Information processing device, information processing method, and information processing program

Abstract

An information processing device according to one embodiment comprises: an acquisition unit that acquires observation data including the number of events and the even occurrence coordinates, and a numerical-integration setting value including an numerical-integration evaluation point; an inverse M matrix processing unit that selects, for a matrix calculated from the evaluation point and two discretionary points, a positive value kernel function in which the non-diagonal components of an inverse matrix of the matrix are all negative or zero; a model training unit that, on the basis of the observation data and an equivalent kernel function represented by the numerical-integration setting value and the positive value kernel function, is trained on parameters of an intensity function estimated using the positive value kernel function as though the occurrence coordinates of the event have been observed; and an output control unit that outputs the parameters, the positive value kernel function, and the numerical-integration setting value.

Description

Information processing device, information processing method, and information processing program

[0001] The present invention relates to an information processing device, an information processing method, and an information processing program.

[0002] There is known a technique for estimating the probability of occurrence of an event (hereinafter referred to as an intensity function) at each point in a one-dimensional or multi-dimensional space using data on point events (hereinafter referred to as events) that occur in the space. For example, in Non-Patent Document 1, N event coordinates (x １ , x ２ , ..., x Ｎ ) is observed, a method has been proposed for estimating the intensity function λ(x) using an equation using a positive definite kernel function k(x, x').

[0003] Flaxman, Teh, and Sejdinovic, "Poisson Intensity Estimation with Reproducing Kernels", Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, pp.270-279, 2017. Johnson, "Inverse M-Matrices", Linear Algebra and its Applications, 47:195-216, 1982.

[0004] In Non-Patent Document 1, the square root of the intensity function is expressed as a linear sum of equivalent kernel functions. This equivalent kernel function can generally take negative values. Therefore, the square root of the intensity function in Non-Patent Document 1 can also take negative values. If the square root of the intensity function changes from a positive value to a negative value or from a negative value to a positive value in a certain region, the intensity function takes a value of zero in that region, resulting in a problem of large local fluctuations.

[0005] This invention has been made with the above-mentioned circumstances in mind, and aims to propose a technique that can avoid situations in which the estimated intensity function takes an unnatural zero value by designing the equivalent kernel function to take a non-negative value.

[0006] In order to solve the above problem, an information processing device of one embodiment of the present invention includes an acquisition unit that acquires observation data including the number of events and occurrence coordinates of the events, and a set value of a numerical integration including an evaluation point of the numerical integration; an inverse M-matrix processing unit that selects, for a matrix calculated from the evaluation point and any two points, a positive definite Kernel function such that the off-diagonal elements of the inverse matrix of the matrix are all negative or zero; a model learning unit that learns parameters of an intensity function estimated using the positive definite Kernel function based on the observation data and an equivalent Kernel function represented by the positive definite Kernel function and the set value of the numerical integration, assuming that the occurrence coordinates of the events are observed; and an output control unit that outputs the parameters, the positive definite Kernel function, and the set value of the numerical integration.

[0007] According to one aspect of the present invention, a technique is provided that can avoid situations in which the estimated intensity function takes an unnatural zero value by designing the equivalent kernel function to take a non-negative value.

[0008] Fig. 1 is a diagram showing an example of an intensity function calculated in Non-Patent Document 1 and an actual intensity function. Fig. 2 is a block diagram showing an example of a hardware configuration of an information processing device according to an embodiment. Fig. 3 is a block diagram showing a software configuration of the information processing device according to an embodiment in association with the hardware configuration shown in Fig. 2. Fig. 4 is a flowchart showing an example of a processing operation of the information processing device according to an embodiment.

[0009] Hereinafter, an information processing device, an information processing method, and an information processing program will be described in detail with reference to the drawings. In the following embodiments, parts with the same numbers perform the same operations, and redundant description will be omitted. For example, when there are multiple identical or similar elements, a common symbol may be used to describe each element without distinguishing between them, or a subnumber may be used in addition to the common symbol to describe each element with distinction between them.

[0010] [Intensity Model of Non-Patent Document 1] First, we will explain the intensity of Non-Patent Document 1. The intensity model of Non-Patent Document 1 is defined by the following equation.

[0011]

[0012]

[0013] Here, the parameters {z ｎ} Ｎ ｎ＝１ is obtained by solving the following simultaneous equations:

[0014]

[0015] The function h(x, x') defined by the integral equation of formula (2) is called an equivalent kernel function. Generally, formula (2) cannot be solved analytically, so it is solved by an approximation method.

[0016] As described above, the equivalent kernel function h(x, x') can generally take negative values. When the equivalent kernel function takes negative values, the square root of the intensity function given by its linear sum, as expressed in equation (1), can also take negative values. When the square root of the intensity function changes from a positive value to a negative value or from a negative value to a positive value in a certain region, the intensity function takes a value of zero in that region, resulting in locally large fluctuations. This is a drawback of expressing the square root of the intensity function as a linear sum of equivalent kernel functions, and is unnatural behavior.

[0017] FIG. 1 shows an example of the intensity function calculated in Non-Patent Document 1 and an actual intensity function. In FIG. 1(a), the solid line represents the actual intensity function λ(x), and the dotted line represents the estimated λ(x). In FIG. 1(b), the solid line represents the square root of the intensity function λ(x), and the dotted line represents √(λ(x)). Furthermore, the circles in FIG. 1(a) indicate the points where √(λ(x)) switches between positive and negative.

[0018] As shown in Figure 1, the intensity function λ(x) estimated by Non-Patent Document 1 deviates significantly from the actual intensity function λ(x) in the region where √(λ(x)) switches between positive and negative, indicating low estimation accuracy.

[0019] [Embodiment] (Summary) Next, an outline of a method for solving the problem in one embodiment will be described. In one embodiment, the equivalent kernel function is designed to always take a non-negative value. This solves the problem in Non-Patent Document 1.

[0020] (I) For the integral equation of formula (2), the integral term is approximated by numerical integration and solved to obtain an equivalent kernel function in the following format:

[0021]

[0022] where J is the evaluation score of the numerical integration, (q １ , q ２ , …, q Ｊ ) is the evaluation point of the numerical integration, and (w １ , w ２ , ..., w Ｊ ) is the weighting factor for numerical integration, and t represents the matrix / vector transposition operation.

[0023] (II) J node points (q １ , q ２ , …, q Ｊ ) and a ((j+2) × (J+2)) matrix calculated from any two points (x, x') defined by the following formula:

[0024]

[0025] whereas the matrix Ω Ｊ＋２ A positive definite kernel function k(x, x') is used such that all off-diagonal elements of the inverse matrix of the matrix Ω are negative or zero. Ｊ＋２ The inverse matrix of must satisfy the following condition:

[0026]

[0027] In this case, the matrix Ω Ｊ＋２ is a matrix called an Inverse M-Matrix (see, for example, Non-Patent Document 2). Due to the inherent properties of this Inverse M-Matrix, it is mathematically guaranteed that the equivalent kernel function h(x, x') defined by equation (4) takes a non-negative value for any input pair (x, x').

[0028] In this way, by designing the equivalent kernel function h(x, x') to take a non-negative value, the estimation accuracy of the intensity function λ(x) is improved.

[0029] 2 is a block diagram showing an example of the hardware configuration of an information processing device 1 according to an embodiment. The information processing device 1 is realized by a computer such as a PC (Personal Computer). The information processing device 1 includes a control unit 11, an input / output interface 12, and a storage unit 13. The control unit 11, the input / output interface 12, and the storage unit 13 are connected to each other via a bus so as to be able to communicate with each other.

[0030] The control unit 11 controls the information processing device 1. The control unit 11 includes a hardware processor such as a central processing unit (CPU).

[0031] The input / output interface 12 is an interface that enables transmission and reception of information between the input device 2 and the output device 3. The input / output interface 12 may include a wired or wireless communication interface. That is, the information processing device 1, the input device 2, and the output device 3 may transmit and receive information via a network such as a LAN or the Internet.

[0032] The storage unit 13 is a storage medium. The storage unit 13 is configured by combining a nonvolatile memory that can be written to and read from at any time, such as a hard disk drive (HDD) or a solid state drive (SSD), a nonvolatile memory such as a read-only memory (ROM), and a volatile memory such as a random access memory (RAM). The storage unit 13 has a storage area including a program storage area and a data storage area. The program storage area stores an operating system (OS), middleware, and application programs required to execute various processes.

[0033] The input device 2 includes, for example, a keyboard, a pointing device, etc., which are used by the owner of the information processing device 1 (for example, a user, an administrator, or a supervisor) to input instructions to the information processing device 1. The input device 2 may also include a reader for reading data to be stored in the storage unit 13 from a memory medium such as a USB memory, or a disk device for reading such data from a disk medium. The input device 2 may also include an image scanner.

[0034] The output device 3 includes a display that displays output data to be presented to the owner from the information processing device 1, a printer that prints the output data, etc. The output device 3 may also include a writer that writes data to be input to another information processing device 1 such as a PC or a smartphone onto a memory medium such as a USB memory, and a disk device that writes such data onto a disk medium.

[0035] Fig. 3 is a block diagram showing the software configuration of the information processing device 1 according to an embodiment in relation to the hardware configuration shown in Fig. 2. The storage unit 13 includes an acquired data storage unit 131, a processing result storage unit 132, and a learning result storage unit 133.

[0036] The acquired data storage unit 131 stores various data acquired by the acquisition unit 111 (described later) of the control unit 11. The data stored in the acquired data storage unit 131 includes observation data, set values ​​for numerical integration, and the like. The observation data includes at least the number of events (e.g., N) and the coordinates where each event occurs. The set values ​​for numerical integration include the evaluation score, evaluation score, and weighting coefficient for the numerical integration.

[0037] The processing result storage unit 132 stores data processed by the inverse M matrix processing unit 112, which will be described later. The processed data is stored in the form of, for example, the above-mentioned matrix Ω Ｊ＋２ This includes positive definite kernel functions such as the Inverse M-Matrix.

[0038] The learning result storage unit 133 stores the parameters of the estimation model learned by the model learning unit 113 (described later).

[0039] The control unit 11 includes an acquisition unit 111, an inverse M matrix processing unit 112, a model learning unit 113, and an output control unit 114. These functional units are realized by the hardware processor executing an application program stored in the storage unit 13.

[0040] The acquisition unit 111 acquires data necessary for learning the parameters of the estimation model, such as observed data and set values ​​in numerical integration, and stores the data in the acquired data storage unit 131 .

[0041] The inverse M matrix processing unit 112 calculates the matrix Ω calculated from the data acquired by the acquisition unit 111. Ｊ＋２ A positive definite kernel function that satisfies the condition that is an Inverse M-Matrix is ​​selected. Details of this selection process will be described later.

[0042] The model learning unit 113 calculates the parameters {z ｎ} Ｎ ｎ＝１ is learned based on an equivalent kernel function obtained from a positive definite kernel function. The details of the learning method will be described later.

[0043] The output control unit 114 calculates the parameters {z ｎ} Ｎ ｎ＝１ etc. are displayed on the display of the output device 3. For example, the data displayed on the display of the output device 3 is the parameters {z ｎ} Ｎ ｎ＝１ , the coordinates of the occurrence of the event contained in the observed data, the positive definite kernel function, and the set value of the numerical integration.

[0044] 4 is a flowchart showing an example of a processing operation of the information processing device 1 according to an embodiment. For example, the control unit 11 of the information processing device 1 reads and executes a program stored in the storage unit 13, thereby realizing the operation of this flowchart.

[0045] The operation may be started at any timing, for example, when the owner of the information processing device 1 issues an instruction to learn an estimation model via the input device 2.

[0046] In step ST101, the acquisition unit 111 acquires observation data. The acquired observation data is stored in the acquired data storage unit 131. Here, the acquired observation data includes the number of events (denoted as N) and the coordinates of the occurrence of the events (x １ , x ２ , ..., x Ｎ However, the number of dimensions of the event occurrence coordinates is arbitrary.

[0047] In step ST102, the acquisition unit 111 acquires the set values ​​of the numerical integration. For example, the acquisition unit 111 acquires the evaluation score (denoted as J) in the numerical integration, the evaluation score ((q １ , q ２ , …, q Ｊ )), and the weighting factor for numerical integration ((w １ , w ２ , ..., w Ｊ The acquisition unit 111 stores the set value of the numerical integration in the acquired data storage unit 131.

[0048] In step ST103, the inverse M-matrix processing unit 112 performs Inverse M-Matrix. For example, the inverse M-matrix processing unit 112 acquires the observed data and the set values ​​of the numerical integration stored in the acquired data storage unit 131. Then, the inverse M-matrix processing unit 112, which operates as a selection unit, selects the ((j+2)×(J+2)) matrix Ω defined by equation (5) and calculated from the observed data and the set values ​​of the numerical integration. Ｊ＋２ is an Inverse M-Matrix (for example, equation (6)).

[0049] For example, as described above, the inverse M matrix processing unit 112 calculates the evaluation score (q １ , q ２ , …, q Ｊ ) and the matrix Ω calculated from any two points (x, x') Ｊ＋２For the matrix, a positive definite Kernel function is selected such that all off-diagonal elements of the inverse matrix of the matrix are negative or zero. Furthermore, an equivalent Kernel function (e.g., expressed by Equation (4)) represented by the selected positive definite Kernel function and the set value of the numerical integration is designed to take a non-negative value. That is, the equivalent Kernel function is expressed by a predetermined integral equation (e.g., Equation (2)), and is expressed by the selected positive definite Kernel function, the evaluation score of the numerical integration, the evaluation score of the numerical integration, and the weighting coefficient of the numerical integration by approximating and solving the integral term of the predetermined integral equation with numerical integration.

[0050] Below are examples of how the inverse M-matrix processing unit 112 selects a positive definite kernel function. However, the selection method is not limited to these. When the coordinates at which an event occurs are one-dimensional, the matrix Ω is used for an exponential kernel function. Ｊ＋２ is always an Inverse M-Matrix. For example, a positive definite kernel function k(x, x') is expressed as follows:

[0051]

[0052] where τ and α are parameters of a positive definite kernel function.

[0053] ・If the following positive definite kernel function is used, regardless of the number of dimensions of the input data values, the matrix Ω Ｊ＋２ becomes an Inverse M-Matrix.

[0054]

[0055]

[0056] However, w ｍａｘ is the weighting factor for numerical integration (w １ , w ２ , ..., w ｊ ) shall be the largest weighting factor among them.

[0057] In step ST104, the model learning unit 113 learns an estimation model. The model learning unit 113 acquires the observed data, the set value of the numerical integration, and the positive definite Kernel function stored in the processing result storage unit 132. Based on the observed data and the equivalent Kernel function represented by the positive definite Kernel function k(x, x') and the set value of the numerical integration, the model learning unit 113 calculates the parameters {z ｎ} Ｎ ｎ＝１ is obtained by solving the simultaneous equations of Equation (3). That is, in one embodiment, the learning is performed by solving the simultaneous equations of Equation (3) to obtain the parameters {z ｎ} Ｎ ｎ＝１ The model learning unit 113 obtains the calculated parameters {z ｎ} Ｎ ｎ＝１ , the observed data, the set value of the numerical integration, and the positive definite kernel function k(x, x′) are stored in the learning result storage unit 133 .

[0058] In step ST105, the output control unit 114 outputs the estimated model of the intensity function. The output control unit 114 acquires the estimated model of the intensity function stored in the learning result storage unit 133, and controls the display of the output device 3 to display the acquired estimated model. For example, the output control unit 114 acquires the parameter {z ｎ} Ｎ ｎ＝１ , the coordinates of the occurrence of the event included in the observation data (x １ , x ２ , ..., x Ｎ ), positive definite kernel function k(x, x'), evaluation point of numerical integration (q １ , q ２ , …, q Ｊ ), and the weighting factor (w １ , w ２ , ..., w Ｊ ) on the display of the output device 3.

[0059] According to one embodiment, in a method for estimating an intensity function using a positive definite Kernel function, the equivalent Kernel function is designed to take a non-negative value, thereby improving the accuracy of estimating the intensity function.

[0060] Other Embodiments The present invention is not limited to the above-described embodiments. For example, the approximation method for solving equation (2) may be any approximation method capable of solving equation (2). Furthermore, the data displayed on the display of the output device 3 is not limited to the above, and may be any of the acquired data and calculated data.

[0061] The flow of each process described above is not limited to the procedures described, and the order of some steps may be changed, or some steps may be performed simultaneously in parallel. Furthermore, the series of processes described above do not need to be performed consecutively, and each step may be performed at any timing.

[0062] Furthermore, the techniques described in the above embodiments can be stored as a program (software means) that can be executed by a computer on a storage medium such as a magnetic disk (e.g., a floppy disk, a hard disk, etc.), an optical disk (e.g., a CD-ROM, a DVD, an MO, etc.), or a semiconductor memory (e.g., a ROM, a RAM, a flash memory, etc.), and can also be distributed by transmitting it via a communication medium. The program stored on the medium also includes a configuration program that configures the software means (including not only execution programs but also tables and data structures) that the computer executes. The computer that realizes this device loads the program stored on the storage medium and, in some cases, configures the software means using the configuration program, and executes the above-mentioned processing by controlling the operation of this software means. Note that the term "storage medium" as used herein is not limited to storage media for distribution, but also includes storage media such as magnetic disks and semiconductor memories installed inside the computer or in devices connected via a network.

[0063] In short, this invention is not limited to the above-described embodiments, and various modifications can be made in the implementation stage without departing from the spirit of the invention. Furthermore, the embodiments may be implemented in combination as appropriate as possible, and in such cases, the combined effects can be obtained. Furthermore, the above-described embodiments include inventions at various stages, and various inventions can be extracted by appropriately combining the disclosed multiple constituent elements.

[0064] REFERENCE SIGNS LIST 1... Information processing device 11... Control unit 111... Acquisition unit 112... Inverse M matrix processing unit 113... Model learning unit 114... Output control unit 12... Input / output interface 13... Storage unit 131... Acquired data storage unit 132... Processing result storage unit 133... Learning result storage unit 2... Input device 3... Output device

Claims

1. An information processing device comprising: an acquisition unit that acquires observation data including the number of events and the coordinates at which the events occur, and a set value of a numerical integration including an evaluation point of the numerical integration; an inverse M-matrix processing unit that selects a positive definite Kernel function for a matrix calculated from the evaluation point of the numerical integration and any two points, such that all off-diagonal elements of the inverse matrix of the matrix are negative or zero; a model learning unit that learns parameters of an intensity function estimated using the positive definite Kernel function based on the observation data and an equivalent Kernel function represented by the positive definite Kernel function and the set value of the numerical integration, assuming that the coordinates at which the events occur are observed; and an output control unit that outputs the parameters, the positive definite Kernel function, and the set value of the numerical integration.

2. The information processing device according to claim 1, wherein the set value of the numerical integration further includes an evaluation score of the numerical integration and a weighting coefficient of the numerical integration, and the equivalent kernel function is expressed by a predetermined integral equation, and is expressed by the positive definite kernel function, the evaluation score of the numerical integration, the evaluation point of the numerical integration, and the weighting coefficient of the numerical integration by approximating and solving the integral term of the predetermined integral equation with a numerical integration.

3. An information processing method executed by a processor of an information processing device, comprising: acquiring observation data including the number of events and the coordinates at which the events occur, and a set value of a numerical integration including an evaluation point of the numerical integration; selecting a positive definite Kernel function for a matrix calculated from the evaluation point and any two points, such that the off-diagonal elements of the inverse matrix of the matrix are all negative or zero; learning parameters of an intensity function estimated using the positive definite Kernel function assuming that the coordinates at which the events occur are observed, based on an equivalent Kernel function represented by the positive definite Kernel function and the set value of the numerical integration and the observation data; and outputting the parameters, the positive definite Kernel function, and the set value of the numerical integration.

4. An information processing program comprising instructions to be executed by a processor of an information processing device, the instructions comprising: acquiring observation data including the number of events and occurrence coordinates of the events, and a set value of numerical integration including an evaluation point of the numerical integration; selecting a positive definite Kernel function for a matrix calculated from the evaluation point and any two points, such that all off-diagonal elements of the inverse matrix of the matrix are negative or zero; learning parameters of an intensity function estimated using the positive definite Kernel function assuming that the occurrence coordinates of the events are observed, based on an equivalent Kernel function represented by the positive definite Kernel function and the set value of the numerical integration and the observation data; and outputting the parameters, the positive definite Kernel function, and the set value of the numerical integration.

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