I / F unit 4B to the output device ODB.

[0090] (Operation example) Next, an operation example of the purchase behavior prediction device SVB configured as described above will be described.

[0091] FIG. 8 is a flowchart showing an example of the processing procedure and processing content of the parameter estimation process of the purchase behavior prediction model and the purchase behavior prediction process using the learned purchase behavior prediction model, which are executed by the control unit 1B of the purchase behavior prediction device SVB.

[0092] (1) Management of purchase behavior history For example, assume that an administrator newly inputs the collected purchase behavior history from the input device IDB together with the registration request. Then, under the control of the operation information reception processing unit 11B, the control unit 1B of the purchase behavior prediction device SVB detects the registration request in step S20 and moves to step S21, where it acquires the newly collected purchase behavior history. Then, in step S22, the operation information reception processing unit 11B registers the acquired purchase behavior history in the purchase behavior history storage unit 31B.

[0093] Note that the process of the administrator modifying or deleting the purchase behavior history stored in the purchase behavior history storage unit 31B is also similarly performed under the control of the operation information reception processing unit 11B.

[0094] (2) Parameter Estimation In the learning phase of the purchase behavior prediction model, assume that the administrator inputs a parameter estimation request on the input device IDB. Then, when the control unit 1B of the purchase behavior prediction device SVB receives the parameter estimation request in step S23, it executes the parameter estimation process as follows in step S24 under the control of the parameter estimation processing unit 12B.

[0095] FIG. 9 is a flowchart showing an example of the processing procedure and processing content of the parameter estimation process executed by the parameter estimation processing unit 12B.

[0096] Based on the purchase behavior history stored in the purchase behavior history storage unit 31B, the parameter estimation processing unit 12B first introduces the intensity function λ m (t) of the point process representing the purchase probability for each product or service.

[0097] That is, the parameter estimation processing unit 12B designs the intensity function of product or service m using a black box function with time t as the input. At this time, to ensure the flexibility of the intensity function, the intensity function λ m (t) is described using a neural network. However, if the intensity function λ m (t) is directly modeled by a neural network, the calculation of the integral included in the log-likelihood of the point process may become difficult.

[0098] Therefore, in step S240, in order to analytically calculate the integral of the intensity function included in the likelihood of the point process, instead of directly modeling λ m (t) with a neural network, the parameter estimation processing unit 12B uses a neural network with time t and product or service m as inputs for its integral Λ m (t),

Number

[0099] Under this formulation, the intensity function λ m (t) is

Number

[0100] Here, f ′(t, m; θ f ) is the derivative of the neural network f(t, m; θ f ), and

Number

[0101] At this time, the intensity function λ0(t) of the first type of product or service m = 0 corresponds to the variable x(t) in the Lotka-Volterra equation defined by the above-mentioned equations (4) and (5). Similarly, the intensity function λ1(t) representing the purchase probability of the second type of product or service corresponds to the variable y(t) in the Lotka-Volterra equation. Therefore, in steps S241 and S242, the parameter estimation processing unit 12B replaces x(t) included in equation (4) of the Lotka-Volterra equation with λ0(t) and y(t) included in equation (5) with λ1(t) respectively, so that the change in the purchase probability of the first type of product or service m = 0 is

Number

[0102] Similarly, the change in the purchase probability of the second type of product or service m = 1 is

Number

[0103] By the way, when learning the prediction model, the parameter estimation processing unit 12B estimates the parameters {a, b, c, d} of the Lotka-Volterra equation and the parameters θ of the neural network that minimize the likelihood L defined by the following equation. f are estimated.

[0104]

Equation

[0105] Here, L data is the likelihood representing the goodness of fit of the learning model to the data, and L ode is a term representing the constraint by the differential equation. α is a hyperparameter representing the importance of the second term.

[0106] In step S243, the parameter estimation processing unit 12B defines the likelihood of the point process shown in the first term on the right side of the above equation (22) as

Equation

[0107] The black box function λ m (·) and its integral Λ m (·) can be expressed as

Equation

[0108] Note that the derivative f′ of the neural network included in the first term of the above equation (24) m(t) can be easily calculated by using automatic differentiation implemented in a deep learning package such as PyTorch, for example.

[0109] Also, in step S244, the parameter estimation processing unit 12B uses the difference between the right and left sides of the above equations (20) and (21) for the second term on the right side of the above equation (22).

Number

[0110] Here, {τ1, …, τ J} are representative points on a predefined time axis. L ode represents the error of the differential equation at J representative points. In this example, the mean squared error is used as the error metric, but other error functions can also be used.

[0111] The above equation is obtained by taking the difference between the left and right sides of the above differential equations (20) and (21) and substituting the time τ j of the representative point. By adding the constraint term of the above equation (25) to the likelihood L, the parameters of the intensity function λ(·) can be learned such that the output follows the differential equations defined by the above equations (4) and (5).

[0112] In step S245, the parameter estimation processing unit 12B uses the first-order derivative f′(t, m) = df(t, m) / dt and the second-order derivative f′′(t, m) = d 2 f(t, m) / dt 2 of the neural network f(t, m) for the above equation (25) and

Number

[0113] In the second embodiment, the case of using the Lotka-Volterra equation was described as an example, but it is also possible to apply other similar theoretical models. Also, any method may be used for parameter optimization, but in order to efficiently calculate the derivative of the neural network included in the above equation (26), the backpropagation method may be used.

[0114] In step S246, the parameter estimation processing unit 12B estimates the parameters {a, b, c, d} of the Lotka-Volterra equation and the parameters θ of the neural network that minimize the likelihood L. f Then, the estimated optimal parameters are stored in the parameter storage unit 32B in step S247.

[0115] (3) Prediction of purchase behavior and output of the prediction result When the estimation process of the optimal parameters for the purchase behavior prediction model is completed as described above, the control unit 1B of the purchase behavior prediction device SVB shifts to the prediction phase.

[0116] In the prediction phase, when a prediction request is input from the input device IDB, the control unit 1B of the purchase behavior prediction device SVB detects the prediction request in step S25 under the control of the purchase behavior prediction processing unit 13B and shifts to step S26, where first the prediction conditions are acquired. As the prediction conditions, for example, the future time period to be predicted is specified.

[0117] Subsequently, in step S27, the purchase behavior prediction processing unit 13B inputs the prediction conditions as explanatory variables to the infectious disease occurrence prediction model with the optimal parameters set. Then, using the purchase behavior prediction model, it predicts the product or service that will be the target of the purchase behavior and the purchase time in the above time period, and obtains the prediction result.

[0118] Finally, under the control of the prediction information output processing unit 14B, the control unit 1B of the purchase behavior prediction device SVB generates data for displaying the prediction result obtained by the purchase behavior prediction processing unit 13B in step S28, and outputs the generated display data from the input / output I / F unit 4B to the output device ODB. As a result, on the output device ODB, for example, the name of the product or service targeted for purchase behavior in the future time zone specified as the prediction target and the purchase time thereof are displayed. Note that the output form of the prediction result can adopt any form.

[0119] (Function and Effect) As described above, in the second embodiment, the intensity function λ m (t) of the point process representing the purchase probability of each product or service m is defined as the derivative of the neural network, and the intensity function λ m (t) is replaced with the variables x(t) and y(t) of the Lotka-Volterra equation to define the purchase probabilities of the first type of product or service m = 0 and the second type of product or service m = 1, respectively. Also, the likelihood L(θ f , a, b, c, d; D) is defined by the likelihood L data (θ f ,; D) of the point process and αL ode (θ f , a, b, c, d) representing the constraints of the differential equation. Then, in the learning phase, by applying the past purchase behavior history to the defined relational expressions, the parameters {a, b, c, d} of the Lotka-Volterra equation and the parameter θ f of the neural network that minimize the likelihood L(θ f , a, b, c, d; D) are estimated respectively. Also, in the prediction phase, using the purchase behavior prediction model with the estimated parameters set, the purchase behavior of the target product or service in the future time zone is predicted, and the prediction result is output.

[0120] Therefore, according to the second embodiment, when learning the parameters of the point process based on the neural network, by imposing a differential equation representing the Lotka-Volterra equation on the likelihood of the point process as a constraint on the loss function, prior knowledge regarding purchase behavior can be incorporated into the framework of the point process based on the neural network. At the same time, data on past large-scale purchase behavior histories can be utilized, thereby enabling highly accurate prediction of purchase behavior.

[0121] [Other Embodiments] (1) Each processing function and storage unit included in the infectious disease occurrence prediction device SVA and the purchase behavior prediction device SVB may be arranged in one information processing device, or may be distributed and arranged in a plurality of information processing devices such as servers and personal computers. For example, the parameter estimation processing unit and the event prediction processing unit may be arranged in different information devices, and the parameters estimated by one information processing device may be transferred to the other information processing device as necessary and set in the learning model.

[0122] (2) In the first and second embodiments, the cases of predicting the occurrence of infectious diseases and predicting purchase behavior, respectively, have been described as examples. However, the present invention is not limited thereto, and can also be applied to the prediction of various events such as the prediction of the occurrence of crimes, the prediction of the occurrence of disasters such as earthquakes, heavy rains, and strong winds, and the prediction of taxi dispatch requests.

[0123] (3) In addition, regarding the type of theoretical model and the processing functions of the event prediction device, various modifications can be made without departing from the gist of the present invention.

[0124] The embodiments of the present invention have been described in detail above, but the description up to this point is merely an exemplification of the present invention in all respects. Needless to say, various improvements and modifications can be made without departing from the scope of the present invention. That is, in practicing the present invention, a specific configuration corresponding to the embodiment may be appropriately adopted.

[0125] In short, the present invention is not limited to the above-described embodiments as they are, and at the implementation stage, the components can be modified and embodied without departing from the gist thereof. Further, various inventions can be formed by appropriately combining a plurality of components disclosed in the above-described embodiments. For example, some components may be deleted from all the components shown in the embodiments. Furthermore, components from different embodiments may be appropriately combined.

Explanation of Reference Numerals

[0126] SVA…Infection Occurrence Prediction Device SVB…Purchase Behavior Prediction Device IDA, IDB…Input Device ODA, ODB…Output Device 1A, 1B…Control Unit 2A, 2B…Program Storage Unit 3A, 3B…Data Storage Unit 4A, 4B…Input / Output I / F Unit 5A, 5B…Bus 11A, 11B…Operation Information Reception Processing Unit 12A, 12B…Parameter Estimation Processing Unit 13A…Infection Occurrence Prediction Processing Unit 13B…Purchase Behavior Prediction Processing Unit 14A, 14B…Prediction Information Output Processing Unit 31A…Infection Occurrence History Storage Unit 31B…Purchase Behavior History Storage Unit 32A, 32B…Parameter Storage Unit

Claims

1. An event occurrence history acquisition processing unit that acquires information representing a past occurrence history of an event to be predicted, In the learning phase, a parameter estimation processing unit that estimates parameters of a prediction model that predicts the occurrence of the event Comprising, The parameter estimation processing unit, A process of defining a point process model in which an intensity function of a point process representing the occurrence probability of the event is represented by a derivative of a neural network, A process of defining a relational expression for parameter estimation represented by a term representing the likelihood of the point process model and a constraint term consisting of a differential equation representing a predetermined theoretical model reflecting domain knowledge related to the event, Based on the information representing the past occurrence history and the relational expression, a process of estimating the parameters of the theoretical model and the parameters of the point process model such that the likelihood value obtained by adding the constraint term to the term representing the likelihood of the point process model is minimized An event prediction device that performs.

2. The parameter estimation processing unit, A process of defining a point process model in which an intensity function of a point process representing the occurrence probability of an infectious disease is represented by a derivative of a neural network, A process of defining the relational expression represented by a term representing the likelihood of the point process model and a constraint term consisting of a differential equation representing a theoretical model reflecting domain knowledge related to the occurrence of the infectious disease, Based on the information representing the past infectious disease occurrence history and the relational expression, a process of estimating the parameters of the theoretical model and the parameters of the point process model such that the likelihood value obtained by adding the constraint term to the term representing the likelihood of the point process model is minimized The event prediction device according to claim 1, which performs.

3. The parameter estimation processing unit, A process of defining a point process model in which an intensity function of a point process representing the purchase probability of a product or service is represented by a derivative of a neural network, A process of defining the relational expression represented by a term representing the likelihood of the point process model and a constraint term consisting of a differential equation representing a theoretical model reflecting domain knowledge related to the purchase behavior of the product or service, Based on the information representing the past infectious disease occurrence history and the relational expression, a process of estimating the parameters of the theoretical model and the parameters of the point process model such that the likelihood value obtained by adding the constraint term to the term representing the likelihood of the point process model is minimized The event prediction device according to claim 1, which performs.

4. A condition acquisition processing unit that acquires information representing future prediction conditions of the event; A prediction processing unit that acquires the estimated parameter, sets it in the prediction model, inputs the information representing the prediction condition into the prediction model with the parameter set as an explanatory variable, and outputs information representing an event prediction result output as an objective variable from the prediction model; The event prediction device according to claim 1, further comprising:

5. An event prediction method executed by an information processing device, comprising: A process of acquiring information representing a past occurrence history of an event to be predicted; In a learning phase, a process of estimating parameters of a prediction model for predicting the occurrence of the event; Comprising: The process of estimating the parameter is: A process of defining a point process model in which an intensity function of a point process representing the occurrence probability of the event is represented using a derivative of a neural network; A process of defining a relational expression for parameter estimation represented by a term representing the likelihood of the point process model and a constraint term composed of a differential equation representing a predetermined theoretical model reflecting domain knowledge regarding the event; Based on the information representing the past occurrence history and the relational expression, a process of estimating the parameters of the theoretical model and the parameters of the point process model such that the likelihood value obtained by adding the constraint term to the term representing the likelihood of the point process model is minimized; An event prediction method comprising:

6. A program for causing a processor included in the event prediction device to execute all of the processes performed by each of the processing units included in the event prediction device according to any one of claims 1 to 4.

Images