JP7559959B2 - Model generation device, model generation method, and program - Google Patents

Description

The present invention relates to a model generation device, a model generation method, and a program for generating a model for analyzing the relationship between marked event sequences and covariates.

A statistical model is known for marked event sequences, where each event has a feature called a mark. In particular, we consider the presence of a separate covariate time series that influences the occurrence of the marked event sequence.

The above situation will be explained using an example of a neuronal firing sequence whose firing frequency changes in response to external stimuli. When measuring neuronal firing activity through an experiment, the neuron from which each firing occurred can be determined based on information about the potential waveform. By regarding the information that characterizes each firing as a mark, the firing sequence of multiple neurons can be represented as a single marked event sequence. To find out how a population of neurons of interest fires in response to external stimuli, the firing sequence with added features can be considered as a marked event sequence, and the time series of the external stimuli as a covariate, and the occurrence frequency of the marked event sequence can be estimated as a function of the covariate. Other examples are listed below.

<Earthquakes> The time of an earthquake's occurrence can be considered the time of the event, and the earthquake's magnitude and location can be considered the mark of the event. Other information that affects the occurrence of an earthquake corresponds to covariates, such as geology and strata.

<Purchase data> The date when the product was purchased can be considered the time when the event occurred, and the information about the purchased product can be considered the mark of the event. Other information that affects the popularity of the product corresponds to covariates, such as the number of views of the listed page and the number of links posted.

<Financial product trading> The time when a transaction is completed can be considered the time when an event occurs, and the brand and price of the traded financial product can be considered the mark of the event. Other information that affects the transaction of the financial product in question corresponds to covariates, such as the trading volume of other financial products and economic indices.

<Posts on social media> The time of posting on social media can be considered the time an event occurred, and the content and link relationships can be considered the mark of the event. Other information that influences SNS posts corresponds to covariates, such as the number of searches for a particular word or articles on a news site.

Next, the relevant technical fields are listed below.

(a) Marked point process model. A statistical model used to represent the distribution of an event sequence in which each event has features. The distribution of a marked point process is determined by a conditional intensity function, which is a function of the expected number of events occurring. When performing statistical modeling, a model equivalent to this conditional intensity function is prepared in advance, and estimation is performed by maximizing an appropriate objective function.

(b) Variational Autoencoder (VAE). A generative model that uses a neural network. It is often used to generate data that is distributed on a high-dimensional manifold, such as images and videos. It assumes that there exists a latent variable that follows a certain prior distribution, and that data is generated by transforming that latent variable using a conditional distribution that includes a neural network. This conditional distribution is called a decoder.

(c) Variational inference. When the likelihood under a model cannot be explicitly written down, a family of distributions called variational posterior distributions is used to derive a lower bound on the likelihood, and parameters are estimated by maximizing this lower bound. In the case of VAE, a distribution that includes a neural network called an encoder is used. Lower bounds based on divergences other than the Kullback-Leibler divergence and methods that minimize the upper bound of the likelihood instead of maximizing the lower bound have also been proposed.

(d) State space model. A probabilistic model that is mainly applied to time series, it assumes that the values at each time point in the time series are generated independently from the underlying latent variables, and expresses the relationship between the latent variables by a joint distribution. From the observed time series, the posterior distribution of the underlying latent variables and the model parameters are learned. Recent research has proposed a black-box state space model in which part of the state space model is replaced with a neural network so that it can be applied to time series that evolve nonlinearly.

Non-Patent Document 1 is a document particularly relevant to the present invention. Non-Patent Document 1 discloses a method in which a firing sequence of multiple neurons is regarded as a marked event sequence, and external stimuli that may affect the firing activity are regarded as covariates, a joint intensity function (described later) is estimated by kernel density estimation, and the estimated joint intensity function is used to reconstruct the external stimuli from the firing sequence.

F Kloosterman, S P Layton, Z Chen, and M A Wilson, “Bayesian decoding using unsorted spikes in the rat hippocampus,” Journal of Neurophysiology, vol. 111, no. 1, pp. 217 - 227, 2014.

と定義される。ただし、k∈Kはマーク、N()は(0,T]×K上の計数測度、x_t∈X,t∈(0,T]は共変量の時系列、H_tは時刻tまでに得られた履歴の情報である。本発明では、マーク付き点過程のうち、非定常ポアソン過程で各時刻での発生頻度がその時刻での共変量の値の関数で表せるもののみを考える。このとき、条件付き強度関数は

のように、X×K上で定義されたある非負値関数λ(x,k)を使って表すことができる。このλ(x,k)は、共変量の値がxであるときに、マークがkであるようなイベントの単位時間当たりの発生数の期待値に相当する。以降、このλ(x,k)を同時強度関数とよぶことにする。 In order to explain the problem that the present invention aims to solve, the definition of a marked point process and its likelihood will be explained. A marked point process is a stochastic process that generates the above-mentioned marked event sequence. Since the distribution of a marked point process is determined by a conditional intensity function, to know the distribution, it is sufficient to estimate the conditional intensity function instead. The conditional intensity function is a function that corresponds to the expected value of the number of events per unit time given the past history, and

where k∈K is the mark, N() is the counting measure on (0,T]×K, x _t ∈X,t ∈(0,T] is the time series of the covariates, and H _t is the historical information obtained up to time t. In this invention, we consider only marked point processes that can be expressed as a function of the value of the covariates at that time in a nonstationary Poisson process. In this case, the conditional intensity function is

It can be expressed as follows, using a non-negative function λ(x,k) defined on X×K. This λ(x,k) corresponds to the expected number of occurrences per unit time of an event with mark k when the value of the covariate is x. Hereafter, this λ(x,k) will be called the joint intensity function.

のポアソン分布から生成する。そののち、λ(x_t,k)に比例する確率密度関数をもつ(0,T]×K上の分布に従って{(t_i,k_i)}ⁿ _i=1を選ぶ。したがって、{x_t}_t∈(0,T]が与えられたもとでの{(t_i,k_i)}ⁿ _i=1の確率は

となる。いま、共変量x_tは定間隔Δで観測されているとし、その時刻を{t_j}^m _j=1とする。このとき、{(t_i,k_i)}ⁿ _i=1が与えられたもとでの対数尤度は

となる。ただし、第二項は時間についての積分をx_tj, j=1,...,mによる和で近似した。推定の際は、あらかじめλ(x,k)のモデルを用意しておき、そのなかで上の対数尤度関数を最大にするものをもとめればよい。以下に、同時強度関数の推定の際の課題を列挙する。 Now, suppose that a sequence of marked events {(t _i ,k _i )} ⁿ _i=1 is observed on (0,T]×K. Then, a sequence of marked events according to the joint intensity function λ(x,k) can be generated by the following procedure. First, the total number of events n is calculated by the average

Then, choose {(t _i ,k _i )} ⁿ _i=1 according to a distribution on (0,T]×K with a probability density function proportional to λ(x _t ,k). Thus, the probability of {(t _i ,k _i )} ⁿ _i=1 given {x _t } _t∈(0,T] is

Now, suppose that the covariate _xt is observed at regular intervals Δ, and the time is { _tj } ^mj ₌₁ . In this case, the log likelihood given {( _ti , _ki )} ⁿⁱ ₌₁ is

where the second term is an approximation of the integral over time, expressed as the sum over x _tj , j=1,...,m. When estimating, a model of λ(x,k) is prepared in advance, and the one that maximizes the log-likelihood function above is found. The following are some of the challenges in estimating the joint intensity function.

<Challenge 1> Existing marked point process models can be broadly divided into two types: simple parametric models and models using neural networks. The former models are difficult to apply when the relationship between covariates and marks is unclear or when they are high-dimensional. The latter models are formulated for predicting events and are not suitable for predicting covariates. In addition, they use a simple distribution for the marks and cannot express complex distributions.

<Problem 2> The likelihood of a marked point process includes an integral term with respect to the mark. Therefore, when the joint intensity function is expressed by a neural network, the likelihood calculation itself becomes difficult.

<Issue 3> State space models including neural networks are useful for modeling the generation process of covariates that evolve nonlinearly over time. However, when using such models, the true joint intensity function in the space of latent variables is determined data-driven by the neural network, making it difficult to prepare an appropriate model for the joint intensity function in advance.

In view of the above problems, the present invention aims to provide a model generation device capable of generating a model that expresses the relationship between marked event sequences and covariates with high accuracy.

The model generation device of the present invention includes a model memory unit, a marked event sequence latent variable time series calculation unit, a marked event sequence marginal distribution parameter calculation unit, and an event sequence model parameter update unit.

The model memory unit is a simultaneous intensity function model including an inference model and a generation model, and stores a simultaneous intensity function model that expresses the simultaneous probability density function when the simultaneous intensity function of a marked event series is expressed as the product of a scale parameter and a simultaneous probability density function, using a decoder including a neural network.

The marked event sequence latent variable time series calculation unit inputs a marked event sequence and the time series of the corresponding covariate latent variables into the inference model and calculates the time series of the latent variables for the marked event sequence.

The marked event sequence marginal distribution parameter calculation unit inputs the time series of the latent variables of the marked event sequence into the generative model and calculates the parameters of the marginal distribution of the marked event sequence.

The event sequence model parameter update unit uses parameters of the marginal distribution of the marked event sequence to update the parameters of the generative model and the inference model so as to increase the lower bound of the likelihood of the marked event sequence.

The model generation device of the present invention can generate a model that represents the relationship between marked event sequences and covariates with high accuracy.

FIG. 2 is a block diagram showing the functional configuration of the marked event sequence analyzer according to the first embodiment. 4 is a flowchart showing the operation of the marked event sequence analyzer according to the first embodiment. FIG. 4 is a block diagram showing the functional configuration of a parameter estimation unit according to the first embodiment. 4 is a flowchart showing an operation of a parameter estimation unit according to the first embodiment. FIG. 2 is a block diagram showing a functional configuration of a marked event sequence prediction unit according to the first embodiment. 4 is a flowchart showing the operation of a marked event sequence prediction unit according to the first embodiment. FIG. 2 is a block diagram showing the functional configuration of a covariate time series prediction unit according to the first embodiment. 11 is a flowchart showing the operation of a covariate time series prediction unit according to the first embodiment. FIG. 2 is a diagram showing an example of the functional configuration of a computer.

Hereinafter, an embodiment of the present invention will be described in detail. Components having the same functions are given the same numbers, and duplicate explanations will be omitted.

In the following examples, we will only consider the case where the conditional intensity function can be expressed as a function of the covariates and the marks. This function is called the joint intensity function, and is used to predict a marked event sequence given a covariate, or to predict a covariate given a marked event sequence.

ニューラルネットワークを利用することで、高次元かつ背後の関係性が未知である共変量とマーク付きイベント系列にも事前知識なしで適用できる（課題１）。また、ＶＡＥの定式化にならうことで，尤度に含まれるマークの積分を低次元の潜在変数上での積分に置き換えることができる（課題２）。 The marked event sequence analyzer of this embodiment uses a joint intensity function model using VAE. The joint intensity function model decomposes the joint intensity function of a marked event sequence into a product of a scale parameter and a joint probability density function as follows, and expresses the decomposed joint probability density function using a decoder _pθ (x,k|z) including a neural network.

By using neural networks, it can be applied to high-dimensional covariates and marked event sequences with unknown underlying relationships without prior knowledge (Problem 1).Furthermore, by following the VAE formulation, the integral of the marks included in the likelihood can be replaced with an integral over low-dimensional latent variables (Problem 2).

尤度の最大化をその下限の最大化に置き換えることで、安定したパラメータ推定が可能となる（課題２）。 In the marked event sequence analysis apparatus of this embodiment, under the above-mentioned model, a lower bound on the likelihood is derived using two encoders q _φ (z|x, k) and q _φ (z|x) as follows, and parameters are estimated by maximizing this lower bound.

By replacing the maximization of the likelihood with the maximization of its lower bound, stable parameter estimation becomes possible (problem 2).

The marked event sequence analysis device of this embodiment estimates a joint intensity function under covariates that evolve nonlinearly over time by combining the above-mentioned model with a state space model for covariate time series. By using a state space model including a neural network, it is possible to estimate a joint intensity function in a data-driven manner for any covariate time series, and it is also possible to predict a covariate time series from a marked event sequence (Problem 3).

Below, with reference to Figure 1, the functional configuration of the marked event sequence analysis device of Example 1 using a joint intensity function model using VAE is explained.

As shown in the figure, the marked event sequence analysis device 1 of this embodiment includes a model storage unit 10, a parameter estimation unit 11, a marked event sequence prediction unit 12, and a covariate time series prediction unit 13. Since the model parameters can be updated by the model storage unit 10 and the parameter estimation unit 11, the marked event sequence prediction unit (device) 12 and the covariate time series prediction unit (device) 13 may be connected as separate devices to the model generation device 5 that includes only these functional components (10, 11).

The models used by the marked event sequence analysis device 1 of this embodiment are divided into two: a joint intensity function model for marked event sequences and a state space model for covariate time series.

The joint intensity function model for marked event sequences includes two inference models (first and second inference models) and a generative model. The state space model for covariate time series includes an estimation model and a generative model.

The generative model describes the generation process of marked event sequences and covariate time series. The inference model is introduced as an auxiliary to estimate the parameters of the generative model and approximates the posterior distribution of latent variables given observed data.

[Model storage unit 10]
The model storage unit 10 pre-stores a joint intensity function model for marked event sequences and a state space model for covariate time series.

[Parameter Estimation Unit 11]
The parameter estimation unit 11 derives a lower limit of the likelihood based on a model stored in advance in the model storage unit 10, and estimates parameters by maximizing the lower limit (S11, FIG. 2).

The parameter estimation unit 11 estimates the parameters of the above model under the condition that the marked event sequence and the covariate time series are given. First, the inference model is used to calculate the lower bound of the likelihood of the generative model. The parameters of the generative model and the inference model are estimated by maximizing this lower bound of the likelihood using a stochastic gradient method.

3, the parameter estimation unit 11 includes a covariate latent variable time series calculation unit 111, a covariate marginal distribution parameter calculation unit 112, a covariate model parameter update unit 113, a marked event sequence latent variable time series calculation unit 114, a marked event sequence marginal distribution parameter calculation unit 115, and an event sequence model parameter update unit 116. Below, the detailed operation of each functional configuration will be described with reference to FIG. 4.

<Covariate latent variable time series calculation unit 111>
The covariate latent variable time series calculation unit 111 inputs the covariate time series to a covariate time series inference model, and calculates the time series of the latent variable of the covariate (S111).

<Covariate marginal distribution parameter calculation unit 112>
The covariate marginal distribution parameter calculation unit 112 inputs the time series of the latent variables of the covariates calculated in S111 into a generation model of the covariate time series, and calculates parameters of the marginal distribution of the covariates (S112).

<Covariate model parameter update unit 113>
The covariate model parameter update unit 113 calculates a lower limit of the likelihood of the covariate time series using the parameters of the marginal distribution of the covariates calculated in S112, and updates the parameters of the generative model and the inference model of the covariate time series so as to increase the lower limit of the likelihood (S113).

<Marked Event Series Latent Variable Time Series Calculation Unit 114>
The marked event series latent variable time series calculation unit 114 inputs the time series of the latent variables of the covariates calculated in the corresponding step S111 and the corresponding marked event series into two inference models (first and second inference models) for the marked event series, and calculates the time series of the latent variables of the marked event series (S114).

<Marked Event Sequence Marginal Distribution Parameter Calculation Unit 115>
The marked event sequence marginal distribution parameter calculation unit 115 inputs the time series of the latent variables of the marked event sequence calculated in step S114 into a generative model for the marked event sequence, and calculates parameters of the marginal distribution of the marked event sequence (S115).

<Event sequence model parameter update unit 116>
The event sequence model parameter update unit 116 calculates a lower limit of the likelihood of the marked event sequence using the parameters of the marginal distribution of the marked event sequence calculated in step S115, and updates the parameters of the generative model and the inference model for the marked event sequence so as to increase the lower limit of the likelihood (S116).

The parameter estimation unit 11 repeats the processing of steps S111 to S116 until convergence. The parameter estimation unit 11 outputs the converged parameters.

[Marked event sequence prediction unit 12]
The marked event sequence prediction unit 12 uses the parameters estimated by the parameter estimation unit 11 to calculate a predictive distribution of the marked event sequence given the covariate time series (S12).

As shown in Fig. 5, the marked event sequence prediction unit 12 includes a covariate latent variable time series calculation unit 121 and a marked event sequence prediction distribution calculation unit 122. Below, the detailed operation of each functional component will be described with reference to Fig. 6.

<Covariate latent variable time series calculation unit 121>
The covariate latent variable time series calculation unit 121 inputs the covariate time series to an inference model for the covariate time series, and calculates the time series of the latent variable of the covariate (S121).

<Marked Event Sequence Prediction Distribution Calculation Unit 122>
The marked event sequence predictive distribution calculation unit 122 calculates and outputs a predictive distribution of the marked event sequence from the time series of the latent variables of the covariates calculated in S121 and the generative model and inference model for the marked event sequence (S122).

[Covariate time series prediction unit 13]
The covariate time series prediction unit 13 uses the parameters estimated by the parameter estimation unit 11 to calculate the predictive distribution of the covariate time series given the marked event series (S13).

As shown in Fig. 7, the covariate time series prediction unit 13 includes a predictive distribution initialization unit 131, a predictive distribution update unit 132, and a predictive distribution output unit 133. Below, the detailed operation of each functional component will be described with reference to Fig. 8.

<Predictive distribution initialization unit 131>
The predictive distribution initialization unit 131 initializes the predictive distribution for the time series of the latent variables of the covariates (S131).

<Predictive distribution update unit 132>
The predictive distribution update unit 132 updates the predictive distribution using the generative model and inference model for the marked event series and the generative model for the covariate time series (S132). The predictive distribution update unit 132 repeats the process of step S132 until convergence (convergence?: Y→S133, N→S132).

<Prediction distribution output unit 133>
The predictive distribution output unit 133 inputs the predictive distribution that converged in step S132 into a generative model for the covariate time series, calculates parameters of the marginal distribution of the covariate time series, and outputs a distribution corresponding to the obtained parameters as the predictive distribution of the covariate time series (S133).

<Additional Notes>
The device of the present invention has, as a single hardware entity, an input section to which a keyboard or the like can be connected, an output section to which a liquid crystal display or the like can be connected, a communication section to which a communication device (for example, a communication cable) capable of communicating with the outside of the hardware entity can be connected, a CPU (which may also have a central processing unit, cache memory, registers, etc.), memories such as RAM and ROM, an external storage device such as a hard disk, and a bus connecting the input section, output section, communication section, CPU, RAM, ROM, and external storage device so that data can be exchanged between them. If necessary, the hardware entity may also be provided with a device (drive) capable of reading and writing recording media such as a CD-ROM. A physical entity equipped with such hardware resources is, for example, a general-purpose computer.

The external storage device of the hardware entity stores the programs required to realize the above-mentioned functions and the data required in processing these programs (not limited to an external storage device, but for example the programs may be stored in a ROM, which is a read-only storage device). Data obtained by processing these programs is stored appropriately in RAM, an external storage device, etc.

In a hardware entity, each program stored in an external storage device (or ROM, etc.) and the data required to process each program are loaded into memory as needed, and interpreted, executed, and processed by the CPU as appropriate. As a result, the CPU realizes a specified function (each of the components represented as the above, ... unit, ... means, etc.).

The present invention is not limited to the above-described embodiments, and appropriate modifications can be made without departing from the spirit of the present invention. Furthermore, the processes described in the above embodiments are not limited to being executed chronologically in the order described, but may be executed in parallel or individually depending on the processing capacity of the device executing the processes or as necessary.

As mentioned above, when the processing functions of the hardware entities (the devices of the present invention) described in the above embodiments are realized by a computer, the processing contents of the functions that the hardware entities should have are described by a program. Then, by executing this program on a computer, the processing functions of the hardware entities are realized on the computer.

The various processes described above can be implemented by loading a program that executes each step of the above method into the recording unit 10020 of the computer 10000 shown in Figure 9, and operating the control unit 10010, input unit 10030, output unit 10040, etc.

The program describing the processing contents can be recorded on a computer-readable recording medium. Examples of computer-readable recording media include magnetic recording devices, optical disks, magneto-optical recording media, and semiconductor memories. Specifically, for example, hard disk drives, flexible disks, and magnetic tapes can be used as magnetic recording devices; DVDs (Digital Versatile Discs), DVD-RAMs (Random Access Memory), CD-ROMs (Compact Disc Read Only Memory), and CD-Rs (Recordable)/RWs (ReWritable) can be used as optical disks; MOs (Magneto-Optical discs) can be used as magneto-optical recording media; and EEP-ROMs (Electrically Erasable and Programmable-Read Only Memory) can be used as semiconductor memories.

The program may be distributed, for example, by selling, transferring, lending, etc. portable recording media such as DVDs and CD-ROMs on which the program is recorded. Furthermore, the program may be distributed by storing the program in a storage device of a server computer and transferring the program from the server computer to other computers via a network.

A computer that executes such a program, for example, first stores the program recorded on a portable recording medium or the program transferred from a server computer in its own storage device. Then, when executing a process, the computer reads the program stored on its own recording medium and executes the process according to the read program. As another execution form of this program, the computer may read the program directly from the portable recording medium and execute the process according to the program, or may execute the process according to the received program each time a program is transferred from the server computer to this computer. In addition, the server computer may not transfer the program to this computer, but may execute the above-mentioned process by a so-called ASP (Application Service Provider) type service that realizes the processing function only by issuing an execution instruction and obtaining the results. Note that the program in this embodiment includes information used for processing by an electronic computer that is equivalent to a program (such as data that is not a direct command to the computer but has a nature that specifies the processing of the computer).

In addition, in this embodiment, a hardware entity is constructed by executing a specific program on a computer, but at least a portion of these processing contents may also be realized by hardware.

Claims (4)

a model storage unit that stores a joint intensity function model including an inference model and a generation model, the joint intensity function of a marked event sequence being expressed as a product of a scale parameter and a joint probability density function, the joint intensity function model being expressed using a decoder including a neural network;
a marked event sequence latent variable time series calculation unit that inputs the marked event sequence and a time series of a latent variable of the corresponding covariate to the inference model and calculates a time series of a latent variable of the marked event sequence;
a marked event sequence marginal distribution parameter calculation unit that inputs a time series of latent variables of the marked event sequence into the generative model and calculates parameters of the marginal distribution of the marked event sequence;
an event sequence model parameter update unit that updates parameters of the generative model and the inference model using parameters of a marginal distribution of the marked event sequence so as to increase a lower limit of the likelihood of the marked event sequence. 2. The model generating device according to claim 1,
The model storage unit includes:
A state space model including an inference model and a generation model in addition to the joint intensity function model, the state space model for the covariate time series being stored;
a covariate latent variable time series calculation unit that inputs the covariate time series into a covariate time series inference model and calculates a time series of a latent variable of the covariate;
a covariate marginal distribution parameter calculation unit that inputs a time series of the latent variables of the covariates into a generation model of the covariate time series and calculates parameters of the marginal distribution of the covariates;
a covariate model parameter update unit that updates parameters of a generation model and an inference model of the covariate time series using parameters of the marginal distribution of the covariate so as to increase a lower limit of the likelihood of the covariate time series. a simultaneous intensity function model including an inference model and a generation model, the simultaneous intensity function of a marked event sequence being expressed as a product of a scale parameter and a simultaneous probability density function, the simultaneous intensity function model being expressed using a decoder including a neural network;
a marked event sequence latent variable time series calculation step of inputting the marked event sequence and a time series of latent variables of the corresponding covariates into the inference model and calculating a time series of latent variables of the marked event sequence;
a marked event sequence marginal distribution parameter calculation step of inputting a time series of latent variables of the marked event sequence into the generative model and calculating parameters of the marginal distribution of the marked event sequence;
an event sequence model parameter updating step of updating parameters of the generative model and the inference model using parameters of a marginal distribution of the marked event sequence so as to increase a lower bound of the likelihood of the marked event sequence;
A model generation method executed by a model generation device. A program that causes a computer to function as a model generation device as described in claim 1 or 2.

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