JPH10111862A - Device for analyzing time sequence based on recurrent neural network and its method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To estimate the probability distribution of time sequence data in a large scale problem at high speed by using the internal state of a neural network. SOLUTION: The realization value of a hidden state vector in a recurrent neural network which expresses a hidden Markovian model is generated as a 'particle' through the use of a Monte Carlo method. At first, (βn <(j)> ) of a time (n) is calculated in terms of recurrent from the forward prediction particle (pn <(j)> ) of the time (n), the backwards filtering particle (cn+1 <(j)> ) of the time n+1, observation data xn of the time (n) and the weighting coefficient (βn+1 <(j)> )(S6). Then, the smoothing particle (uu <(j)> ) of the time (n) is generated by re-extracting the particle from (pn <(j)> )(S5). Processings S5 and S6 are repeated so as to calculate the aggregation string of the smoothing particles and a probability distribution function is synthesized.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a time series analysis apparatus and method for estimating a probability distribution from given time series data by using an internal state of a neural network.

[0002]

2. Description of the Related Art Hidden Markov models
The del: HMM) method is one of the analysis methods widely used in speech recognition and secondary structure analysis of genes. The Markov model refers to a state transition model in which the transition probability to a certain state depends on the previous state. In the hidden Markov model, a change in the amount of observation caused by such a state transition is observed, but the state itself is not observed.

To date, various enhancements have been made to compensate for the lack of expressiveness of the Hidden Markov Model. The main extensions are summarized below. (1) Same expression form as ordinary hidden Markov model a. As an observation model, an HMM-COD (continuous density function) assuming a continuous probability density function such as a Gaussian density function is used.
ty function model (BH Juang, Ste
phen E. Levinson and MM Sondhi. Maximum Likel
ihood Estimation for Multivariate Mixture Observat
ions of Markov Chains.IEEE Transactions on Infor
mation Theory, IT-32 (2): 307-309, 1986.).

B. HM using an autoregressive model with Gaussian noise as an observation model
Method using M-AR model (BH Juang and LR
Rabiner. Mixture autoregressive hidden Markov mod
el for speech signal.IEEE Transactions on Acoust
ic Speech Signal Processing, ASSP-33 (6): 1401-1413,
1985.).

C. A method using a model (nonexponential-HMM) in which the time remaining in one state follows various distributions (Stephen E. Levinson. Continuously variable dura)
tionhidden Markov models for automatic speech reco
gnition. Computer, Speech and langauge 1 (1): 29-4
5 1986.). (2) Expression form by neural network Simple Recurrent Neural Network (SRN) for calculating probability distribution
N), calculation method of general hidden Markov model (Sakakibara Yasubumi and Mostefa Golea. Simple R
ecurrent Networksas Generalized Hidden markov Mode
ls with Distributed Representations. InProceeding
s of International Conference on Neural Networks (I
CNN'95), volume 2, pages 979-984. IEEE, 1995.).

[0006] The SRNN model is similar to the HMM-COD model in that a Gaussian density function is adopted as an observation model. In the HMM-COD model, the state transition probability is given by a numerical value. Therefore, in the parameter estimation of the model, this numerical value is directly estimated. In addition, a variance expression is not explicitly given to a statistic such as a hidden state vector (hidden variable vector) or an average value of observation data. Here, the distributed expression means an expression obtained by superimposing a plurality of distributions.

On the other hand, in the SRNN, the state transition probability is obtained as a non-linear function of the parameters of each neuron, and the statistic of the observation data is expressed in a distributed manner as the parameters of each neuron. For example, the average value of observation data is given by superimposing several parameters corresponding to a plurality of internal states represented by a hidden state vector.

[0008] Therefore, in the SRNN model, it is possible to delicately change the average value and the like of the observation data, and the expression power is higher than that of the HMM-COD model. It is also easy to extend this like an HMM-AR model or a nonexponential-HMM model.

FIG. 35 shows a schematic configuration of the SRNN.
You. In FIG. 35, the network parameter unit 2
Is c time-series data at time n
x_n ¹,. . . , X_n ^c Is input from the input layer 1 and the time n
K data h which is the output of the hidden element layer 3 at -1
_n-1 ¹,. . . , H_n-1 ^kIs input from the context layer 4.

[0010] These input data are appropriately weighted by the network parameter section 2 and the hidden element layer 3
Is input to The hidden element layer 3 is composed of k hidden elements, and outputs a hidden state vector (h _n ¹ ,..., H _n ^k ) having k elements. This hidden state vector is temporarily stored in the context layer 4 and is stored at the next time n + 1.
To the network parameter unit 2 at

This SRNN has no output to the outside,
The internal state at each time is represented by the value of the hidden state vector. This internal state includes the time series data x _n ¹ ,. . . , X _n ^c are used to define the energy function that defines the probability distribution. This model is
It corresponds to a configuration for calculating the probability distribution of time-series data in consideration of all transition paths of the hidden state vector of the RNN.

In FIG. 35, since the context layer 4 is composed of one register, it is called a simple recursive neural network. In a general recursive neural network, the context layer 4 is composed of a plurality of register layers. Be composed.

By the way, for a filter particle that performs recursive calculation, a probability density function can be approximately calculated from the operation of the neural network. However, in general, it is difficult to associate the operation of the neural network with the probability density function, and this is an issue to be solved in the future.

[0014]

However, the conventional method of calculating a probability distribution using SRNN has the following problems.

The SRNN is superior in expression power to the ordinary hidden Markov model, but is inferior in computational efficiency. In particular, for a large-scale problem such as a problem in which the dynamic range of observation data is wide, the calculation time becomes an exponential function of the number of elements. The reason is as follows.

In the conventional calculation method, it is necessary to perform a recursive calculation of a predicted density function, a filtered density function, and a smoothed density function by an SRNN having k hidden elements on the observation data sequence. These recursive computations are called forward computation, backward computation, and optimal hidden state estimation, respectively, in the field of Hidden Markov Model research.

In the recursive calculation, an evaluation calculation such as a predicted density function must be performed using a transition probability distribution between all hidden states. However, since the hidden state vector of the SRNN having k hidden elements can take 2 ^k different values, it has the corresponding 2 ^k hidden states as internal states. Therefore, as k increases, SRNN
In the direct calculation of, efficient recursive calculation cannot be performed. In fact, it is almost impossible to evaluate a large-scale problem in a realistic calculation time.

Therefore, if the amount of calculation is reduced by reducing the value of k, the number of hidden elements is reduced, so that the variation of the statistic that can be expressed is limited. Therefore, S
The ability of RNN, which is an advantage of RNN, cannot be used effectively.

An object of the present invention is to provide a time series analysis apparatus and method capable of quickly estimating a probability distribution of time series data in a large-scale problem using an internal state of a recursive neural network. That is.

[0020]

FIG. 1 is a diagram showing the principle of a time-series analyzer according to the present invention. 1 is used in an information processing apparatus that calculates a hidden Markov model represented by using a neural network, and includes a storage unit 11, a generation unit 12, and an estimation unit 13.

The storage means 11 stores the state transition probability of the internal state of the recurrent neural network expressing the probability distribution of the observation data. The generation unit 12 generates a hidden variable realization value that defines the internal state by the Monte Carlo method using the state transition probability.

The estimating means 13 estimates the probability distribution of the observation data using the actual value. The state transition probability stored in the storage unit 11 is a probability that when a plurality of internal states are represented by a plurality of realization values of a hidden state vector, a transition from a state represented by a certain realization value to a state represented by another realization value is obtained. means. This state transition probability is stored, for example, as an element of a state transition probability matrix as shown in FIG.

The state transition probability matrix of FIG. 1 corresponds to a k-dimensional hidden state vector, whose dimension 2 ^k corresponds to the number of possible hidden state vector realizations. Each element of the realization value of the hidden state vector becomes the realization value of the hidden variable. In this state transition probability matrix, an element p at i row and j column
_ij (i = 1,..., 2 ^k , j = 1 ^,.
Represents the probability of transition from the state represented by the j-th realization value to the state represented by the i-th realization value.

The Monte Carlo method used here is
This means a method of approximately calculating a probability distribution function describing a probability distribution of observation data using a plurality of realization values of a hidden state vector. If the Monte Carlo method is used, the calculation of the probability distribution function with a high calculation load can be replaced with a simple approximation calculation, and the recursive calculation of the neural network can be speeded up. Therefore, it becomes possible to apply SRNN to a large-scale problem.

According to the Monte Carlo method, the generation means 12 receives a given realization value corresponding to a certain state,
A column of the state transition probability matrix corresponding to the realization value is read out, and a realization value corresponding to another state is generated according to the elements p _ij (i = 1,..., 2 ^k ) of the column.

Then, the estimating means 13 synthesizes a probability distribution function for each time using a set of actualized values for each time, and outputs them as a sequence of probability distribution functions. If the output probability distribution function sequence is graphed and displayed, the probability distribution estimation result can be easily recognized.

For example, the storage unit 11 in FIG. 1 corresponds to the memory 32 in FIG.
Corresponds to the forward predicted particle generator 23, the smooth particle generator 24, and the backward predicted particle generator 25 in FIG. 8, and the estimating unit 13 corresponds to the display device 29.

[0028]

Embodiments of the present invention will be described below in detail with reference to the drawings. In the present invention, the SRN
For fast calculation of N, the available hidden state vectors are restricted to reduce the amount of calculation. Further, the calculation method proposed by Kitagawa is applied to the recursive calculation of the predicted density function, the filtration density function, the smoothed density function, and the like, and the likelihood calculation for the observed data, thereby speeding up the calculation based on SRNN.

Here, prediction refers to estimating the future state from information up to the present, filtering refers to estimating the current state from information up to the present, and smoothing refers to estimating the current state from the information up to the present. It is to estimate the past state from the information up to.

Kitagawa has proposed a calculation method (Monte Carlo method) for a nonlinear, non-Gaussian, multidimensional state space model (Genshiro Kitagawa. Non-Gaussian State-Spa).
ce Modeling of Nonstationary Time Series. Journal
of the American Statistical Association 82 (400):
1032-1041, 1987. / Genshiro Kitagawa. A Monte
Carlo Filtering and Smoothing Method for Non-Gauss
ian Nonlinear StateSpace Models. Research Memoran
dom 462 The Institute of Statistical Mathematics
12 1993.). The filter calculation by the Monte Carlo method is known at the schema level, and can be applied to many real problems.

In the present invention, this method is adopted as a method for calculating the SRNN specifically at high speed. If the Monte Carlo method is used, the recursive calculation can be significantly reduced by approximately calculating each probability density function described above with a large number of realization values. Therefore, it becomes possible to apply SRNN to a large-scale problem.

In addition, through simulation experiments on a large-scale problem, it was found that the number of hidden states actually used by the SRNN was very small. For this reason, it has been found that even if approximation using a small number of hidden states as a representative point is performed using the Monte Carlo method, the result of prediction or the like does not deteriorate. Therefore, by employing an approximation limited to a small number of hidden states, application to a large-scale problem becomes possible without impairing the expressive power of SRNN.

Incidentally, the calculation method of the present invention uses the SRNN
The purpose of this is to execute model analysis at high speed.
Model analysis is to approximately describe the probability structure of an information source that has generated an observation data sequence, and the problem is to select an appropriate parameter model and identify parameters for the observation data sequence.

Here, the input data of the SRNN at the time n is expressed as 外 1 (hereinafter, referred to as a vector x _n).

[0035]

[Outside 1]

Then, the sequence of the observation data from time 1 to N is represented by the ｛vector x ₁ ,. . . , Vector x _N ｝
Becomes Model analysis also refers to estimating the dynamics of a stochastic structure from observation data using an appropriate model. In the model analysis by SRNN, a hidden Markov model having a Gaussian density function, which is described by a parameter of a nonlinear function, is used as an observation model, and an appropriate parameter of the SRNN is identified for observation data. Once the appropriate parameters are determined, the transition probability between the most likely hidden state vectors and the average value of the Gaussian density function for the observed data can be calculated.

Further, a maximum likelihood hidden state vector sequence is identified for the observation data. In parameter identification, SRN
It is necessary to calculate a predicted density function sequence for observation data that can be calculated from the internal state of N, and to identify a maximum likelihood hidden state vector sequence, it is necessary to calculate a smooth density function sequence for observation data (Kitakawa Genshiro. Time series analysis programming, Iwanami Computer Science, Iwanami Shoten, 193
3. ). Calculating these density functions in a direct way is inefficient.

In the present calculation method, the number of hidden state vectors is limited, and each density function is replaced by a set of “particles” by the Monte Carlo method, thereby approximating the model efficiently.

Here, "particle" refers to a realization value of a hidden state vector generated according to each density function, and is a vector having the same dimension as the hidden state vector. Then, the value of each element (hidden variable) is 0 or 1. Therefore, the k-dimensional hidden state vector has 2 ^k "particles" as realized values.

Next, referring to FIGS. 2 to 4,
An outline of a process of calculating a predicted density function or a smoothed density function for an SRNN observation data sequence using “particles” of the Monte Carlo method will be described.

In FIGS. 2, 3 and 4,
g (vector x _n ; vector ω)

[0042]

[Outside 2]

Is a Gaussian density function of the vector x _n such that the vector ω is an average value and the variance matrix is a unit matrix. FIG. 2 shows a recursive generation process of the forward prediction particles and the forward filtration particles. Forward means generating particles according to the flow of time. Therefore, the forward predictive particle is a realized value of a hidden state vector representing the result of estimating the internal state after the specific time from the observation data up to the specific time, and the forward filtering particle is the observation value up to the specific time. It is a realization value of a hidden state vector representing a result of estimating the internal state at the specific time from the data. The processing flow of FIG. 2 is as follows.

Process S1: The m forward prediction particles {p _n ^(j) } (j = 1,..., M) at time n are converted to time n
From the m forward filtered particles {f _n-1 ^(j) } at −1 and the state transition probability matrix ３ (hereinafter referred to as p (vector h | vector h ′)).

[0045]

[Outside 3]

The following is achieved. Here, the forward prediction particle p _n ^(j)
And the forward filtering particles f _n-1 ^(j) are, for example, {0, 1,
1,0,. . . , 1} of the same dimension as the hidden state vector h. P (vector h | vector h ') represents the transition probability from the state corresponding to the hidden state vector h' to the state corresponding to the hidden state vector h.

Process S2: weight coefficient α _n ^(j) = g (vector x _n ; vector ω (p _n ^(j) ))
From the forward prediction particles {p _n ^(j) } at time n

[0048]

[Outside 4]

By re-extracting, the forward filtered particles {f _n ^(j) } at time n are generated. Here, the vector ω (p _n ^(j) ) representing the average value of the Gaussian density function is defined by the following equation.

[0050]

(Equation 1)

In the equation (1), (p _n ^(j) ) ⁱ is k
Represents the i-th element of the dimensional vector p _n ^(j) ,
(Hereinafter, referred to as the vector w _i) is a vector x _n i
Th

[0052]

[Outside 5]

Represents a weight vector to be multiplied when inputting to the hidden element. Therefore, the dimensions of the vector w _i are
It has the same dimension as the vector _xn . In FIG. 2, the forward filtering particles {f ₀ ^(j) } at time 0 are given as initial values, and the processes S1 and S2 are recursively repeated to calculate a set sequence of forward predicting particles. The set of particles means m particles at one time, and the set sequence means a time series of the set of particles.

Next, the time is traced back from time N to time n, and prediction and filtering of the past hidden state are calculated. FIG. 3 shows a recursive generation process of such backward predicted particles and backward filtered particles. Backward means that particles are generated against the flow of time. Therefore, the backward predicted particle is a realization value of a hidden state vector representing the result of estimating the internal state before the specific time from the observation data after the specific time, and the backward filtered particle is the observed value after the specific time. It is a realization value of a hidden state vector representing a result of estimating the internal state at the specific time from the data. The processing flow of FIG. 3 is as follows.

Process S3: backward predicted particle ｛en at time _n
^(j) ｝ is replaced by the backward filtered particles {c _{n + 1} ^(j)時刻 at time n + 1.
And a state transition probability matrix p (vector h / vector h ').

Outer 6, which is proportional to; (a vector ω ^(e _n ^(j)) vector x _n) weighting factor ε _n ^(j) = g: [0056] step S4
As a weight and the particles from the backward predicted particle at time _n {e n ^(j)}

[0057]

[Outside 6]

By re-extracting, backward filtered particles {c _n ^(j) } at time n are generated. The definition of the vector ω (e _n ^(j) ) is the same as in the equation (1). In FIG. 3, the backward filtered particles {c _{N + 1} ^(j) } at time N + 1 are given as initial values, and the processes S3 and S4 are recursively repeated to calculate a set of backward filtered particles.

Next, the observed data sequence {vector x ₁ ,. . . , U _n, which approximate the optimal probability density sequence on the hidden state vector, for the vector x _N }
^(j) {n = 1,. . . , N).

FIG. 4 shows the double filter method (Genshiro Kitag
awa.The two-filter formula forsmoothing and an i
mplementation of the Gaussian-sum smoother.Annal
s of the Institute of Statistical Mathematics 46
(4): 605-623, 1994.). The smooth particle is a realized value of a hidden state vector representing a result of estimating an internal state at one time within a specific time from observation data within a specific time. FIG.
Is as follows.

Process S5: weighting factor ｛β defined by the following equation
By re-extracting the particles from the predicted particles {p _n ^(j) } at time n according to the weight proportional to _n ^(j) ｝ (j = 1,..., m), the smooth particles at time n generating a {u _n ^(j)}.

[0062]

(Equation 2)

In the equation (2), d 'is a predetermined integer and 1≤d'≤m. Also, d ′ j
The value of _i is 1,. . . , M in any manner. The selection method of j _i may be changed according to the target problem.

Process S6: {β _{n + 1} ^(j) } at time n + 1
, The forward prediction particle {p _n ^{(j )} } at time n, and time n +
From the 1 backward filtered particles {c _{n + 1} ^(j) } and the vector x _n that is the observation data at time n, {β _n ^(j) } at time n is recursively calculated by equation (2). . At this time, ｛β
_The previously calculated {β _n ^(j) } is used as _{n + 1} ^(j) }.

Then, by repeating the processes S5 and S6 recursively, a set sequence of smooth particles is calculated. The meaning of the double filter method will be described later. next,
The processing algorithm shown in FIGS. 2 to 4 will be described in more detail. First, an energy function defining the operation of the SRNN and a state transition probability will be described.

[0066] at time n SRNN state, (vector h _n, the vector x _n) is represented by the state (vector h _n, the vector x _n) is the energy function defined above,

[0067]

(Equation 3)

It is known that the following is obtained. (3)
^Where h _n ^j is a k-dimensional hidden state vector h _n
, And the vector x _n is a c-dimensional vector. In addition, the model parameter vector λ in Expression (4) corresponds to the SRNN parameter held by the network parameter unit 2 in FIG.

The vector w _j represents the weight of the input from the input layer 1 to the j-th hidden element, the vector u _j represents the weight of the input from the context layer 4 to the j-th hidden element, and θ
_j represents the input bias to the j-th hidden element. The vector w _j is a c-dimensional vector like the vector x _n , and the vector u _j is a k-dimensional vector like the vector h _n .

The conditional joint probability distribution on (vector h _n , vector x _n ) determined by the energy function of equation (3) is given by the following equation.

[0071]

(Equation 4)

[0072] Here, the notation vector h _n ∈ {0, 1} ^k, which means that each element of the vector h _n is 0 or 1, the sum symbol Σ in this regard, a vector h _n
Means the sum of all 2 ^k possible values of Further, the vector ω (vector h _n ) is defined by the following equation, similarly to equation (1).

[0073]

(Equation 5)

The state transition density function p (vector h _n
| Vector h _n−1 , vector λ) is defined by the following equation.

[0075]

(Equation 6)

The joint probability distribution of equation (5) is
Number g (vector x_n; Vector ω (vector h_n))When
State transition density function p (vector h_n| Vector h_n-1,
Vector λ). This joint probability distribution
This is shown in FIG. In FIG.
Le h_nVector ω (vector
h _n) Values correspond to local maxima in the probability distribution.
I understand.

The system vector at time n (hidden state
State vector) h_nIs the previous state by Markov assumption
State transition probability distribution p (vector h_n| Vect
Le h _n-1, Vector λ).

Now, let us write 2 ^k possible values of the vector h _n as

[0079]

[Outside 7]

(Vector h _n | vector h _n−1 , vector λ) can be represented by a matrix as shown in FIG. In the state transition probability matrix of FIG. 6, the element p _ij (vector λ) at the i-th row and the j-th column represents the transition probability from the state corresponding to the vector h ^(j) to the state corresponding to the vector h ⁽ⁱ⁾ . Given a parameter vector λ, an arbitrary element p _ij (vector λ) of the state transition probability matrix can be calculated from equation (7).

The probability density function of the vector x _n given the hidden state vector h _n is given by:

[0082]

(Equation 7)

When the joint probability distribution of equation (5) is rewritten using equation (8),

[0084]

(Equation 8)

Is as follows. Hereinafter, the description of the parameter vector λ will be omitted in the formal conversion. Next, a method of deriving each density function of prediction, filtering, and smoothing in SRNN will be described. Here, with the aid of Kitagawa's filter schema, the parameter vector λ and the observed data sequence X _N = {vector x ₁ ,. . . , Vector x
_A method for calculating the log likelihood of SRNN when _N } is given and a method for estimating an optimal hidden state vector, that is, a method for estimating a smooth density function sequence, are derived.

First, when the forward prediction and the forward filtering with respect to the hidden state vector are calculated, the forward prediction density function becomes

[0087]

(Equation 9)

The forward filtration density function is:

[0089]

(Equation 10)

Is as follows. Here, X _n-1 = {vector x ₁ ,. . . , Vector x _n-1 }. Also, the predicted density function for the observed vector _xn is

[0091]

[Equation 11]

Is given by Therefore, the SR for the observation data sequence when the parameter vector λ is given
As the likelihood of the NN, for example, the sum of logarithmic values of the predicted density function calculated recursively can be used. This log likelihood is given by the following equation.

[0093]

(Equation 12)

Further, the filtration density function of the observed value is:

[0095]

(Equation 13)

Is as follows. Also, X _N ⁿ = {vector x _n ,. . . , Vector x _N }, the backward prediction density function becomes

[0097]

[Equation 14]

[0098] The backward filtration density function is

[0099]

(Equation 15)

Is as follows. Furthermore, the observation data sequence X _N
The optimal hidden state vector that can be estimated from is determined by the following smooth density function.

[0101]

(Equation 16)

From the right side of equation (17), the smooth density function p
(Vector h _n | X _N ) is obtained by calculating the weight p (X _N ⁿ | vector h _n ) and the forward prediction density function p (vector h _n |
X _N-1 ). This weight p (X
_N ⁿ | vector h _n ) can be further rewritten as:

[0103]

[Equation 17]

On the right side of the equation (18), p (vector
x_n| Vector h_n, X_N ^{n + 1}) Is p (vector x_n|
Vector h_n) Has been rewritten. This is a vector
Le h _nIs given, the vector x_nIs the probability distribution of
X_N ^{n + 1}= ｛Vector x_{n + 1},. . . ,
Kutor x_NThe observation data in｝ is unnecessary as a condition.
You.

At the bottom of the right side of equation (18), p (X _N
^{n + 1} | vector h _{n + 1} ), p (X _N ⁿ
It can be seen that the | vector h _n ) is calculated recursively.
Therefore, the hidden state vector can be selected as the maximum likelihood value of the smoothed density function at each time obtained by the recursive calculation.

However, there are a case where there are a plurality of peaks of the smooth density function, and a case where the variance of the smooth density function changes with time. In such a case, in order to prevent loss of information obtained from the smoothed density function sequence, it is preferable to use the smoothed density function sequence as an estimation result as it is, instead of obtaining the hidden state vector corresponding to the maximum likelihood value. .

Further, using the equation (18), p (X_N ⁿ|
Hector h_n), The vector h_{n + 1}
{0,1}^kP (X_N ^{n + 1}| Vect
Le h _{n + 1}) P (vector h_{n + 1}| Vector h_nSum of)
Must be calculated. For this reason, the Monte Carlo method
Calculation method that approximates expressions (17) and (18) using
Method, all forward-looking particles at each time must be stored.
Must. Therefore, the realized value of a high-dimensional vector
To save time, a huge memory space is required.

Therefore, instead of calculating the sum of Equation (18) as it is, there is a method of approximately calculating the sum using backward filtered particles. This is called a double filter method. 2
In the double filter method, the forward prediction particles at each time need only be generated recursively as needed, and the memory can be largely saved.

FIG. 7 shows an approximate calculation process of smooth particles based on the double filter method. In the double filter method, the smoothing particles {u _n ^(j)} at time n, as shown in FIG. 4, the forward prediction particles {p _n ^(j)} at time n and time n
+1 can be calculated using the backward filtered particles {c _{n + 1} ^{( j)} }.

[0110] In this way, back to order time from the time N, continue to produce blunt particles {u _n ^(j)}. At this time,
As shown in FIG. 3, the backward filtered particles {c _{n + 1} ^(j) } are obtained from the backward filtered particles {c _{n + 2} ^(j) } at time n + 2.
It is generated only through the backward prediction particle {en _{+ 1} ^(j) } at time n + 1. The backward filtered particles ｛c _{N + 1} ^{(j
) Since} ｝ is given as an initial value, backward filtered particles can be easily obtained.

On the other hand, as shown in FIG. 2, the forward prediction particle {p _n ^(j) } is calculated from the forward prediction particle {p _n-1 ^(j) } at time _n−1 at time n− 1 through the forward filtering particles {f _{n- 1} ^(j) }. However, since the forward filtration particles {f ₀ ^(j) } at time 0 are given as the initial values, the calculation of the forward prediction particles {p _n ^(j) } requires from time 1 to time n−1. It is necessary to sequentially obtain the forward prediction particles and the forward filtration particles.

For example, in STAGE 1 of FIG.
In order to calculate the smooth particle {u _N ^(j) } at time N, the backward filtered particle {c _{N + 1} ^(j) } at time N _{+ 1} and the forward predicted particle {p _N ^(j) } at time N are used. ing. In order to obtain the forward prediction particle {p _N ^(j) }, the calculation of the forward filter from time 1 to time N must be performed. However, thereafter, as the calculation proceeds to STAGE2 and STAGE3, the required amount of calculation of the forward filter decreases.

Here, the forward filter represents a calculation for alternately generating forward predicted particles and forward filtered particles, and the backward filter represents a calculation for alternately generating backward predicted particles and backward filtered particles. In the calculation in FIG. 7, both the forward filter and the backward filter are calculated, and this method is called a double filter method.

Next, a method for limiting the hidden state of the SRNN will be described. If all k hidden elements are used, 2 ^k hidden state vectors are available. However, it is empirically known that the number of hidden states used for expressing the dynamics of the system model is at most k. The probability that the remaining 2 ^k -k hidden states will be used is approximately equal to zero.

Therefore, it is desired to efficiently calculate each density function of SRNN by limiting the hidden state to be used in advance. However, how to choose an appropriate hidden state vector is a difficult problem.

For example, a set of hidden state vectors in which at most logk elements are 1 out of k elements of the hidden state vector can be considered. In this case, the size of the set is 2 ^logk / logk. This size is k
= 70,000, and k = 100, about 4,000,000, which is not practical for a large-scale circuit.

Also, sparse coding (Shun-ichi
Amari. Characteristics of Sparsely Encoded Associ
ative Memory.Neural Networks 2: 451-457, 1989.
/ Robert Hecht-Nielsen. Neurocomputing. Addison-
Wesley 1990.) may be used. In this case, the number of elements of the set of hidden state vectors is k ² / log k
About one. Therefore, if a set of hidden state vectors having a size of about k polynomials selected by an appropriate method can be selected according to observation data, it is expected that the efficiency of calculation will be increased.

Also, Freund et al. Show an algorithm for learning a feature map using a two-layer neural network introducing a hidden state vector (Yaov Frederick).
undand David Haussler. Unsupervised Learning of D
istribution over Binary Vectors using Two-layer ne
tworks. Technical report University of Californi
a Santa Cruz, 1994.).

The core projection algorithm uses k vectors h ^(j) out of 2 ^k hidden state vectors h.
｛Vector h ^(j) = (δ _j (1) _,.
(K)) Limited to | 1 ≦ j ≦ k}, it can be considered that the speed is increased. However, δ _j (i) becomes 1 only when i matches j, and becomes 0 in other cases. Therefore, the vector h ^(j) represents a hidden state vector in which only the j-th element is 1 and all other elements are 0.

In the present embodiment, the set of hidden state vectors to be used can be limited by any method including the above-mentioned limitation example. Then, in FIG. 6, the calculation amount can be reduced by setting the state transition probability corresponding to the unused hidden state vector to 0.

According to the calculation method for limiting the number of hidden state vectors, the amount of calculation can be reduced while maintaining the high expressiveness of SRNN by the high-dimensional hidden state vector. Therefore, in general, a better estimation result can be obtained as compared with the case where the calculation is performed using a low-dimensional hidden state vector from the beginning.

Next, a method of approximating each density function of SRNN by the Monte Carlo method will be described. Here, based on Kitagawa's Monte Carlo filter schema, SRN
A Monte Carlo calculation method of prediction, filtration, and smoothing density by N is derived. In the Monte Carlo method, the calculation is performed by replacing each density function with the above-mentioned “particle”.

The forward prediction particles {p _n ⁽¹⁾ ,. . . , P _n
^(m) ｝ is the forward prediction density function p (vector h _n |
X _n-1 ), which are generated according to the forward filtering particles {f _n ^{( 1)} ,. . . , F _n ^(m) } are the realized values generated according to the forward filtration density function p (vector h _n | X _n ).

Further, the backward prediction particles
｛E_n ⁽¹⁾,. . . , E_n ^(m)｝ Is the backward predicted density function
p (vector h_n｜ X_N ^{n + 1}Realization generated according to
Value, the backward filtered particles Δc_n ⁽¹⁾,. . . , C_n
^(m)｝ Is the backward filtration density function p (vector h_n|
X _N ⁿ).

[0125] Further, the smoothing particles {u _n ^(1),. . . , U _n
^(m) } is a realization value generated according to the smooth density function p (vector h _n | X _N ). The number m of particles is determined depending on the complexity of the model and the accuracy required for the estimator. First, a fixed value such as m = 1000 or 10000 is determined and adjusted. You can choose a value. The method of generating various “particles” necessary for calculating the SRNN by the Monte Carlo method is as follows.

Here, it is assumed that the state transition probability p (vector h ^{(i )} | vector h ^(j) ) is provided as a state transition table (state transition probability matrix) according to the above-described limiting method of Freund et al. The magnitude | H | of the set H of possible hidden state vectors is | H | = poly (k), that is, k polynomials. As k is larger, the effect of the Monte Carlo method can be expected.

The method for generating the forward prediction particle p _n ^(j) is as follows.

[0128]

(Equation 18)

Here, the symbol "-" indicates that the particles on the left side are generated according to the probability distribution on the right side. The method of generating the forward filtration particles f _n ^(j) is as follows.

[0130]

[Equation 19]

The right side of the equation (22) is the m forward prediction particles {p _n ⁽¹⁾ ,. . . , P _n ^(m) }, the corresponding probability α _n ^(j) / Σ _{i = 1} ^m α _n ⁽ⁱ⁾ (j =
1,. . . , M).

The method of generating the backward prediction particles e _n ^(j) is as follows.

[0133]

(Equation 20)

The method of producing the backward filtered particles c _n ^(j) is as follows.

[0135]

(Equation 21)

The method of generating the smooth particles u _n ^(j) is as follows.

[0137]

(Equation 22)

P (X _N ⁿ │ on the right side of equation (27)
p _n ⁽ⁱ⁾ ) corresponds to the weight p (X _N ⁿ | vector h _n ) in equation (17) and can be calculated by equation (2). Next, the configuration and operation of the time-series analysis device according to the present embodiment will be described with reference to FIGS.

FIG. 8 is a block diagram of a time-series analysis device incorporating the above-described SRNN high-speed calculation method. 8 includes a re-extraction device (RS) 21, a time-series data collection device (OBS) 22, a forward predictive particle generator (FPF) 23, a smooth particle generator (TFS) 24, and a backward predictive particle generator. Device (BPF) 25, likelihood calculating device (LLH) 26, learning device (LM) 27, model parameter setting device (PM) 28, and display device (PNT)
29.

The time-series data collection device 22 supplies time-series data to the forward prediction particle generation device 23, the smooth particle generation device 24, the backward prediction particle generation device 25, and the display device 29.

The forward predictive particle generator 23 includes a smooth particle generator 24, a likelihood calculator 26, and a display 29.
Is supplied to the set of forward prediction particles. In addition, the backward predicted particle generator 25 supplies a set of backward filtered particles to the smooth particle generator 24 and the display device 29.
In addition, the smooth particle generation device 24 supplies the display device 29 with a collection of smooth particles.

The re-extraction device 21 re-extracts the particles according to the weight set, and supplies the set of re-extracted particles to the forward predicted particle generator 23, the smooth particle generator 24, and the backward predicted particle generator 25.

The likelihood calculating device 26 calculates the likelihood of the model parameter from the set of predicted particles and supplies it to the learning device 27. Further, the learning device 27 searches for an optimal parameter based on the likelihood of the model parameter and supplies it to the model parameter setting device 28.

The model parameter setting device 28 supplies the state transition probability and the input weight vector as parameters to the forward predicted particle generator 23, the smooth particle generator 24, and the backward predicted particle generator 25.

The display device 29 calculates and displays a density function sequence from a set of particles, and also displays time-series data. The operation in which the time-series analysis device of FIG. 8 receives the observed time-series data sequence and outputs a smoothed density function sequence is as follows.

First, the time-series data collection device 22 operates as shown in FIG.
, A time-series data sequence {vector x ₁ ,. . . , Vector x _N } to the forward predicted particle generator 23, the smooth particle generator 24, the backward predicted particle generator 25, and the display 29.

Next, the forward predictive particle generator 23 calculates a set of forward predictive particles using the appropriate parameters supplied from the model parameter setting device 28 while using the re-extraction device 21. In addition, the backward predicted particle generation device 25 calculates a set of backward filtered particles while using the re-extraction device 21. The data flow related to the generation of the forward predicted particles is as shown in FIG. 10, and the data flow related to the generation of the backward filtered particles is as shown in FIG.

Next, the smooth particle generation device 24 generates a set of weights for re-extraction of the given smooth particles, a vector x _n which is observation data at time n, a set of forward prediction particles at time n,
From the set of backward filtered particles at time n + 1, a set sequence of weights for re-extraction of smooth particles is calculated. Then, the re-extraction device 21 is activated, and the set of forward prediction particles at time n is re-extracted according to the set of weights for re-extraction of smooth particles at time n, thereby generating a set of smooth particles at time n. The flow of data related to the generation of smooth particles is as shown in FIG.

Then, the display device 29 displays the obtained sequence of smooth particles as a smooth density function sequence. Also,
The parameter setting operation of the time series analyzer is as follows.

First, the likelihood calculating device 26 calculates the log likelihood as shown in the following equation based on the set of forward predictive particles, and calculates the log likelihood of the model parameter vector λ given by the equation (13). Approximate the degree l (vector λ).

[0151]

(Equation 23)

Next, the learning device 27 includes the likelihood calculating device 26
The maximum likelihood parameter vector λ that maximizes the likelihood is estimated using the gradient method, the simulated annealing method, or the like, based on the likelihood of the model parameter calculated in (1).

In this case, the gradient method (gradient method) is based on a derivative obtained by differentiating a likelihood with a parameter.
Refers to the method of obtaining the maximum likelihood parameter (Sakakibara Yasub
umiand Mostefa Golea.Simple Recurrent Networks a
s Generalized Hidden markov Models with Distribute
d Representations. In Proceedings of Internationala
l Conference on Neural Networks (ICNN'95), volume
2, pages 979-984. IEEE, 1995.).

The simulated annealing method is one of the iterative search methods in which starting from an appropriate parameter, if there is one that can improve the likelihood in the vicinity of the parameter, the operation of replacing it is repeated. However, in this method, even if nearby parameters cannot improve the likelihood,
Add an operation to replace it with a certain probability (Will
iam H. Press Saul A. Teukolsky, William T. Vetter
ling and Brian P. Flannery. NUMERICAL RECIPES in
C. The Art of Scientific Computing. Cambridge Un
iversity Press second edition 1992.).

The learning device 27 is not limited to these methods.
The maximum likelihood parameter can be determined by an arbitrary method.
Then, the model parameter setting device 28 uses the model parameter vector λ output from the learning device 27 on the basis of a predetermined condition for limiting the set H of hidden state vectors, and uses the state transition probability matrix M (H) Is calculated. Then, M (H), together with the weight vector w _j (j = 1,..., K) obtained by the learning device 27, the forward predicted particle generator 23, the smooth particle generator 24, and the backward predicted particle generator 25. The flow of data related to the generation and supply of parameters is as shown in FIG.

FIG. 14 is a configuration diagram of an information processing device (computer) that realizes the time-series analysis device of FIG. FIG.
4 includes a CPU (central processing unit) 31, a memory 32, an input device 33, an output device 34, an external storage device 35, a medium drive device 36, and a network connection device 37. Are connected to each other.

The CPU 31 executes a program stored in the memory 32 to realize each processing of the time series analyzer. The memory 32 stores data used for processing in addition to the above-described programs. Examples of the memory 32 include a ROM (read only memory) and a RAM (rand
om access memory) is used.

The input device 33 corresponds to, for example, a keyboard, a pointing device, etc., and is used for inputting a request or instruction from a user. The output device 34 corresponds to the display device 29, a printer, or the like, and is used for outputting calculation results and the like.

The external storage device 35 is, for example, a magnetic disk device, an optical disk device, a magneto-optical disk device, or the like. The above-mentioned program and data are stored in the external storage device 35 and, if necessary, stored in the memory 32.
Can be loaded and used. The external storage device 35 is also used as a database for storing parameters and analysis results.

The medium driving device 36 drives the portable recording medium 39 and accesses the stored contents. Portable recording medium 3
9 is a memory card, floppy disk, CD
Any computer readable recording medium such as a ROM (compact disk read only memory), an optical disk, a magneto-optical disk, etc. can be used. The above-mentioned program and data are stored in the portable recording medium 39, and can be used by loading them into the memory 32 as needed.

The network connection device 37 is a LAN (lo
It is connected to an arbitrary communication network such as a cal area network, performs data conversion and the like accompanying the communication, and communicates with an external information provider device 40 (database or the like). Thereby, the time-series analysis device can receive the above-described program and data from the device 40 via the network as needed, and load them into the memory 32 for use.

Next, the operation of the time series analyzer of FIG. 8 will be described in detail with reference to FIGS. FIG. 15 is an operation flowchart of the time-series analysis device.
When the time-series analyzer is activated (step S11),
First, time-series data is collected (step S12). Next, the parameters of the SRNN are learned (step S1).
3) Perform tuning of the SRNN (step S1)
4). Then, the time series data is smoothed and the result is output (step S15), and the process waits (step S16).

FIG. 16 shows the operation of step S12 in FIG. 15, FIG. 17 shows the operation of step S13, FIG. 18 shows the operation of step S14, and FIG.
The operation of FIG.

In FIG. 16, when data collection is started, the time-series analyzer calls the time-series data collector 22 (step S21). Time series data collection device 22
Observes the time series data (step S22), and
, The time series data {vector x ₁ ,. . . , Vector x _N } (step S
23), and waits (step S24).

The time series data {vector x ₁ ,. . . , Vector x _N }, as shown in FIG.
Forward predictive particle generator 23, smooth particle generator 24,
It is used by the backward predicted particle generation device 25 and the display device 29.

Next, when learning is started in FIG. 17, the time series analyzer calls the learning device 27 (step S31). The learning device 27 starts estimation of the maximum likelihood parameter vector λ 2 by the non-linear optimization method (step S32).

First, the learning device 27 uses the nonlinear optimization method 1
Using two simulated annealing methods, a vector λ that maximizes this objective function is determined (step S33). Here, the log likelihood of equation (29) is used as the target function. The calculation operation of the objective function is as follows.

First, the model parameter setting device 28 is called (step S41). The model parameter setting device 28, as shown in FIG. 13, uses the state transition probability matrix M (H ) Is calculated and set in the forward predictive particle generator 23 using M (H) and the weight vector w _j as parameters (step S).
42), and waits (step S43).

Next, the forward predictive particle generation device 23 is called (step S44). Forward-looking predicted particle generator 23
Receives the vector x _n from the time-series data collection device 22, calculates {α _n ^(j) } according to the equation (21) (step S45), and waits (step S46).

Next, the likelihood calculating device 26 is called (step S47). The likelihood calculating device 26 calculates the likelihood of Expression (29) using {α _n ^(j) } obtained by the forward prediction particle generating device 23, and returns the value to the learning device 27 (step S48). ), And waits (step S49).

The learning device 27 receives, for each value of the vector λ determined in each trial of annealing, the value of the corresponding objective function, and calculates the vector λ that maximizes the objective function in all trials. The likelihood parameter vector λ is determined (step S34). And this vector λ
Is saved (step S35), and the process waits (step S35).
36).

Next, when tuning is started in FIG. 18, the time-series analyzer calls the model parameter setting device 28 (step S51). The model parameter setting device 28 receives the vector λ 2 from the learning device 27 (Step S52), and calculates the maximum likelihood state transition probability matrix M from Expression (7) according to the limiting condition for the hidden state vector.

Then, the weight (input load) vectors w _j and M included in the vector λ are given to the forward predicted particle generator 23, the smooth particle generator 24, and the backward predicted particle generator 25 (step S53). , And waits (step S54).

Next, when smoothing is started in FIG. 19, the time-series analyzer first sets the control variable i to 1 (step S60), and starts the forward predictive particle generator 23 (step S61).

As shown in FIG. 10, the forward predictive particle generation device 23 utilizes the re-extraction device 21 to make the time n = N−
An i + 1 forward prediction particle {p _n ^(j) } is generated (step S62). At this time, according to the operation of the forward filter shown in FIGS. 2 and 7, forward prediction particles from time 1 to time n are recursively generated. However, the forward filtration particles at time 0 are randomly generated as initial values.

Then, the forward prediction particles {p _n ^(j) } are output to the smooth particle generation device 24 (step S63), and the process stands by (step S64). At this time, the storage areas of the forward prediction particles and the forward filtration particles are cleared.

Next, the backward predicted particle generator 25 is started (step S65), and as shown in FIG. 11, the backward filtered particles {c
_{n + 1} ^{( j)} } is generated (step S66). At this time,
According to the operation of the backward filter shown in FIGS. 3 and 7, backward filtered particles {c _{n + 1} ^(j) } are generated from the backward filtered particles {c _{n + 2} ^(j) } at time n + 2. However, the backward filtered particles at time N + 1 are randomly generated as initial values.

Then, the backward filtered particles {c _{n + 1} ^(j) } are output to the smooth particle generator 24 (step S67).
It waits (step S68). At this time, the calculation results of the backward predicted particles and the backward filtered particles are stored in the storage area as they are.

Next, the smooth particle generation device 24 is started (step S69), and as shown in FIG. 12, using the re-extraction device 21, the forward prediction particles {p _n ^(j) } and the backward filtration particles { c _{n + 1} ^(j) } to the smooth particle {un} at time _n
^(j) Generate｝ (step S70). Then, the output smoothing particles {u _n ^(j)} to the display device 29 (step S
71), and waits (step S72). At this time, the calculation result of the smooth particles is stored in the storage area as it is.

Next, the time-series analyzer determines whether n has reached 1 (step S73), and if not, sets i = i + 1 (step S74), and repeats the operation from step S61. . Then, when n reaches 1, the display device 29 displays the estimation result of the time-series data based on the smooth particles from time 1 to time N (step S75), and ends the operation.

Next, the operations of the forward predicted particle generator 23, the backward predicted particle generator 25, the smooth particle generator 24, and the re-extractor 21 will be described individually. FIG. 20, 2
1 is a flowchart of the operation of the forward predictive particle generation device 23 in steps S62, S63, and S64 in FIG. 19, and FIGS. 22 and 23 are steps S66, S67, and S64.
FIG. 24 is a flowchart of the operation of the backward predictive particle generation device 25 at 68, and FIG.
1 is a flowchart of the operation of the smooth particle generation device 24 in S72. FIG. 25 is a flowchart of the operation of the re-extraction device 21 called from each of these devices.

However, in FIGS. 20 to 25, the iterative process related to the control variable i in FIG. 19 is described as another iterative process closed in each device using another control variable.

The forward predictive particle generator 23 calculates the number m of particles, the observed data sequence {vector x ₁ ,. . . , A vector x _N }, a state transition probability matrix M (H), and an initial probability p ₀ (H) of the forward filtration particles, and a set sequence {p _n ^(j) } of the forward prediction particles (j = 1,. , M, n =
1,. . . , N). However, the number m of particles and the initial probability p ₀ (H) are given in advance.

In FIG. 20, the forward predictive particle generator 23 first randomly generates m particles in accordance with the initial probability p ₀ (H), and generates a set of forward filtered particles at time 0 ｛f ₀ ^(1). ,. . . , F ₀ ^(m) } (step S81). Next, n = 1 is set (step S82), and generation of forward prediction particles is started (step S83).

Here, first, j = 1 is set (step S
84), j-th forward filtered particle f _{n-1 at time n-1}
^(j) is selected (step S85). Next, among the elements of the state transition probability matrix M (H), a column column (f _n-1 ^(j) ) corresponding to the particle f _n-1 ^(j ) is selected. Then, a forward prediction particle _pn ^(j) is generated according to the state transition probability (step S86).

For example, when k = 2, the number of possible hidden variables is 2 ² = 4, and the realized values of the hidden state vector h _n are (0,0), (1,0), (0,1). ), (1,
There are four cases 1). Here, in order to speed up the calculation, the range of the vector h _{n to be} used is defined as a set H = ｛(1,
0), (0, 1)}. At this time, the state transition probability matrix M (H) representing the transition probability between time n and time n + 1 is as shown in FIG. 26, for example.

In M (H) of FIG. 26, the transition probabilities of the column corresponding to the vector (1, 0) are 0,
They are 0.25, 0.75 and 0. Therefore, p ((0,0) | (1,0)) = 0 p ((1,0) | (1,0)) = 0.25 p ((0,1) | (1,0)) = 0.75 p ((1,1) | (1,0)) = 0. FIG. 27 illustrates these transition probabilities as probability distributions defining transitions from the vector (1, 0). According to this distribution, a particle (1, 0) is generated with a 25% probability, and a particle (0, 1) is generated with a 75% probability.
Is generated. However, the particles (0,0) and (1,
1) is not generated.

The transition probabilities of the column corresponding to the vector (0, 1) are 0, 0.5, 0.5, and 0 in order from the top. Therefore, p ((0,0) | (0,1)) = 0 p ((1,0) | (0,1)) = 0.5 p ((0,1) | (0,1)) = 0.5 p ((1,1) | (0,1)) = 0. FIG. 28 illustrates these transition probabilities as probability distributions that define transitions from the vector (0, 1). According to this distribution, a particle (1,0) or (0,1) is generated with a probability of 50%, and a particle (0,
0) and (1,1) are not generated.

As described above, by partially setting the elements of the state transition probability matrix M (H) to 0, the generated particles are limited, and it becomes possible to use only a predetermined hidden state. .

[0190] Next, the particle p _n produced by the above method
^(j) is defined as a set of forward predictive particles up to j−1 ｛p _n
⁽¹⁾ ,. . . , P _n ^(j-1) } (step S8 ⁾ .
7) Compare j and m (step S88). If j is smaller than m, j = j + 1 is set (step S89),
The operation after step S85 is repeated.

When j reaches m, a set of forward predictive particles {p _n ⁽¹⁾ _,. . . , _Pn ^{( m)} }, the smoothed particle generator 24, the likelihood calculator 26, and the display 29.
(Step S90), and the generation of the weight coefficient of the re-extraction load is started (FIG. 21, step S91).

Here, first, j = 1 is set (step S
92), weighting coefficient α corresponding to the forward prediction particle p _n ^(j)
_n ^(j) is calculated in accordance with equation (21) (step S9)
3).

As described above, the generated particles are represented by ｛(1,
0), (0, 1)}, the vector ω (p _n ⁽ⁱ⁾ ) of the average value of the equation (21) becomes the vector ω ((1,
0)) or the vector ω ((0, 1)). From equation (6), vector ω ((1,0)) = vector w ₁ , vector ω ((0,1)) = vector w ₂ , and coefficient α _n ⁽ⁱ⁾ is g (vector x _n ; vector w ₁ ) or g (vector x _n ; vector w ₂ ).

Next, the coefficient α_n ^(j)To j-1
Set of coefficients ｛α_n ⁽¹⁾,. . . , Α _n ^(j-1)In addition to｝
(Step S94), j and m are compared (Step S9)
5). If j is smaller than m, j = j + 1 (step
Step S96), the operation after step S93 is repeated.

When j reaches m, the set of coefficients {α _n ⁽¹⁾ ,. . . , Α _n ^(m) } to the likelihood calculating device 26 (step S97), and the generation of forward filtered particles is started (step S98).

Here, first, the forward prediction particles {p _n ⁽¹⁾ ,. . . , P _n ^(m) } and their corresponding weights {α _n ⁽¹⁾ / Σ _{i = 1} ^m α _n ⁽ⁱ⁾ ,. . . , Α _n ^(m)
/ Σ _{i = 1} ^m α _n ^{( i)} ｝ and the re-extraction device 21
Is started (step S99). Then, the forward filtered particles {f _n ⁽¹⁾ ,. . . , F _n ^{(m )} } from the re-extraction device 21 and output to the display device 29 (step S10).
0).

Next, n and N are compared (step S10).
1) If n is smaller than N, n = n + 1 is set (step S102), and the operation after step S83 in FIG. 20 is repeated. Then, when n reaches N, the operation is terminated and a standby state is set (step S103). Thus, the set of forward predictive particles {p _n ^(j) } (j = 1,.
m, n = 1,. . . , N) are output to the smooth particle generation device 24 and the display device 29.

The backward predictive particle generator 23 generates the number m of particles, the observation data sequence {vector x ₁ ,. . . , A vector x _N }, a state transition probability matrix M (H), and an initial probability p _N (H) of the backward filtered particles, and a set sequence {c _{n + 1} ^{(j )} } (j = 1 , ...,
m, n = N,. . . , 1) are output. Here, the number m of particles and the initial probability p _N (H) are given in advance.

In FIG. 22, the backward predictive particle generator 23 first randomly generates m particles according to the initial probability p _N (H), and generates these at time N + 1 as a set of backward filtered particles ｛c _{N + 1} ^{( 1)} ,. . . , C _{N + 1} ^(m) } (step S111). Then, a set of particles ｛c _{N + 1}
⁽¹⁾ ,. . . , C _{N + 1} ^(m) } to the smooth particle generator 24
And output to the display device 29. Next, n = N is set (step S112), and generation of backward prediction particles is started (step S113).

Here, first, j = 1 is set (step S
114), j-th backward filtered particle c _{n + 1 at time n + 1}
^(j) is selected (step S115). Then, among the elements of the state transition probability matrix M (H), selecting the column column corresponding to particles ^{_{c n + 1 (j) (}} c n + 1 (j)). Then, similarly to step S86 of FIG. 20, in accordance with the state transition probability, to generate a backward prediction particles e _n ^{(j) (step} S116).

Next, a particle e _n ^(j) is defined as a set {e _n ⁽¹⁾ ,. . . ,
In addition to ^{_{e n (j-1)}}} ( step S117), it compares the j and m (step S118). j if j is less than m
= J + 1 (step S119), and step S1
The operation after 15 is repeated.

[0202] When j reaches m, the set of backward prediction particles {e _n ^(1),. . . , E _n ^{( m)} } on the display device 2
9 (step S120), and the generation of the weight coefficient of the re-extraction load is started (FIG. 23, step S121).

Here, first, j = 1 is set (step S
122), a weighting coefficient ε _n ^(j) corresponding to the backward prediction particle e _n ^(j) is calculated according to the equation (25) (step S).
123).

As described above, the generated particles are represented by ｛(1,
0), (0, 1)}, the coefficient ε _n ^{(i) of the} equation (25 ⁾ is also g (vector x _n ; vector w ₁ )
Alternatively, it can be calculated as the value of g (vector x _n ; vector w ₂ ).

Next, the coefficient ε_n ^(j)To j-1
Set of coefficients ｛ε_n ⁽¹⁾,. . . , Ε _n ^(j-1)In addition to｝
(Step S124), j and m are compared (Step S124)
125). If j is smaller than m, set j = j + 1
(Step S126), the operation after step S123
repeat.

When j reaches m, the set of coefficients {ε _n ⁽¹⁾ ,. . . , Ε _n ^(m) } (step S127), and the generation of backward filtered particles is started (step S128).

[0207] Here, first backward prediction particles {e _n ^(1),. . . , And e _n ^(m)}, the weight corresponding to these ^{_{{ε n (1) / Σ}} i = 1 m ε n (i),. . . , Ε _n ^(m)
/ Σ _{i = 1} ^m ε _n ^{( i)} ｝ and the re-extraction device 21
Is started (step S129). Then, (26) backward filtered particles re-extracted in accordance with equation {c _n ^(1),. . . , C _n ^{( m)} } from the re-extraction device 21 and outputs them to the smooth particle generation device 24 and the display device 29 (step S130).

Next, n and 2 are compared (step S13).
1), if n is greater than 2, n = n-1 (step S132), and the operations after step S113 in FIG. 22 are repeated. Then, when n reaches 2, the operation is terminated and a standby state is set (step S133). Thus, the set of backward-filtered particles {c _{n + 1} ^(j) } (j =
1,. . . , M, n = N,. . . , 1) are output to the smooth particle generation device 24 and the display device 29.

Further, the smooth particle generation device 24 generates the number m of particles, the observation data sequence {vector x ₁ ,. . . , The vector x _N}, the state transition probability matrix M (H), and (2) as an input an integer d 'in formula, the set column of smooth particles {u _n ^(j)}
(J = 1,..., M, n = N,. Here, the number m of particles and the integer d 'are given in advance.

In FIG. 24, the smooth particle generator 24
First calculates the re-extraction load of the smooth particles at time N + 1 as ｛β _{N + 1}
⁽¹⁾ ,. . . , Β _{N + 1} ^(m) ｝ = {1 / m,. . . , 1 /
m} (step S141) and t = 1 (step S142).

Next, at time n = N−t + 1, the forward prediction particles {p _n ⁽¹⁾ ,. . . , P _n ^(m) } are generated using the forward prediction particle generator 23 (step S143), and the backward filtration particles {c _{n + 1} ⁽¹⁾ ,. . . , C
_{n + 1} ^(m) } is generated using the backward prediction particle generation device 25 (step S144). Then, the generation of the weight coefficient for re-extracting the smooth particles at the time n is started (step S145).

Here, first, j = 1 is set (step S
146) A weight coefficient β _n ^(j) corresponding to the forward prediction particle p _n ^(j) is calculated according to the equation (2) (step S1).
47). At this time, the transition probability on the right side of equation (2)
Is a state transition probability matrix M (H

[0213]

[Outside 8]

Is calculated by replacing the corresponding element of
You. Next, the coefficient β_n ^(j)Is the collection of coefficients up to j-1
Total β_n ⁽¹⁾,. . . , Β _n ^(j-1)In addition to｝ (step
S148), j is compared with m (step S149).
If j is smaller than m, j = j + 1 is set (step S
150), and repeat the operation from step S147.

Then, when j reaches m, the forward movement of time n
Predicted particle ｛p_n ⁽¹⁾,. . . , P _n ^(m)こ れ ら and these
Weight ｛β corresponding to_n ⁽¹⁾/ Σ
_{i = 1} ^mβ_n ⁽ⁱ⁾,. . . , Β _n ^(m)/ Σ
_{i = 1} ^mβ_n ⁽ⁱ⁾再 and the re-extraction device 21
(Step S151). Then, according to equation (28),
Particles u re-extracted_n ⁽¹⁾,. . . , U_n
^(m)受 け 取 り is received from the re-extraction device 21 and displayed on the display device 29.
It outputs (step S152).

Next, t and N are compared (step S15).
3) If t is smaller than N, t = t + 1 is set (step S154), and the operation after step S143 is repeated. Then, when t reaches N, the operation is terminated and a standby state is set (step S155). Thus, a set sequence of smooth particles ^{_{{u n (j)} (}} j = 1, ..., m, n =
N,. . . , 1) are output to the display device 29.

Further, the re-extraction unit 21 generates a set {a ^{(1 )} ,... Of m particles given from the forward predicted particle generator 23, the backward predicted particle generator 25, or the smooth particle generator 24. . . , A ^(m) } and the corresponding set of weights {γ ⁽¹⁾ ,. . . , Γ ^{(m )} } and m
The set {b ⁽¹⁾ ,. . . , B ^(m) }.

Here, the particles a ^(j) (j = 1,.
m) is a forward prediction particle p _n ^(j) or backward prediction particles e _n ^(j), the weight gamma ^{(j) _{is, α n (j) / Σ}} i = 1 m
α _n ^{(i )} , ε _n ^(j) / Σ _{i = 1} ^m ε _n ⁽ⁱ⁾ , and β _n
^(j) is any weight of _{^{/ Σ i = 1 m β n}} (i). In addition, the re-extracted particles b ^(j) are forward filtered particles f _n
^(j), backward filtered particles c _n ^(j), and smooth particles u _n
It is output as one of the particles in ^(j) .

In FIG. 25, the re-extraction unit 21 first sets a set of weights {γ ⁽¹⁾ ,. . . , Γ ^{(m )} }, the cumulative load ψ ^(l) = Σ _{j = 1} ^l γ ^(j) (l = 1,..., M) is calculated, and ψ ⁽⁰⁾ = 0, ψ ^{(m )} = 1 (step S16)
1). Next, assuming that l = 1 (step S162), a random number r∈ [0,
1) is generated (step S163).

Next, by using a dichotomy for finding a value while dividing the section, j is found such that ψ ^(j) ≤ r <ψ ^{(j ),} and a given set of particles ｛a ⁽¹⁾ ,. . . ,
a ^(m) } and select a particle a ^(j) (step S1 ^).
64). Then, set b ^(l) = a ^(j) (step S1
65), 1 is compared with m (step S166).

If l is smaller than m, l = l + 1 is set (step S167), and the operations after step S163 are repeated. When l reaches m, the set of particles ｛b
⁽¹⁾ ,. . . , B ^(m) } to the corresponding device (step S168), and terminates the operation and enters a standby state (step S169). Thus, the set of particles {a ⁽¹⁾ ,. . . , A ^(m) } from another set {b ⁽¹⁾ ,. . . , B ^(m) } are re-extracted.

The method for re-extracting particles shown in FIG. 25 is merely an example, and the set {a ⁽¹⁾ ,. . . , A ^(m) } from the set {b ⁽¹⁾ ,. . . , B ^(m) } may be re-extracted.

Next, the data display operation in step S75 of FIG. 19 will be described. FIG. 29 is a flowchart of a display operation of an estimation result based on a set sequence of forward prediction particles, and FIG. 30 is a flowchart of a display operation of an estimation result based on a set sequence of smooth particles.

In FIG. 29, the display device 29 displays the number m of particles, the dimension k of the particles (dimension of the hidden state vector) k, the length N of the observation data sequence, and the set {w ₁ ,. . . , W _k }, a set of forward predictive particles {p
_n ^(j) ｝ (j = 1,..., m, n = 1,.
, The predicted density function sequence of the time series data is displayed. Here, the number m of particles, the dimension k of the particles, the length N of the observation data sequence, and the set of input loads {w ₁ ,. . . , W _k ｝
Is given in advance.

The display device 29 first sets n = 1 (step S 171), and outputs the forward predicted particles {p _n ⁽¹⁾ ,. . . , P _n ^(m) } (step S172).

Next, different particles included in the set of forward prediction particles are selected, and their list is set to 外. Here, i0 represents the number of different particles, and i0 ≦
ma

[0227]

[Outside 9]

X (m, 2 ^k ). Also, outside 10
(Hereinafter, referred to as h _i tilde), the squirrel

[0229]

[Outside 10]

Represents the i-th element (particle) contained in G. Then, each element h included in the set of forward prediction particles
enumerate the number q _i of _i tilde, {q _1,. . . , Q
_i0 } (steps S173 to S180).

Here, first, i = 1, j = 1, h ₁ tilde = p _n ⁽¹⁾ , q ₁ = 0 (step S173),
The same particles as p _n ^(j) are listed {h ₁ tilde,. . . , H
It is checked whether it is included in _i tilde # (step S174). p _n ^(j) is the list {h ₁ tilde,. . . ,
be contained in h _i tilde} obtains the p _n ^(j) = h _s tilde become s (1 ≦ s ≦ i) , the q _s = q _s +1 (step S175).

If p _n ^(j) is a list {h ₁ tilde,. . . , H _i tilde チ ル, h
It is assumed that _{i + 1} tilde = p _n ^(j) and q _{i + 1} = 1. Then, a list of particles {h ₁ tilde,. . . , H _i tilde｝ h
_{i + 1} tilde, and a list of the corresponding total number {q ₁ ,. . . , Q _i } and q _{i + 1} (step S
176), i = i + 1 is set (step S177).

Next, j = j + 1 is set (step S17).
8) Compare j and m (step S179). j is m
If it is below, the operation after step S174 is repeated,
If j exceeds m, the value of i at that time is set to i0 (step S180).

Next, the list $ h₁tilde,. . . , H_i0
Tilde｝ and ｛q₁,. . . , Q _i0From｝,
To synthesize a predicted density function (step S181).

[0235]

(Equation 24)

Here, h _i tilde = (h _i1 , ..., h
_ik ), the vector ω (h _i tilde) =
It is a _{Σ s = 1} ^k h is a vector w _s. When the target time-series data is one-dimensional data and the predicted density function of the equation (30) is a one-dimensional mixed Gaussian density function, as shown in FIG. S1
82).

The obtained predicted density function is displayed on the screen as the predicted density function at time n (step S18).
3) With n = n + 1 (step S184), n and N are compared (step S185). If n is less than or equal to N, the operation from step S172 is repeated, and if n exceeds N, the operation ends. Thus, the predicted density function from time 1 to N is displayed.

Further, in FIG. 30, the display device 29
The number m of particles, the dimension k of the particles, the length N of the observation data sequence,
The set of input weights {w ₁ ,. . . , W _k}, the set sequence ^{_{{u n (j)} (}} j = 1 of the smoothing particles, ..., m, n
= N,. . . , 1) as an input, a smooth density function sequence of the time series data is displayed.

[0239] The display device 29, first n = N is set (at step S191), smoothing the particles at time n from the smoothing particle generator ^{_{24 {u n (1),}} . . . , U _n ^(m) } (step S192).

Next, different particles included in the set of smooth particles are selected, and the list of the selected particles is set as {h ₁ tilde,. . . , H _i0 tilde}. Then, the number q _i of each element h _i tilde included in the set of smooth particles is counted, and {q ₁ ,. . . , Q _i0 } (step S193)
To S200).

[0241] Here, first i = 1, j = 1, h 1 tilde ^{_{= u n (1), q}} 1 = 0 is set (at step S193),
The same particles as u _n ^(j) are listed {h ₁ tilde,. . . , H
It is checked whether it is included in _i tilde # (step S194). u _n ^(j) is the list {h ₁ tilde,. . . ,
be contained in h _i tilde}, I seek s (1 ≦ s ≦ i) as a u _n ^(j) = h _s tilde, and q _s = q _s +1 (step S195).

Also, if u _n ^(j) is a list {h ₁ tilde,. . . , H _i tilde チ ル, h
_{i + 1} tilde = u _n ^(j), placing a q _{i +} 1 = 1. Then, a list of particles {h ₁ tilde,. . . , H _i tilde｝ h
_{i + 1} tilde, and a list of the corresponding total number {q ₁ ,. . . , Q _i } and q _{i + 1} (step S
196), and i = i + 1 is set (step S197).

Next, j = j + 1 is set (step S19).
8) Compare j and m (step S199). j is m
If it is below, the operation after step S194 is repeated,
If j exceeds m, the value of i at that time is set to i0 (step S200).

Next, the list $ h₁tilde,. . . , H_i0
Tilde｝ and ｛q₁,. . . , Q _i0From｝,
Thus, a smooth density function is synthesized (step S201).

[0245]

(Equation 25)

When the time series data to be processed is one-dimensional data and the smoothed density function of the equation (31) is a one-dimensional mixed Gaussian density function, this is approximated by a step function as shown in FIG. (Step S202).

Then, the obtained smoothed density function is displayed on the screen as the smoothed density function at time n (step S20).
3) With n = n-1 (step S204), n and 1 are compared (step S205). If n is 1 or more, the operation from step S192 is repeated, and if n is less than 1, the operation is ended. Thus, the smoothed density function from time 1 to N is displayed.

In FIGS. 29 and 30, the method of generating / displaying the density function based on the forward predicted particles and the smooth particles has been described. In addition, the respective density functions based on the forward filtered particles, the backward predicted particles, and the backward filtered particles are also described. Can be generated / displayed in the same manner.

Next, the results of estimating one-dimensional time-series data x that changes with time t using the time-series analyzer of FIG. 8 will be described. It is assumed that the target time-series data x follows a piecewise stationary probability density function as in the following equation.

[0250]

(Equation 26)

Here, N (μ, σ ² ) represents a Gaussian density function having an average μ and a variance σ ² . The test time-series data generated by the equation (32) is, for example, as shown in FIG. In the generation of this time series data, t = 10
It can be seen that the discontinuous switching of the average value at 0 appears as a leap in the data trend. The problem is,
It is whether the time series analyzer can predict this trend well and smooth the trend from the entire observation data sequence.

When the data of FIG. 32 is analyzed by the time-series analyzer and the predicted density function sequence calculated from the set of forward predicted particles for this data is displayed according to the display method of FIG. 29, the result is as shown in FIG. . In FIG.
The predicted density function at each time is approximated by a step function. Also, the part where the size of the dot is small, that is,
The whitish part at the center corresponds to the peak of the distribution.

According to the display method shown in FIG. 30, FIG.
FIG. 34 shows a smooth density function sequence calculated from the set sequence of smooth particles for the data of. Referring to FIG. 34, discontinuous switching at t = 100 clearly appears. From this, SRN by Monte Carlo method
From the set of N smooth particles, it can be seen that the jumping trend has been successfully extracted.

The time-series analysis method based on SRNN described above estimates the state of a network in which the statistic changes discontinuously over time, such as the traffic of an information network and the traffic of a road network, and optimizes network resources. It can be used for control.

The SRNN can represent a nonlinear function in a distributed manner with a plurality of distribution functions. Therefore, for example, when the statistic is represented by a non-linear function of a certain hidden parameter, such as when the measured amount is piecewise stationary and includes a trend that changes discontinuously in each section, The state of the network can be accurately estimated.

[0256]

According to the present invention, it is possible to speed up the calculation of the probability density based on the internal state of a recursive neural network that retains various expression powers in a distributed representation of the probability distribution of time series data. it can. Therefore, the probability distribution of time-series data in a large-scale problem can be quickly estimated from known observation data.

[Brief description of the drawings]

FIG. 1 is a principle diagram of the present invention.

FIG. 2 is a diagram illustrating a recursive generation process of forward prediction particles and forward filtration particles.

FIG. 3 is a diagram illustrating a recursive generation process of backward predicted particles and backward filtered particles.

FIG. 4 is a diagram illustrating a recursive generation process of smooth particles.

FIG. 5 is a diagram showing a probability distribution function.

FIG. 6 is a diagram showing a state transition probability matrix.

FIG. 7 is a diagram showing a double filter method.

FIG. 8 is a configuration diagram of a time-series analysis device.

FIG. 9 is a diagram showing a flow of time-series data.

FIG. 10 is a diagram showing a flow of data related to the forward predictive particle generation device.

FIG. 11 is a diagram showing a flow of data related to the backward predictive particle generation device.

FIG. 12 is a diagram showing a flow of data related to the smooth particle generation device.

FIG. 13 is a diagram showing a flow of generation and supply of parameters.

FIG. 14 is a configuration diagram of an information processing apparatus.

FIG. 15 is an operation flowchart of the time series analyzer.

FIG. 16 is a flowchart of a data collection operation.

FIG. 17 is a flowchart of a learning operation.

FIG. 18 is a flowchart of a tuning operation.

FIG. 19 is a flowchart of a smoothing operation.

FIG. 20 is an operation flowchart (part 1) of the forward predictive particle generation device.

FIG. 21 is an operation flowchart (part 2) of the forward predictive particle generation device.

FIG. 22 is an operation flowchart (part 1) of the backward prediction particle generation device.

FIG. 23 is an operation flowchart (part 2) of the backward prediction particle generation device.

FIG. 24 is an operation flowchart of the smooth particle generation device.

FIG. 25 is an operation flowchart of the re-extraction device.

FIG. 26 is a diagram showing a state transition probability matrix in which hidden state vectors are limited.

FIG. 27 is a diagram showing a probability distribution corresponding to a column of (1, 0).

FIG. 28 is a diagram showing a probability distribution corresponding to the column (0, 1).

FIG. 29 is a flowchart of a display operation of a predicted density function sequence.

FIG. 30 is a flowchart of a display operation of a smooth density function sequence.

FIG. 31 is a diagram showing a step function.

FIG. 32 is a diagram showing time-series data for a test.

FIG. 33 is a diagram showing a predicted density function sequence calculated from a set sequence of predicted particles.

FIG. 34 is a diagram showing a smooth density function sequence calculated from a set sequence of smooth particles.

FIG. 35 is a diagram schematically showing a simple recursive neural network.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Input layer 2 Network parameter part 3 Hidden element layer 4 Context layer 11 Storage means 12 Generation means 13 Estimation means 21 Re-extraction device 22 Time series data collection device 23 Forward prediction particle generation device 24 Smooth particle generation device 25 Backward prediction particle generation device 26 Likelihood calculation device 27 Learning device 28 Model parameter setting device 29 Display device 31 CPU 32 Memory 33 Input device 34 Output device 35 External storage device 36 Medium drive device 37 Network connection device 38 Bus 39 Portable recording medium 40 Information provider apparatus

Claims (18)

[Claims] 1. A time series analysis apparatus for an information processing apparatus for calculating a hidden Markov model represented by using a neural network, comprising: an internal state of a recursive neural network expressing a probability distribution of observation data. A storage unit for storing a state transition probability, a generation unit for generating a realization value of a hidden variable that defines the internal state by a Monte Carlo method using the state transition probability, and the observation data using the realization value. Estimating means for estimating the probability distribution of the time series. 2. The recursive neural network according to claim 1,
A simple recursive neural network having a hidden element layer and one context layer, wherein a hidden variable representing a previous internal state held in the context layer is weighted by a parameter and recursed into the hidden element layer. 2. The time-series analysis device according to claim 1, wherein the time-series analysis device is configured to input the time series. 3. The storage means stores, as the state transition probability, a transition probability of a hidden state vector having the hidden variable as an element from a first realization value to a second realization value. 2. The time-series analysis apparatus according to claim 1, wherein when the first realization value is given, the second realization value is generated according to the state transition probability. 4. The storage means stores a plurality of transition probabilities of a plurality of realization values of the hidden state vector as elements of a state transition probability matrix, and the generation means provides the first realization value given by the first realization value. When one of the plurality of realization values is set as the transition probability, the corresponding element of the state transition probability matrix
4. The time-series analysis device according to claim 3, wherein the time-series analysis device generates one. 5. The storage means stores transition probabilities between realization values belonging to a limited set of a plurality of realization values of the hidden state vector, and the generation means sets the first realization value as 5. The time-series analysis device according to claim 4, wherein when given, one of the realized values belonging to the limited set is generated by using a corresponding element of the state transition probability matrix as a transition probability. . 6. The forward predicting particle, which is a realization value representing a result of estimating an internal state after the specific time from the observation data up to a specific time, and generating the identification information from the observation data up to the specific time. Alternately generating forward filtered particles, which are realization values representing the result of estimating the internal state of time, and the estimating means generating the probability distribution using the set of forward predicted particles or forward filtered particles. The time-series analysis device according to claim 1, wherein: 7. The backward predicting particle, which is a realization value representing a result of estimating an internal state before the specific time from observation data after a specific time, and the identification information from the observation data after the specific time. Alternately generating backward filtered particles, which are realization values representing the result of estimating the internal state of time, and the estimating means generating the probability distribution using the set of backward predicted particles or backward filtered particles. The time-series analysis device according to claim 1, wherein: 8. The method according to claim 1, wherein the generation unit generates a smooth particle that is a realization value representing a result of estimating an internal state at one time within the specific time from observation data within a specific time. The time-series analysis device according to claim 1, wherein the probability distribution is generated using a set of smooth particles. 9. The method according to claim 1, wherein the generating unit includes: a forward filter unit that alternately generates a forward predicted particle and a forward filtered particle; a backward filter unit that alternately generates a backward predicted particle and a backward filtered particle; 9. The time-series analyzer according to claim 8, further comprising: a smooth particle generation unit configured to generate the smooth particles using filtered particles. 10. The forward filtering means generates the forward prediction particles from the forward filtering particles according to the state transition probability, and the backward filtering means generates the forward prediction particles from the backward filtering particles according to the state transition probability. The time-series analysis device according to claim 9, wherein particles are generated. 11. The smooth particle generation means calculates a weight of re-extraction of particles using the state transition probability, and re-extracts and extracts the forward predicted particles from the set of forward predicted particles according to the weights. The time-series analysis device according to claim 9, wherein the forward prediction particles are output as the smooth particles. 12. A likelihood calculating means for calculating a likelihood of a parameter of the recursive neural network with respect to the observation data sequence by a Monte Carlo method,
2. The apparatus according to claim 1, wherein the generation unit generates the realization value using a parameter that improves the likelihood.
The time-series analysis device as described. 13. A learning unit for obtaining a maximum likelihood parameter that maximizes the likelihood using a calculation result of the likelihood calculation unit, and at least a part of the maximum likelihood parameter is set in the storage unit. 13. The time-series analysis apparatus according to claim 12, further comprising parameter setting means, wherein the generation means generates the realization value using at least a part of the maximum likelihood parameter. 14. The time-series analysis according to claim 13, wherein said parameter setting means calculates said state transition probability from said maximum likelihood parameter and sets the obtained state transition probability in said storage means. apparatus. 15. The time-series analysis device according to claim 1, further comprising an output unit that outputs an estimation result of the observation data based on the probability distribution estimated by the estimation unit. 16. A time-series analysis device for an information processing device for calculating an observation model represented by using a neural network, wherein a state transition probability of an internal state of the neural network representing a probability distribution of observation data is provided. A generating unit that generates a realization value of a variable that defines the internal state using the state transition probability; and an estimating unit that estimates a probability distribution of the observation data using the realization value. And a time-series analysis device. 17. A recording medium on which a program for a computer for calculating an observation model expressed by using a neural network is recorded, wherein a state transition probability of an internal state of the neural network expressing a probability distribution of observation data is provided. A program for causing the computer to realize a function of generating a realization value of a variable that defines the internal state and a function of estimating a probability distribution of the observation data using the realization value is recorded. Computer readable recording medium. 18. A method for calculating an observation model represented by using a neural network, wherein a state transition probability of an internal state of the neural network representing a probability distribution of observation data is generated, and the state transition probability is calculated by using the state transition probability. A time-series analysis method, wherein a realization value of a variable defining an internal state is generated, and a probability distribution of the observation data is estimated using the realization value.