JP4662139B2 - Data output device, data output method, and program - Google Patents

Description

  The present invention relates to a data output device, a data output method, and a program, and in particular, a data output that makes it possible to easily obtain data such as a time-series vector that changes smoothly using a state transition probability model. The present invention relates to an apparatus, a data output method, and a program.

  Voice (signal), and further, a voice parameter extracted from the voice is time-series data (time-series data). As a model for modeling the time-series data, for example, there is an HMM (Hidden Markov Model). .

In recent years, HMM has been widely used for speech recognition. The HMM is a kind of state transition probability model in which data is output according to state transitions. When the state transitions, the state transition probability a _ij which is the probability of transition from the state S _i to the state S _j The transition destination state S _j is defined by an output probability density function b _j (x) representing a probability distribution for outputting data (observed value) x.

As the output probability density function, for example, a mixed normal distribution is assumed. Further, the output probability density function, as a function representing a probability distribution data (observed values) x is output when a transition from the state S _i to state S _j, and the suffix i in the state S _i before transition Transition It may be expressed as b _ij (x) using the suffix _j of the later state S _j .

According to the HMM, statistical characteristics of time series data to be learned are modeled. The Baum-Welch method is widely used as an HMM learning method, that is, an estimation method of the state transition probability a _ij and the output probability density function b _j (x) that defines the HMM. Here, the HMM is described in Non-Patent Document 1.

  Currently, HMMs are widely used from isolated word speech recognition to large vocabulary continuous speech recognition, and speech recognition devices that perform such speech recognition have been put into practical use.

  Incidentally, in recent years, a method using an HMM for speech synthesis has been proposed.

  In speech synthesis using HMM, speech parameters such as time series pitch and spectrum (time series) are modeled by HMM, speech parameters are generated from HMM, and speech signals are synthesized (generated) from the speech parameters. Is done. In synthesizing an audio signal from an audio parameter, an inverse filter that performs a process opposite to the process of extracting an audio parameter such as a spectrum from the audio signal is used.

  For example, a filter that synthesizes a speech signal from a mel cepstrum coefficient, which is a kind of speech parameter, includes an MLSA filter (Mel logarithmic spectrum approximation filter). Here, the MLSA filter is described in Non-Patent Documents 2 and 3, for example.

  As a method for generating a speech parameter that is time-series data used for speech synthesis from an HMM, for example, there is a method for generating a speech parameter by an HMM using a dynamic feature amount. Here, HMMs using dynamic feature quantities are described in Non-Patent Documents 4 and 5.

  Here, the speech parameter represents a feature of speech and is generally a vector, and hence is also referred to as a feature vector as appropriate.

When a feature vector is generated by an HMM using dynamic features, a duration (which is a self-transition) time for each state continues (self-transition) based on the state transition probability a _ij of the HMM. Based on the maximization of likelihood, the most probable state transition is determined in the optimum state sequence, that is, the HMM. Then, a feature vector is generated from each state based on the likelihood maximization while changing the state in the order according to the optimum state series.

If generation of a feature vector x in the state S _j is performed using the output probability density function b _j of that state S _j (x), that the generation of a feature vector x, give no constraint, the likelihood According to the maximization, an average vector of the output probability density function b _j (x) is generated as the feature vector x. Therefore, in this case, once the state S _j, also feature vector x generated from the state S _j, would uniquely determined on an average vector of the state S _j of the output probability density function b _j (x), as a result It is difficult to obtain a time-series feature vector that changes smoothly.

  Therefore, in an HMM using dynamic feature amounts, dynamic feature amounts are used to obtain time-series feature vectors that change smoothly.

That is, now, a feature vector at time t, if it is assumed that expressed the c _t, the feature vector time series of length T is, c _1, c _2, can be expressed., And c _T. In this case, the dynamic features, and d _t of formula (1), is a _t of formula (2) is used.

・・・（１）

... (1)

・・・（２）

... (2)

The dynamic feature quantity d _{t in} equation (1) is a vector that represents the amount of change in the feature vector c _t and is called a delta parameter. Dynamic features a _t of formula (2) is a vector representing a change amount of the delta parameters d _t, called delta delta parameters.

Now, a vector ot whose components are a feature vector c _t and dynamic feature quantities (vectors) d _t and a _t is _expressed as in Expression (3).

・・・（３）

... (3)

In an HMM using dynamic features, HMM learning is performed using time series vectors o ₁ , o ₂ , o ₃ ,..., O _T , and time series are used using the learned HMM. Vector o ₁ , o ₂ , o ₃ ,..., O _T are generated. Then, when generating the time-series vectors o ₁ , o ₂ , o ₃ ,..., O _T , the equations (1) and (2) are considered. As a result, the vector o _t is output from the state S _j of the HMM, not the average vector of just the output probability density function b _j (o _t), the feature vector c _t which is a component of the vector o _t, It becomes a time-series vector (time-series vector) that changes smoothly.

According to the HMM using the dynamic feature amount, it is possible to obtain smoothly synthesized feature vectors c ₁ , c ₂ ,..., C _T and generate a natural synthesized sound.

However, the HMM using the dynamic features, in addition to the feature vector c _t, for using the delta parameter d _t and delta delta parameters a _t as dynamic features as dynamic features, only the delta parameters d _t even the use of, dimensionality of vector o _t of the HMM learning is increased two times, more, as the dynamic features, in the case of using also the delta delta parameters a _t, the vector o _t where HMM learns The number of dimensions increases three times.

Further, due to the increase in the number of dimensions of the vector o _t , the amount of processing required for learning the HMM and generating a vector from the HMM increases, and furthermore, the parameters of the HMM, that is, the HMM of probability and state transition probability a _ij to define the power density function b _j (x), the data amount such as average vector defining the output probability density function b _j (x) also becomes large.

  On the other hand, a method of generating a smoothly changing feature vector by repeating probabilistic trials of generating time-series feature vectors from the HMM and averaging the results of the probabilistic trials has been proposed. Here, a method of generating a feature vector based on such a probabilistic trial is described in, for example, Patent Document 1 and Non-Patent Document 6.

In the generation of feature vectors based on probabilistic trials, a sequence of a plurality of states (sequence of transition states (state transition sequence)) is obtained probabilistically according to the state transition probability a _ij of the HMM. An average state transition sequence is determined, and further, a trial of generating a time-series feature vector based on the output probability density function b _j (x) from the average state transition sequence is performed many times. Then, by averaging the time series feature vectors generated by the numerous trials, a final time series feature vector is obtained.

  In the generation of feature vectors based on probabilistic trials, unlike the generation of feature vectors by HMM using dynamic features, time-series feature vectors are not generated on the basis of likelihood maximization. An average time series feature vector resulting from the probabilistic trial of generation is generated.

  Therefore, according to the generation of the feature vector based on the probabilistic trial, it is necessary to try the process of generating the time-series feature vector many times, which increases the processing amount.

JP 2004-330361 A Laurence Rabiner, Biing-Hwang Juang, “Basics of Speech Recognition (Up / Down)”, NTT Advanced Technology Corporation Sei Imai, Kazuo Sumita, Chieko Furuichi, "Mel Log Spectrum Approximation (MLSA) Filter for Speech Synthesis", IEICE Transactions (A), J66-A, 2, pp.122-129, 1983 Keiichi Tokuda, Takao Kobayashi, Hironori Saito, Toshiaki Fukada, Kiyoshi Imai, "Spectrum estimation of speech using mel cepstrum as a parameter", IEICE Transactions (A), J74-A, 8, pp.1240-1248, 1991 K. Tokuda, T. Yoshimura, T. Masuko, T. Kobayashi, T. Kitamura, "SPEECH PARAMETER GENERATION ALGORITHMS FOR HMM-BASED SPEECH SYNTHESIS", Proc. Of ICASSP 2000, vol.3, pp.1315-1318, June 2000 Tokuda Keiichi, “Basics of Speech Synthesis with HMM”, IEICE Technical Report, SP2000-74, pp.43--50, Oct. 2000. Tetsuya Inagi, Hiroaki Tanie, Yoshihiko Nakamura, "Keyframe Extraction and Restoration of Time Series Data Using Continuously Distributed Hidden Markov Model", Proc. Of Robotics and Mechatronics Lecture 2003, 2P1-3F-C6 , 2003

  The present invention has been made in view of such a situation, and obtains time-series data that changes smoothly without using dynamic feature values and without repeatedly trying to generate time-series data. Is to be able to.

A data output device or program according to one aspect of the present invention is defined by a state transition probability of state transition and a probability distribution of data output by each state in a data output device that outputs time-series data. For each state of the HMM, based on the state probability estimation means for estimating the state probability that the state outputs data for each time at a predetermined interval, the state probability, and the average value of the data according to the probability distribution, Time-series data generating means for obtaining data for each time of a predetermined interval output from the time-series data, and outputting the data as time-series data, the state probability estimating means for each state of the HMM, the state transition probability of self-transition Is used to obtain the value corresponding to the expected value of the number of times that self-transition occurs as the expected value of the duration of the self-transition, and the transition time for transitioning from one state to another is The probability that a state transition starts from a state at each time, obtained by a recurrence formula using the normal distribution, assuming that it follows a normal distribution whose average value is the expected transition time obtained by adding expected values of time Is obtained as the state probability at each time, and the time-series data generating means outputs data output by the HMM at each time by linear combination of the average values of the data weighted by the state probability of each state. Is a program for causing a computer to function as a data output device or a data output device.
A data output method according to one aspect of the present invention is a data output method for outputting time-series data, wherein each state of the HMM defined by a state transition probability of state transition and a probability distribution of data output by each state A state probability estimation step for estimating a state probability that the state outputs data at a predetermined interval of time, a predetermined value output by the HMM based on the state probability and an average value of data according to the probability distribution A time series data generation step for obtaining data for each time of the interval and outputting as time series data, wherein the state probability estimation step uses a state transition probability of self transition for each state of the HMM, A value corresponding to the expected value of the number of times self-transition occurs is obtained as an expected value of the duration for which the self-transition continues, and the transition time for transitioning from one state to another is the duration Corresponds to the probability that a state transition starts from a state at each time, obtained by a recurrence formula using the normal distribution, assuming that it follows a normal distribution with the expected transition time obtained by adding expected values as an average value. The time series data generation step obtains data output by the HMM at each time by linear combination of the average values of the data weighted by the state probabilities of each state. Data output method.

In one aspect of the present invention, for each state of the HMM defined by the state transition probability that the state transitions and the probability distribution of the data output by each state, the state outputs data at a predetermined interval of time. Based on the state probability and the average value of the data according to the probability distribution, data at a predetermined interval output by the HMM is obtained and output as time-series data. Specifically, for each state of the HMM, using the state transition probability of self-transition, a value corresponding to the expected value of the number of times that self-transition occurs is obtained as the expected value of the duration for which the self-transition continues, A recurrence formula using the normal distribution, assuming that the transition time of transition from one state to another state follows a normal distribution whose average value is the expected transition time obtained by adding the expected value of the duration. The value corresponding to the probability that the state transition starts from the state at each time is obtained as the state probability at each time. Then, data output by the HMM at each time is obtained by linear combination of the average values of the data weighted by the state probabilities of the respective states.

  According to the present invention, it is possible to obtain time-series data that changes smoothly.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 shows a configuration example of an embodiment of a speech synthesizer to which the present invention is applied.

  In FIG. 1, the speech synthesizer includes an HMM storage unit 1, a selection unit 2, an inverse filter 5, and a vector time series output unit 10. The vector time series output unit 10 includes a state probability estimation unit 3 and a vector time series generation unit 4.

  The HMM storage unit 1 stores a plurality of HMMs used for speech synthesis.

  The selection unit 2 selects an HMM used for speech synthesis from the HMMs stored in the HMM storage unit 1 and supplies the selected HMM to the state probability estimation unit 3 and the vector time series generation unit 4.

  The state probability estimation unit 3 estimates a state probability that the state outputs a vector for each state of the HMM supplied from the selection unit 2 at a predetermined interval, and supplies the state probability to the vector time series generation unit 4.

  The vector time series generation unit 4 generates a time interval at a predetermined interval based on the state probability supplied from the state probability estimation unit 3 and the representative vector output from the state of the HMM supplied from the selection unit 2. A vector is obtained and output as a time series vector (vector time series).

  The inverse filter 5 obtains and outputs a speech signal (synthetic sound) by filtering the time-series vector output from the vector time-series generation unit 4.

  Here, when the vector output from the vector time series generation unit 4 is, for example, a feature vector having a mel cepstrum coefficient as a component, for example, an MLSA filter can be employed as the inverse filter 5. Further, when the vector output from the vector time series generation unit 4 is, for example, a feature vector having a mel cepstrum coefficient as a component, the HMM storage unit 1 stores a feature vector having a mel cepstrum coefficient as a component in the HMM. For example, an HMM learned by the Baum-Welch method, which is a learning method for maximizing the likelihood that the learning data is output, is stored.

  Next, FIG. 2 shows an example of the HMM stored in the HMM storage unit 1 of FIG.

  The HMM is a probability model in which a state transition probability and an output probability density function are defined as model parameters (model parameters).

The HMM in FIG. 2 is an HMM called a left-to-right type, and N + 2 states S ₀ , S ₁ ,..., S _N−1 , S _N , S _{N +} indicated by ○ in the figure. ₁ are lined up from left to right. State S ₀ to one of the S _{N + 1,} the left-most state S ₀ is called the initial state, the rightmost state S _{N + 1} is referred to as the end state. In the HMM called the left-to-right type in FIG. 2, in the state S _i (i = 1, 2,..., N) excluding the initial state S ₀ and the end state S _{N + 1} , Only transitions (self-transitions) and state transitions to the right of themselves are allowed. Here, in FIG. 2, an arrow represents a state transition.

Further, in the HMM of FIG. 2, the state transition is made from the initial state S ₀ to the state S ₁ on the right side thereof. Therefore, the state transition probability a ₀₁ from the state S ₀ to the state S ₁ is 1. Further, state transition does not occur in the end state S _{N + 1} . Then, the state transition starts from the initial state S ₀ , reaches the end state S _{N + 1} and ends.

Further, in the HMM of FIG. 2, the probability density (probability distribution) in which the vector x is output in the states S _i (i = 1, 2,..., N) excluding the initial state S ₀ and the end state S _{N + 1.} ) Representing the output probability density function b _i (x). Here, the output probability density function b _i (x) is given by, for example, Expression (4) representing a normal distribution defined by the mean vector μ _i and the covariance matrix Σ _i .

・・・（４）

... (4)

  Here, in Equation (4), K represents the number of dimensions of the vector x that is a random variable, and the superscript T represents the transpose of the matrix.

  In FIG. 2, an HMM that allows only self-transition and state transition to the right side of the self is adopted. However, in addition, transition to another state on the right side is also permitted. It is possible to adopt an HMM. It is also possible to adopt an HMM that is not a left-to-right type.

  Next, processing of the speech synthesizer of FIG. 1 will be described with reference to the flowchart of FIG.

  First, in step S1, the selection unit 2 selects an HMM used for speech synthesis from the HMMs stored in the HMM storage unit 1, and supplies the selected HMM to the state probability estimation unit 3 and the vector time series generation unit 4. Then, the process proceeds to step S2.

  In step S2, the state probability estimation unit 3 performs state probability estimation processing for estimating the state probability that the state outputs a vector for each state of the HMM supplied from the selection unit 2, at a predetermined interval time, The state probability obtained as a result is supplied to the vector time series generation unit 4, and the process proceeds to step S3.

  In step S3, the vector time series generation unit 4 determines a predetermined interval based on the state probability supplied from the state probability estimation unit 3 and the representative vector output from the state of the HMM supplied from the selection unit 2. Vector time series generation processing for obtaining a vector for each time is performed, a time series vector (vector time series) obtained as a result is output, and the process proceeds to step S4.

  In step S4, the inverse filter 5 obtains and outputs an audio signal by filtering the time-series vector output from the vector time-series generation unit 4, and ends the process.

  Next, the state probability estimation process performed by the state probability estimation unit 3 in FIG. 1 in step S2 in FIG. 3 will be described.

In the state probability estimation process, the state probability of the HMM is estimated. The state probability of the HMM is the probability that the state outputs a vector at each predetermined time interval for each state of the HMM, and the state probability that the state S _i outputs the vector x at time t is defined as _Pi This is expressed as (t).

The state probability P _i (t) probabilistically gives a state S _i that outputs a vector x at time t.

Here, as described above, in the HMM, the output probability density function b _i (x) is defined in the states S _{1 to} S _N excluding the initial state S ₀ and the end state S _{N + 1} , and the initial state S ₀ From the end state S _{N + 1} , the vector may not be output, and the vector x may be output from the other N states S _{1 to} S _N.

The state transition from the initial state S ₀ starts at time t = 0, then, as appropriate, while the self-transition, the state _{S 1, S 2, S 3} , ···, transitions S _N, the last time t Assuming that the state S _{N + 1} is reached at = T + 1, the vector x is output in the state transition from the state S ₁ to the state S _N. That is, the vector x is output at each time t in a time interval with a time width of 1 from time t = 1 to time t = T. The length of the time series of the vector x obtained by outputting the vector x at each time interval with a time width of 1 from time t = 1 to time t = T is represented by T. This, of the length of the time series T, when the vector x series (vector x time series), x _1, x _2, x _3, · · ·, represented by x _T.

In the state probability estimation process, the state probability P _i (t) of the HMM necessary for obtaining the time series vectors x ₁ , x ₂ , x ₃ ,..., X _T is expressed as t = 1, 2,. ..., T is estimated for all states S ₁ , S ₂ ,..., S _N for which the output probability density function b _i (x) is defined.

Incidentally, t = 1,2, ···, in any of the time t of T, then the states of HMM, the vector x _t, always output. Thus, summation of the formula as shown in (5), the state S ₁ which can output a vector _{x, S 2, S 3,} ···, for all S _N, state probability at time t P _i (t) Take 1 to get 1.

・・・（５）

... (5)

State probability P _i (t), as described above, at time t, with a probability state S _i outputs a vector x (a probability that the state vector x from the state S _i by the state transition to the S _i is output) Therefore, in obtaining the state probability P _i (t), first, the time spent in the state S _i in the HMM (the time during which self-transition occurs in the state S _i ) is considered.

  Here, FIG. 4 shows an example of a state transition method in the left-to-right type HMM of FIG.

In FIG. 4, state transition starts from the initial state S _{0 at} time t = 0, and transitions from the state (initial state) S ₀ to the state S ₁ on the right side at time t = 1. Thereafter, at time t = 2, 3, 4 respectively, the state transitions from state S ₁ to state S ₁ (self-transition), and at time t = 5, transition from state S ₁ to right adjacent state S ₂ occurs. Further, at time t = 6, 7, respectively, to self-transition from the state S ₂ to state S _2, at time t = 8, it is transitioning from state S ₂ to state S ₃ to the right. Thereafter, the state transits sequentially to the self-transition or the state on the right, and at time t = T-2, the state transitions from the state S _N-1 to the state S _N on the right. Then, at each time t = T−1, T, the state S _N self-transitions to the state S _N, and at the final time t = T + 1, the state _SN transitions to the right adjacent end state S _{N + 1.} ing.

Now, at a certain time t, when the state S _i-1 transits to the right neighboring state S _i , then the self-transition is repeated n-1 times, and then the right neighboring state S _{i + 1} transits , Stays in state S _i for time n. This, the time n stay in state S _i, when referred to as a duration (or duration), the probability that the duration of the state S _i is time n is self-transition to the state S _i from the state S _i Using the state transition probability a _ii that is a probability, it is given by equation (6).

・・・（６）

... (6)

Here, in Expression (6), since the state transition probability a _ii is a probability of self-transition from the state S _i to the state S _i , 1-a _ii is a probability of transition from the state S _i to another state. is there.

The expected value E [n] of the duration n of the state S _i is expressed by equation (7) using equation (6).

・・・（７）

... (7)

The expected value E [n] of the duration n in the equation (7) can be obtained for all the states S ₁ , S ₂ ,..., S _N , and now the expected value E of the duration n of the state S _i Let [n] be expressed as d _i . Here, the expected value d _i of duration n states S _i, as shown in FIG. 4, corresponding to the number of times the self-transition occurs (expected value) of the state S _i.

By accumulating the expected values d ₁ , d ₂ ,..., D _N of the durations of the states S ₁ , S ₂ ,..., S _N as shown in the equation (8), the initial state S _The total duration T (total duration) T from ₀ to the transition to the end state S _{N + 1} can be obtained.

・・・（８）

... (8)

The total duration T expressed by Equation (8) is the length of the vector time series x ₁ , x ₂ , x ₃ ,..., X _T output from the HMM.

Note that the total duration T in Expression (8) is the length of the vector time series x ₁ , x ₂ , x ₃ ,..., X _T output from the HMM, that is, the vector time series x ₁ , x _2. , x ₃ ,..., x _T is the number of vectors, and is therefore an integer value, and therefore the expected duration d _i (= E of equation (7) used to determine the overall duration T. [n]) is converted to an integer by, for example, rounding up after the decimal point.

In the HMM, in the state sequence (state transition sequence) when the state transitions according to the expected value d _i of the duration time of the state S _i obtained by the equation (7), the state S _i-1 The time t at which the transition to the state S _i on the right side will be expressed as t _i .

In FIG. 4, as described above, time t ₂ to transition from the state S ₁ to state S ₂ of the right side are turned 5, the time the transition from state S ₂ to state S ₃ to the right t ₃ becomes 8. In addition, the time t _{N at which} the state S _N-1 transits to the state S _N on the right is T-2.

In HMM of FIG. 2, the state transition is always the state transition from the initial state S ₀ starts from the initial state S _0, always, because a transition to a state S ₁ to the right, right from the state S ₀ time t ₁ to transition to the state S ₁ is always 1.

Furthermore, in HMM of FIG. 2, the transition state, finally, to finish the transition from the state S _N to the end state S _{N + 1,} the state S _N transition prior to the transition to the end state S _{N + 1} time t, equal to the entire duration T, the time t _{N + 1} that the transition from state S _N to the state S _{N + 1} to the right is always T + 1.

As described above, the time t ₁ a transition from the initial state S ₀ to state S ₁ is always 1, further
Time t _{N + 1} to transition from the state S _N to the end state S _{N + 1} is always T + 1. Also, the expected value d _i of the duration of the state S _i may be calculated by Equation (7).

Therefore, the time t ₁ (= 1) at which the state transitions from the initial state S ₀ to the state S ₁ is set as the initial value, and the state S _i with respect to the time t _{i at} which the transition from the certain state S _i-1 to the other state S _{i is performed.} by adding the expected value d _i of the duration of, in the state transition sequence of a state transition ends at end state S _{N + 1,} starting from the initial state S _0, the state S _i to another state S _{i + 1} The transition time t _{i + 1} can be obtained.

Here, hereinafter, the time t at which the state S _i-1 transits to another state (right adjacent state) S _i will be referred to as a transition time t, and the duration of the state S _i is expected as described above. The transition time t _i obtained by performing addition using the value d _i is referred to as an expected transition time t _i .

Now, assuming that the transition time t follows a predetermined probability distribution and, for example, a normal distribution (Gaussian) is assumed as the predetermined probability distribution, the transition time for transition from the state S _i-1 to another state S _i A probability density function q _i (t) representing the probability density (probability distribution) of t is given by equation (9).

・・・（９）

... (9)

According to the probability density function q _i (t) of equation (9), as shown in FIG. 5, the transition time t from the state S _i-1 to another state S _i has an average value of the expected transition time t. _i follows a normal distribution with variance σ ² . Further, according to the probability density function q _i (t) of the equation (9), when the variance σ ² is very small, the transition time t at which the transition to the state S _i becomes a definite value t _i , and the variance σ ² As becomes larger, the transition time t for transitioning to the state S _i becomes a stochastic value.

Here, hereinafter, the probability density function (probability given by) q _i (t) of Equation (9) will be referred to as a forward transition probability as appropriate.

FIG. 6 shows the relationship between the forward transition probability q _i (t) and the state of the HMM.

Forward transition probability q _i (t) at time t, gives the transition probability of transition from state S _i-1 to another state S _i. Similarly, the forward transition probability q _{i + 1} (t) gives the transition probability of transition from state S _i to another state S _{i + 1} at time t.

Further, the probability of self-transition in state S _i at time t is given by Equation 1-q _{i + 1} (t) using the forward transition probability q _{i + 1} (t).

On the other hand, as in the case of obtaining the forward transition probability q _i (t) in the above equation (9), consider a state transition sequence starting from the end state S _{N + 1} and ending at the initial state S _0. With respect to the state transition sequence, it is possible to obtain a time t at which the state S _{i + 1} makes a transition back to another state S _i . The time t a transition back from the state S _{i + 1} to another state S _i, the time t _N to transition back from the end state S _{N + 1} to the state S _N 'a (= T) as an initial value, It can be obtained by adding the expected value d _i of the duration of the state S _i to the time t _{i + 1} ′, which transitions from one state S _{i + 2 back} to the other state S _{i + 1} .

Here, hereinafter, the time t at which the state S _{i + 1} transits from the state S _{i + 1} to the other state (the adjacent state on the left) S _i is referred to as a reverse transition time t. As described above, the state S _i is continued. The reverse transition time t _i ′ obtained by performing addition using the expected value d _i of time is referred to as the reverse expected transition time t _i ′.

Assuming that the reverse transition time t follows a predetermined probability distribution in the same manner as the transition time t, assuming that a normal distribution is assumed as the predetermined probability distribution, for example, from the state S _{i + 1} to another state S _i The probability density function r _i (t) representing the probability density at the reverse transition time t when transitioning to is given by Expression (10) similar to Expression (9).

・・・（１０）

... (10)

According to the probability density function r _i (t) of formula (10), the probability density function (forward transition probability) shown in FIG. 5 q _i in the same manner as in (t), the state S _{i + 1} from the other states S _i The reverse transition time t that makes a reverse transition retroactively follows a normal distribution in which the average value is the reverse expected transition time t _i ′ and the variance is σ ′ ² . Further, according to the probability density function r _i (t) of the equation (10), when the variance σ ′ ² is very small, the transition time t at which the transition to the state S _i becomes a definite value t _i , and the variance σ 'As ² increases, the reverse transition time t for transitioning to the state S _i becomes a stochastic value.

Here, hereinafter, the probability density function (probability given by) r _i (t) in Expression (10) will be referred to as a backward transition probability.

FIG. 7 shows the relationship between the backward transition probability r _i (t) and the state of the HMM.

  In FIG. 7, in order to represent a backward state transition (transition going back in the state), the direction of an arrow representing the state transition is illustrated in the reverse direction to FIG.

The backward transition probability r _i (t) gives a transition probability that makes a transition from the state S _{i + 1} to another state S _i at time t. Similarly, the backward transition probability r _i-1 (t) gives the transition probability of transitioning back from the state S _i to another state S _i-1 at time t.

Further, at time t, the probability of self-transitions in the state S _i is given by the formula _{1-r i-1 (t} ) with backward transition probability r _i-1 (t).

Next, for the state transition sequence in which the state transition starts from the initial state S ₀ and ends at the end state S _{N + 1} , the probability that the transition starts from the state S _{i at} time t = 0 is expressed as Pf _i (0). Therefore, in the HMM of FIG. 2, since the transition always starts from the initial state S _{0 at} the time t = 0, the probability Pf ₀ (0) that the transition starts from the state S _{0 at} the time t = 0 is expressed by the equation (11). ) Is 1 as shown.

・・・（１１）

(11)

In addition, the transition always starts from the state S _{0 at} time t = 0 means that the state S ₁ , S ₂ ,..., S _N , S _{N + 1} other than the state S _{0 at} time t = 0. because there can be no possible transition begins at time t = 0, a probability transition from the state S _i of the other state S ₀ begins Pf _i (0) becomes 0 as shown in equation (12).

・・・（１２）

(12)

For left-to-right type HMM in FIG 2, present in the state S _i at time t (are) probability Pf _i (t), i.e., at time t, the probability transition from the state S _i starts Pf _i ( t) uses the forward transition probability q _i (t) of equation (9), with initial values of the probability Pf ₀ (0) of equation (11) and the probability Pf _i (0) of equation (12). It can be calculated using the recurrence formula of equation (13).

・・・（１３）

... (13)

Here, equation the first term Pf _i-1 (t-1) qi (t) on the right side of (13), the time t-1 to the state S _i-1 Niite, the state S _i to the next time t Represents the probability of transition. Further, equation (13) second term Pf _i of the right side of the (t-1) (1- q i + 1 (t) , the time t-1 to the state S _i Niite, then the time t to the state S _i Represents the probability of self-transition.

Since the transition cannot start from the initial state S _{0 at} a time other than time t = 0, the probability Pf ₀ (t) that the transition starts from the initial state S _{0 at} a time other than time t = 0 is , 0 as shown in equation (14).

・・・（１４）

(14)

Hereinafter, as appropriate, determined as described above, at time t, the probability transition from the state S _i starts Pf _i (t), referred to as a forward state probability Pf _i (t).

Here, FIG. 8 is a table schematically showing the forward state probability Pf _i (t).

In the table of FIG. 8, the horizontal axis represents the state S _i, the vertical axis represents the time t. Then, in the column where the column of the state S _i with the horizontal axis and the row of the time t with the vertical axis intersect, the forward state probability Pf _i (t) at which the transition starts from the state S _i at the time t is described. ing.

Of the columns in the table of FIG. 8, the column where the time t is 0 is described according to the equations (11) and (12), and the column where the state S _i is the initial state S ₀ is the equation (11). And is described according to equation (14). In the following sections, forward state probabilities Pf _i (t) obtained by calculating the recurrence formula of Expression (13) are sequentially described.

Next, the probability that the transition starts from the state S _{i at} time t can be considered for a state transition sequence in which the state transition starts from the end state S _{N + 1} and ends in the initial state S ₀ .

Therefore, if the probability that a transition (backward transition) starting from the state S _i starts at time t = T + 1 is represented as Pb _i (T + 1), in the HMM of FIG. Since a backward transition always starts from the final state S _{N + 1 at} T + 1, the probability Pb _{N + 1} (T + 1) of starting a backward transition from the state S _{N + 1 at} time t = T + 1 is It becomes 1 as shown in Expression (15).

・・・（１５）

... (15)

In addition, at time t = T + 1, the backward transition always starts from state S _{N + 1,} which means that at time t = T + 1, states S _N , S _N−1 , other than state S _{N + 1} ..., since transition cannot start from S ₁ , S ₀ , probability Pb _i (T + 1) that transition starts from state S _i other than state S _{N + 1 at} time t = T + 1 Becomes 0 as shown in Expression (16).

・・・（１６）

... (16)

For left-to-right type HMM in FIG 2, present in the state S _i at time t (have) a probability Pb _i (t), i.e., at time t, the probability transition backward from the state S _i starts Pb _i (t) is a backward transition of the equation (10) in which the probability Pb _{N + 1} (T + 1) of the equation (15) and the probability Pb _i (T + 1) of the equation (16) are initial values. It is possible to calculate using the recurrence formula of Expression (17) using the probability r _i (t).

・・・（１７）

... (17)

At times other than time t = T + 1, a backward transition cannot start from the end state S _{N + 1.} Therefore, at times other than time t = T + 1, the end state S _{N + 1} The probability Pb _{N + 1} (t) at which the transition starts is 0 as shown in Expression (18).

・・・（１８）

... (18)

Hereinafter, the probability Pb _i (t) of the backward transition starting from the state S _{i at} time t, which is obtained as described above, is referred to as the backward state probability Pb _i (t).

Here, FIG. 9 is a table schematically showing the backward state probability Pb _i (t).

In the table of FIG. 9, the horizontal axis represents the state S _i, the vertical axis represents the time t. Then, in the column where the column of the state S _i with the horizontal axis and the row of the time t with the vertical axis intersect, the backward state probability Pb _i (t) at which the backward transition starts from the state S _{i at} time t is described Has been.

Of the columns in the table of FIG. 9, the column where the time t is T + 1 is described according to the equations (15) and (16), and the column where the state S _i is the end state S _{N + 1} is The description is made according to the equations (15) and (18). In the following, the backward state probability Pb _i (t) obtained by calculating the recurrence formula of Expression (17) is sequentially described in the other columns.

Wherein forward state probability Pf _i (t) of (13), the state transition sequence of a state transition ends at end state S _{N + 1,} starting from the initial state S _0, at time t, the transition begins from the state S _i The backward state probability Pb _i (t) of equation (17) is the state S _{i at} time t for a state transition sequence starting from the end state S _{N + 1} and ending at the initial state S _0. The probability that a transition will start from is multiplied by these forward state probabilities Pf _i (t) and backward state probabilities Pb _i (t), that is, the probability of being in state S _i at time t, that is, , the state S _i can be obtained state probability of outputting the vector x (probability state for a vector x is the state _{S i) P i (t)} .

Therefore, state probability P _i (t) is defined by equation (19).

・・・（１９）

... (19)

The state probability P _i (t) in the equation (19) is obtained by multiplying the forward state probability Pf _i (t) and the backward state probability Pb _i (t) by the state S _{1 to} S of the multiplication value. _Since normalization is performed by the summation (Σ) for _N , the above equation (5) is satisfied.

The state probability P _i (t) in the equation (19) indicates that any vector at the time of state transition is present for all the states S ₁ , S ₂ ,..., S _N for which the output probability density function b _i (x) is defined. It can be calculated for each output time t = 1, 2,.

Here, FIG. 10 is a table schematically showing the state probability P _i (t).

In the table of FIG. 10, the horizontal axis represents the state S _i, the vertical axis represents the time t. Then, a sequence of states S _i with a horizontal axis, in the column and row of the time t with a vertical axis intersect at time t, state probability is the probability that the vector is output from the state S _i P _i (t ) Is described.

In each column of the table of FIG. 10, the formula (19) is calculated using the forward state probability Pf _i (t) of the table of FIG. 8 and the backward state probability Pb _i (t) of the table of FIG. State probability P _i (t) obtained by this is described.

Next, FIG. 11 shows a configuration example of the state probability estimation unit 3 of FIG. 1 that performs the state probability estimation process for estimating the state probability P _i (t) as described above.

  The state probability estimator 3 includes a duration length calculator 21, an expected transition time calculator 22, a forward transition probability determiner 23F and a backward transition probability determiner 23B, a forward state probability calculator 24F and a backward state probability calculator 24B, and The state probability calculation unit 25 is configured.

The duration time calculation unit 21 is supplied with the HMM (the state transition probability a _ij ) from the selection unit 2 (FIG. 1).

Duration calculator 21 uses the state transition probability a _ij of the HMM supplied from the selection unit 2, the expected value of the duration n of states S _i represented by the formula _{(7) d i (= E} [ n]) are calculated for all the states S ₁ , S ₂ ,..., S _N and supplied to the expected transition time calculation unit 22.

Furthermore, duration calculator 21, the state S _1, S _2, · · ·, the expected value of S _N respective durations d _1, d _2, · · ·, with d _N, equation (8) Determine the total duration T of. Then, the duration time calculator 21 supplies the total duration T to the necessary blocks.

Expected transition time calculation unit 22 is supplied from the duration calculator 21, the state _{S 1, S 2, ···,} S N expected values d ₁ of each duration, d _2, · · ·, d _N is used to obtain an expected transition time t _i and a reverse expected transition time t _i ′, supply the expected transition time t _i to the forward transition probability determination unit 23F, and the reverse expected transition time t _i ′ This is supplied to the backward transition probability determination unit 23B.

The forward transition probability determination unit 23F uses the expected transition time t _i supplied from the expected transition time calculation unit 22 to obtain the forward transition probability q _i (t) of Expression (9) and supplies it to the forward state probability calculation unit 24F. To do. As the variance σ ² of the forward transition probability q _i (t) in equation (9), for example, a predetermined fixed value can be adopted, or a value obtained as described later can be adopted. You can also.

The backward transition probability determination unit 23B uses the reverse expected transition time t _i ′ supplied from the expected transition time calculation unit 22 to obtain the backward transition probability r _i (t) of Expression (10), and the backward state probability calculation unit 24B. To supply. As the variance σ ′ ² of the backward transition probability r _i (t) in equation (10), for example, a predetermined fixed value can be adopted, or a value obtained as described later is adopted. You can also.

The forward state probability calculation unit 24F uses the forward transition probability q _i (t) of Equation (9) supplied from the forward transition probability determination unit 23F to calculate the recurrence formula of Equation (13), thereby The probability Pf _i (t) is obtained and supplied to the state probability calculation unit 25.

The backward state probability calculation unit 24B calculates the recurrence formula of the equation (17) by using the backward transition probability r _i (t) of the equation (10) supplied from the backward transition probability determination unit 23B. The probability Pb _i (t) is obtained and supplied to the state probability calculation unit 25.

The state probability calculation unit 25 uses the forward state probability Pf _i (t) supplied from the forward state probability calculation unit 24F and the backward state probability Pb _i (t) supplied from the backward state probability calculation unit 24B. The state probability P _i (t) of Expression (19) is obtained and supplied to the vector time series generation unit 4 (FIG. 1) at the subsequent stage.

  Next, the state probability estimation process performed by the state probability estimation unit 3 of FIG. 11 in step S2 of FIG. 3 will be described with reference to the flowchart of FIG.

The duration time calculation unit 21 receives the supply of the HMM from the selection unit 2 (FIG. 1), and is expressed by Equation (7) using the state transition probability a _ij of the HMM from the selection unit 2 in step S21. The expected value d _i (= E [n]) of the duration n of each state S _i of the HMM is calculated and supplied to the expected transition time calculation unit 22, and the process proceeds to step S22.

In step S22, the expected transition time calculation unit 22 uses the expected duration values d ₁ , d ₂ ,..., D _N from the duration length calculation unit 21 and the expected transition time t _i and the reverse expectation. The transition time t _i ′ is obtained, and the expected transition time t _i is supplied to the forward transition probability determining unit 23F, and the reverse expected transition time t _i ′ is supplied to the backward transition probability determining unit 23B, and the process goes to step S23. move on.

In step S23, the forward transition probability determining unit 23F uses the expected transition time t _i from the expected transition time calculating unit 22 to obtain the forward transition probability q _i (t) of Equation (9), and the forward state probability calculating unit 24F. , The backward transition probability determination unit 23B obtains the backward transition probability r _i (t) of Equation (10) using the reverse expected transition time t _i ′ from the expected transition time calculation unit 22, and the backward state probability The calculation unit 24B is supplied and the process proceeds to step S24.

In step S24, the forward state probability calculation unit 24F uses the forward transition probability q _i (t) from the forward transition probability determination unit 23F to obtain the forward state probability Pf _i (t) of Expression (13), and the state probability The backward state probability calculation unit 24B supplies the backward state probability Pb _i (t) of Expression (17) using the backward transition probability r _i (t) from the backward transition probability determination unit 23B. It is obtained and supplied to the state probability calculation unit 25, and the process proceeds to step S25.

In step S25, the state probability calculation unit 25 uses the forward state probability Pf _i (t) from the forward state probability calculation unit 24F and the backward state probability Pb _i (t) from the backward state probability calculation unit 24B. The state probability P _i (t) of Equation (19) is obtained and supplied to the subsequent vector time series generation unit 4 (FIG. 1), and the state probability estimation process is terminated.

  Next, the vector time series generation process performed by the vector time series generation unit 4 of FIG. 1 in step S3 of FIG. 3 will be described.

In the vector time series generation process, based on the state probability P _i (t) obtained by the state probability estimation unit 3 and the output probability density function b _i (x) defined in the state S _i of the HMM, the vector time series x ₁ , x ₂ , x ₃ ,..., X _T are generated.

Now, a probability density function representing a probability distribution (probability density) in which a vector x is output (observed) at time t from the HMM is represented as F _t (x).

The state probability P _i (t) is the probability that some vector is output from the state S _{i at} time t, and the output probability density function b _i (x) is the probability density that the vector x is output from the state S _i. Therefore, the probability density function F _t (x) representing the probability density at which the vector x is output from the HMM at time t, that is, the probability density at which the vector x is output from any state S _i of the HMM is It is given by equation (20).

・・・（２０）

... (20)

Here, considering that the output probability density function b _i (x) is given by the normal distribution shown in the equation (4) and the state probability P _i (t) is a probability satisfying the equation (5). The probability density function F _t (x) follows a mixed normal distribution obtained by mixing a plurality of normal distributions (Gaussian).

That is, the state probability P _i (t) in the probability density function F _t (x) of Expression (20) is given to the normal distribution (output probability density function b _i (x)) shown in Expression (4). It corresponds to the mixing weight. However, in Equation (20), the state probability P _i (t), which is a mixture weight, changes with time t.

When the probability density function F _t (x) in Expression (20) gives the probability density that the vector x is output from the HMM at time t, the expected value E [x] of the vector x output from the HMM at time t Is given by equation (21).

・・・（２１）

... (21)

  By substituting equation (20) into equation (21), the expected value E [x] of vector x output from the HMM at time t can be obtained by equation (22).

・・・（２２）

(22)

Here, the integral ∫ (b _i (x) · x) dx from −∞ to + ∞ of the vector x of b _i (x) · x in the second row from the top of the equation (22) is the output probability density The expected value of the vector x as a representative vector of the vector x given the probability density by the function b _i (x), but the output probability density function b _i (x) is a normal distribution shown in Equation (4) Is given by the average vector μ _i that defines the normal distribution of equation (4) as shown in the third line from the top of equation (22).

According to equation (22), the expected value of the vector x to be output at time t E [x] is, each state of the _{HMM S 1, S 2, ···} , the output probability density function is defined in the S _N b _{1 (x), b 2 (} x), ···, average vector mu ₁ to b _N (x) defines a normal distribution according, μ _2, ···, a mu _N, mixture weight P ₁ (t) , P ₂ (t),..., P _N (t) are calculated by linear combination.

In the vector time series generation process, the expected value E [x] of the vector x obtained by the equation (22) is obtained for each time t = 1, 2,..., T, and the vector time series x ₁ , x ₂ ,..., it is output as x _T.

Next, in FIG. 13, as described above, vectors at predetermined intervals of time t = 1, 2,..., T are obtained, and vector time series x ₁ , x _{2 ,.} 1 shows a configuration example of the vector time series generation unit 4 of FIG.

  The vector time series generation unit 4 includes an expected value acquisition unit 31 and an expected value calculation unit 32.

The expected value acquisition unit 31 is supplied with an HMM (output probability density function b _i (x)) from the selection unit 2 (FIG. 1). Expected value obtaining unit 31 obtains from the output probability density function b _i of the HMM supplied from the selection section 2 (x), the expected value of the output probability density function b _i (x) a vector x according to a probability distribution represented by That is, the calculation result of the integral ∫ (b _i (x) · x) dx from −∞ to + ∞ of the vector x of b _i (x) · x in the second row from the top of the equation (22) is obtained. To the expected value calculation unit 32.

Here, as described above, since the output probability density function b _i (x) is a normal distribution, the expectation value acquisition unit 31 obtains an average vector μ _i that defines the normal distribution as an expectation value of the vector x. It is done.

The expected value calculation unit 32 is supplied with an average vector μ _i as an expected value of the vector x from the expected value acquisition unit 31 and with a state probability P _i (t) from the state probability estimation unit 3 (FIG. 1). Is done. The expected value calculation unit 32 uses the average vector μ _i supplied from the expected value acquisition unit 31 and the state probability P _i (t) supplied from the state probability estimation unit 3 to calculate the expected value from the above equation (22). by performing the calculation of the third row, each state of the _{HMM S 1, S 2, ···} , the output probability density function b ₁ as defined in _{S N (x), b 2} (x), ···, average vector mu ₁ defining a normal distribution b _N (x) is followed, μ _2, ···, a mu _N, mixture weight _{P 1 (t), P 2} (t), ···, P N (t ), That is, the expected result E [x] of the vector x output from the HMM at time t is obtained at each time t = 1, 2,... Output vector time series x ₁ , x ₂ ,..., X _T.

  Next, the vector time series generation process in step S3 of FIG. 3 performed by the vector time series generation unit 4 of FIG. 13 will be described with reference to the flowchart of FIG.

The expected value acquisition unit 31 receives the supply of the HMM from the selection unit 2 (FIG. 1), and outputs the output probability density function from the output probability density function b _i (x) of the HMM supplied from the selection unit 2 in step S31. The expected value of the vector x according to the probability distribution represented by b _i (x) is output from the output probability density function b ₁ (x), b ₂ (x),..., b _N (x) in the HMM from the selector 2. There defined each state S ₁ is, S _2, ···, obtained for S _N, and supplies the expected value calculation unit 32.

That is, the expectation value acquisition unit 31 defines each state S ₁ in which output probability density functions b ₁ (x), b ₂ (x),..., B _N (x) are defined in the HMM from the selection unit 2. , S ₂ ,..., S _N , mean vectors μ ₁ , μ defining the normal distribution represented by the output probability density functions b ₁ (x), b ₂ (x), ..., b _N (x) ₂ ,..., Μ _N are obtained (obtained) and supplied to the expected value calculation unit 32.

Then, the process proceeds from step S31 to step S32. The expected value calculation unit 32 is supplied from the average vectors μ ₁ , μ ₂ ,..., Μ _N supplied from the expected value acquisition unit 31 and the state probability estimation unit 3. , P _N (t), and the product-sum operation result ΣP _i (t) · μ _i is calculated from the state probabilities P ₁ (t), P ₂ (t),. The expected value x _t (= E [x]) of the vector x output from the HMM at time t is obtained.

In step S32, the expected value calculation unit 32 obtains the expected values x ₁ , x ₂ ,..., X _T of the vector x output from the HMM at each time t = 1, 2,. Te, the process proceeds to step S33, the expected value x _1, x ₂ of the vector x, ..., a x _T, a vector time series x ₁ for the entire duration T, x ₂ outputs, ..., as x _T Then, the vector time series generation process ends.

As described above, for each state S _i of the HMM in which the vector x is output according to the state transition, the state probability P _i (t) at which the state S _i outputs the vector x at every time t at a predetermined interval And the state probability P _i (t) and the representative vector output by the state S _i , for example, based on the average vector μ _i for each time t at a predetermined interval output by the HMM. Since the vectors x ₁ , x ₂ ,..., X _T are obtained, that is, without determining the state of the HMM to which the vector x is to be output, it is represented stochastically by the state probability P _i (t), Based on the state probability P _i (t), the vector time series x ₁ , x ₂ , ..., x _T is generated by analytically calculating the expected value of the vector x output by the HMM. As a result, there is no need to use dynamic features, and without repeatedly trying to generate a vector time series, it is possible to change smoothly and efficiently. It is possible to generate a torque time series.

That is, assuming that the transition time t (and reverse transition time t ′) from one state S _i to another state S _{i + 1} follows the probability distribution, the self-transition of the state S _i continues at that transition time t. The state probability P _i (t) representing the probability that the state S _i is in the state of outputting the vector x at the time t is obtained using the duration time d _i . Therefore, the state S _i to state probability P _i (t) becomes higher, with the progress of time t, to transition from state S ₁ to state S _N, state probability P _i (t) changes smoothly , depending on the smooth change of the state probability P _i (t), a vector time series is generated by using the state probability P _i (t) is smoothly changed.

Here, the state probability P _i (t) that varies in accordance with the time t, the vector time series x ₁ finally obtained, x _2, · · ·, the characteristics of temporal changes in x _T larger It depends on you.

That is, for example, in all states S _i, when a constant value state probability P _i (t) does not depend on time t, the vector time series x ₁ unchanged temporally, x _2, · · ·, is x _T can get.

Further, for example, at each time t, the only state probability P _i of a one state (t) is the next 1, the other states of the state probability P _i (t) becomes 0, the vector x at each time t The state to be output is fixed (determined) to one state, and as a result, the state transition sequence when the vector time series is output is fixed. In this case, a vector time series in which average vectors output from the states of the fixed state transition series are arranged is obtained.

In the above case, the output probability density function b _i (x) defined in each state S _i of the HMM follows a normal distribution, but the output probability density function b _i (x) Other than the distribution, for example, a function representing a probability distribution capable of calculating an average vector, such as a mixed normal distribution, can be employed.

Furthermore, the output probability density function b _i (x) is a function that represents a probability distribution that can approximately determine the average vector even if the average vector cannot be determined precisely (exactly). It is possible to adopt.

That is, the output probability density function b _i (x), the b _i (x) · x in the second row from the top of the equation (22), the integral ∫ over + ∞ from -∞ about vector x (b _i ( x) · x) dx operation, that is, the operation to find the vector x with the maximum likelihood output from the state S _i (the expected value E [x] of the vector x output from the state S _i ) is strictly Alternatively, a function that can be performed approximately can be employed.

The calculation result of the integral ∫ (b _i (x) · x) dx from −∞ to + ∞ with respect to the vector x of b _i (x) · x in the second line from the top of the equation (22) is as follows: In addition to the average vector μ _i described above, for example, a vector x that gives the maximum value of the output probability density function b _i (x), the state S _i follows a probability distribution represented by the output probability density function b _i (x). Of the vectors x to be output, so-called representative vectors can be adopted.

  In the above case, the left-to-right type HMM is adopted as the state transition probability model. However, the HMM is not limited to the left-to-right type. It may be an HMM having a state transition with skipping, an HMM having a backward state transition, or an HMM in which transitions between all states are defined.

Furthermore, it is possible to employ a state transition probability model other than the HMM as the state transition probability model. As the state transition probability model other than the HMM, for example, there is a state transition probability model that can estimate the state probability P _i (t), such as a Bayesian network.

  In a Bayesian network, time-series data is modeled by representing dependency relationships between variables in a graph structure and assigning conditional probabilities to each node.

  Note that the determination of the graph structure of the Bayesian network is performed, for example, by selecting a model that takes into account the likelihood of the learning data used for learning and the complexity of the graph structure. A maximum likelihood estimation method or an EM (Expectation Maximaization) algorithm is used. Here, details of the Bayesian network are described in, for example, Yoichi Motomura, “Information Representation for Uncertainty Modeling: Bayesian Network”, 2001, Bayesian Network Tutorial.

Further, as described above, the state probability P _i (t) changes according to the time t. The temporal change in the finally obtained vector time series x ₁ , x ₂ ,..., X _T The characteristics of the vector time series x ₁ , x ₂ , ..., x _T are used to determine the state probability P _i (t) and hence the state probability P _i (t). It is possible to change by adjusting the variance σ ² of the forward transition probability q _i (t) in Equation (9) and the variance σ ′ ² of the backward transition probability r _i (t) in Equation (10). .

For example, if the variance σ ² or σ ' ² is reduced, the transition time from the state S _i-1 to the state S _i approaches a deterministic value, and as a result, the state transition when the HMM outputs a vector time series In other words, since the state transition sequence becomes deterministic, the average vector of the output probability density function b _i (x) defined for each state from each state of such a definite state transition sequence Can be obtained as a vector time series.

On the other hand, when the variance σ ² or σ ′ ² is increased, the state S _i in which the state probability P _i (t) increases is changed from the state S ₁ to the state S _{N as} the time t progresses. The probability p _i (t) changes smoothly, and a vector time series that changes smoothly according to the smooth change of the state probability P _i (t) is obtained.

FIG. 15 and FIG. 16 are diagrams for explaining the contents of a simulation for obtaining a vector time series by changing the variances σ ² and σ ′ ² .

  That is, FIG. 15 shows learning data used for HMM learning.

  In the simulation, a time series of one-dimensional vectors having a length (total duration) T of 100, that is, a time series of scalar data having a length T of 100, was used as learning data for the HMM.

  In FIG. 15, learning data is shown with the horizontal axis as time t and the vertical axis as the data value.

  The learning data in FIG. 15 is 0 at time t = 0, and decreases smoothly with the progress of time t, and has a minimum value near time t = 50. Furthermore, the learning data in FIG. 15 increases smoothly with the progress of time t after reaching the minimum value, and becomes 0 again at time t = 100.

  HMM learning was performed by the Baum-Welch method using the learning data of FIG. As the HMM, a left-to-right HMM with 10 states was used, and learning was performed assuming that the output probability density function follows a normal distribution.

  FIG. 16 shows a time series of one-dimensional vectors (scalar data) generated from the HMM obtained by learning as described above in the vector time series output unit 10 (FIG. 1).

  In FIG. 16, as in FIG. 15, the horizontal axis represents time t, and the vertical axis represents data values.

In the simulation for generating a time series of one-dimensional vectors from the HMM, the variance σ ² of the forward transition probability q _i (t) of the equation (9) used for obtaining the state probability P _i (t) and the equation The variance σ ′ ² of the backward transition probability r _i (t) in (10) is fixed to the same value in all states of the HMM. As the fixed variances σ ² and σ ′ ² , three values of 0.0001, 36.0, and 400 were used.

FIG. 16 shows vector time series obtained when three types of values of 0.0001, 36.0, and 400 are used as the values of variances σ ² and σ ′ ² .

According to FIG. 16, when a very small value of 0.0001 is adopted as the values of variances σ ² and σ ′ ² , the state transition sequence when the HMM outputs a vector time series is determined as described above. As a result, a vector time series with a stepwise change is output, such as an average vector (average value) defining a normal distribution representing the output probability density function from each state of the definite state transition sequence. Can be confirmed.

Further, according to FIG. 16, when a large value of 36.0 is adopted as the values of the variances σ ² and σ ′ ² , it can be confirmed that a vector time series that changes smoothly is output. Further, according to FIG. 16, when a larger value of 400 is adopted as the values of the variances σ ² and σ ′ ² , when the vector time series is viewed as a waveform that changes with time, the waveform However, it can be confirmed that a lazy vector time series is output.

As described above, the characteristics of the vector time series output from the HMM can be changed by adjusting the values of the variances σ ² and σ ′ ² .

In FIG. 16, the vector time series obtained when the values of variances σ ² and σ ′ ² are 36.0 is close to the learning data of FIG. From this, it can be seen that a vector time series having characteristics close to the learning data can be generated by appropriately adjusting the values of the variances σ ² and σ ′ ² .

Further, the adjustment of the variances σ ² and σ ′ ² (values thereof) is configured by, for example, an operation of an operation unit (not shown) by the user, a state probability estimation unit 3 and a vector time series generation unit 4 in FIG. This can be performed in response to a request from an application that uses the vector time series output unit 10 (speech synthesizer in FIG. 1).

Further, the adjustment (determination) of the variances σ ² and σ ′ ² (values) is, for example, the expected value d _i (= E [n]) of the duration of each state S _i obtained by the equation (7). It can also be performed based on.

That is, immediately before the transition of the variance sigma ² of forward transition probability q _i of Equation (9) (t) is the time t from the state S _i-1 to the state S _i (forward transition) is performed, the state S _i Based on the expected value d _i-1 of the continuous duration in which self-transition at _-1 continues, it can be determined by, for example, Expression (23).

・・・（２３）

(23)

In Expression (23), _cf is a constant, and for example, _cf = 0.5 is used.

According to equation (23), wherein the dispersion sigma ² (9) of the forward transition probability q _i (t) is the state S _i-1 of the duration expected value immediately before the forward transition is made to the state S _i based on the d _i-1, is determined to a large value the longer the expected value d _i-1 of its duration, is determined to a small value is shorter expected value d _i-1 duration.

Similarly, the variance σ ′ ² of the backward transition probability r _i (t) in Expression (10) is the state immediately before the transition (backward transition) going back from the state S _{i + 1} to the state S _i at time t. Based on the expected value d _{i + 1} of the duration of continuous self-transition at S _{i + 1} , it can be determined by, for example, Expression (24).

・・・（２４）

... (24)

In Expression (24), c _b is a constant, and for example, c _b = 0.5 is used.

According to equation (24), backward transition probability variance sigma ^'2 of r _i (t) is the expected state S _{i + 1} duration immediately before the backward transition is performed to a state S _i of formula (10) Based on the value d _{i + 1} , a larger value is determined if the expected value d _{i + 1 of the} duration is longer, and a smaller value is determined if the expected value d _{i + 1 of the} duration is shorter.

Next, in the above-described case, the expected value d _i (= E [n]) of the duration of Expression (7) is used as an integer, for example, by rounding up after the decimal point. Due to the integerization, an error occurs in the vector time series output from the HMM as compared with the case where the integerization is not performed.

This error can be reduced by using a value including a decimal point as the expected value d _i of the duration.

That is, in the above-described case, although an explicit explanation is omitted, assuming that the time interval of the learning data used for learning of the HMM is 1, the HMM starts from each time interval having a time width of 1. Since the vector x is output at the time t, the time t takes only an integer value, and therefore the expected duration d _i also takes only the integer value, but the vector x is output from the HMM. By assuming a value including the decimal point as the time, the expected duration d _i can also be a value including the decimal point, thereby reducing errors in the vector time series output from the HMM. can do.

That is, in the state probability estimation unit 3 (FIG. 1), the expected value d _i of the duration of the equation (7) is obtained to the first decimal place, for example, by rounding up the second decimal place. Further, the state probability estimation unit 3 uses the expected value d _i of the duration calculated to the first decimal place, and the forward transition probability q _i (t) of Equation (9) and the backward transition probability of Equation (10). r _i (t) is obtained, and further, the forward state probability Pf _i (t) represented by the recurrence formula of Expression (13) is obtained using the forward transition probability q _i (t) of Expression (9). In addition, the backward state probability Pb _i (t) represented by the recurrence formula of Expression (17) is obtained using the backward transition probability r _i (t) of Expression (10).

However, the forward state probability Pf _i (t) represented by the recurrence formula of Expression (13) and the backward state probability Pb _i (t) represented by the recurrence expression of Expression (17) are Obtain the step size (time interval) as 0.1.

Then, the state probability estimation unit 3 uses the forward state probability Pf _i (t) and the backward state probability Pb _i (t) obtained by setting the step size at time t to 0.1, and sets the step size at time t to 0.1. State probability P _i (t) in equation (19), that is, P _i (0.0), P _i (0.1), P _i (0.2), P _i (0.3),..., P _i (T + 0.8) , P _i (T + 0.9) and P _i (T + 1.0) are obtained.

Here, FIG. 17 shows a state probability P _i (t) obtained when the step size at time t is 1 (upper side in FIG. 17) and a state probability P _i (t) obtained when the step size at time t is 0.1 (see FIG. 17). 17 lower side).

After step size at time t is obtained 0.1 state probability P _i (t) is the vector time series generating unit 4 (FIG. 1), the state probability of the step size of the time t and 0.1 P _i (t) .., T using the values at time t = 1, 2, 3,..., T, and calculating the equation (22), it is possible to obtain a vector time series with time t increment of 1. .

As described above, by reducing the step size at time t for calculating the state probability P _i (t), the overall processing amount is increased, but by making the expected value d _i of the duration into an integer, it becomes a vector time series. The error that occurs can be reduced.

  Note that the step size at time t is desirably determined by balancing the processing amount and the error.

Further, here, the step probability at time t is changed from 1 to 0.1 to calculate the state probability P _i (t), but the step size at time t is other values, for example, 0.5 or 0.01. The error that occurs in the vector time series output from the HMM (the accuracy of the vector time series output from the HMM) and the overall processing amount are adjusted according to the step size at time t. be able to.

Further, the time interval of the vector time series output from the HMM can be adjusted with the step size of the time t for obtaining the state probability P _i (t) as the minimum value. That is, as described above, when the state probability P _i (t) is obtained by setting the step size of time t to 0.1, the time interval of the vector time series output from the HMM is set to 1 as described above. For example, 0.5 or 0.1 can be used.

The adjustment of the step size of the time t for obtaining the state probability P _i (t) and the time interval of the vector time series output from the HMM are performed by, for example, the operation of the operation unit (not shown) by the user or the vector time of FIG. This can be performed in response to a request from an application that uses the series output unit 10.

  Next, in the above-described case, a vector time series is generated from one HMM. However, a vector time series may be generated from an HMM obtained by combining a plurality of HMMs (hereinafter referred to as a combined HMM as appropriate). Is possible.

  FIG. 18 shows a combined HMM in which two left-to-right type HMMs # 1 and # 2 are combined.

In FIG. 18, left-to-right type HMM # 1 having states S _{0 to} S _{N1 + 1} and left-to-right type HMM # 2 having states S ′ _{0 to} S ′ _{N2 + 1} are represented. Are combined in that order to form one combined HMM.

That is, in FIG. 18, the end state S _{N1 + 1} of HMM # 1, 'is deleted and _0, the state S _N1 of HMM # 1, the state S of the HMM # 2' initial state S of HMM # 2 and ₁ Are connected, HMM # 1 and # 2 are coupled.

  The combined HMM can also be handled in the same way as one HMM, and therefore the vector time series output unit 10 generates a vector time series from the combined HMM in the same manner as when generating a vector time series from one HMM described above. Can be generated.

In the combined HMM, the state S _N1 of the HMM # ₁ is changed to the state S′1 of the HMM # 2 instead of the end state S _{N1 + 1} of the HMM # ₁ , and in the combined HMM, also the transition from the state S _N1 of HMM # 1 to the state S _'1 of HMM # 2, it is possible to obtain a vector time series changes smoothly.

  In the above case, two HMMs # 1 and # 2 are combined, but three or more HMMs can be combined.

  Next, processing of the speech synthesizer of FIG. 1 when generating a vector time series by combining HMMs as described above will be described with reference to the flowchart of FIG.

  In step S51, the selection unit 2 in FIG. 1 selects a plurality of HMMs used for speech synthesis from the HMMs stored in the HMM storage unit 1, and proceeds to step S52. To obtain the combined HMM. Then, the selection unit 2 supplies the combined HMM to the state probability estimation unit 3 and the vector time series generation unit 4, and proceeds from step S52 to step S53.

In step S53, the state probability estimation unit 3 performs state probability estimation processing for estimating the state probability P _i (t) for each time t at a predetermined interval for each state S _i of the combined HMM supplied from the selection unit 2. Then, the state probability P _i (t) obtained as a result is supplied to the vector time series generation unit 4, and the process proceeds to step S54.

In step S54, the vector time series generation unit 4 outputs a representative vector output by the state probability P _i (t) supplied from the state probability estimation unit 3 and the state S _{i of the} combined HMM supplied from the selection unit 2. For example, based on the average vector μ _i , vector time series generation processing for obtaining a vector for each time t at a predetermined interval is performed, and the vector time series obtained as a result is output, and the process proceeds to step S55.

  In step S55, the inverse filter 5 obtains and outputs an audio signal by filtering the vector time series output from the vector time series generation unit 4, and the process ends.

  Next, the left-to-right type HMM as shown in FIG. 2 is suitable for expressing (modeling) a certain vector time-series pattern (time-series pattern).

Accordingly, for a left-to-right type HMM as shown in FIG. 20, the state returns from the state S _N immediately before the end state S _{N + 1} to the state S ₁ immediately after the initial state S _0. Considering the HMM that gave the transition, a vector time series of periodic orbits, in which the time series pattern represented by the original HMM is repeated by the transition from state S _N to state S ₁ It is possible to generate a vector time series having a periodic waveform.

The vector time series of the periodic trajectory output from the HMM given the transition from the state S _N to the state S ₁ shown in FIG. 20 can be generated by using the above-described combined HMM.

  That is, three HMMs representing a time series pattern corresponding to a vector time series of one period, for example, a vector time series of a periodic trajectory are prepared. Here, these three HMMs are referred to as HMM # 1, # 2, and # 3.

Then, as shown in FIG. 21, the same three HMMs # 1, # 2, and # 3 are combined in that order in the same manner as in FIG. Now, if one of the same three HMMs # 1, # 2, and # 3 has states S _{0 to} S _{N + 1} , the combined HMM enters state S _N of HMM # 1 as shown in FIG. the state S ₁ of the HMM # 2 is connected, further, a state S _N of the HMM # 2, the state S ₁ of HMM # 3 is connected, an HMM state S ₁ to S _N are arranged repeated 3 times . The combined HMM expresses a time series pattern corresponding to a vector time series for three periods of a vector time series of periodic orbits.

  The combined HMM in which the same three HMMs # 1, # 2, and # 3 are combined as described above can be handled in the same manner as one HMM as in the case of FIG. The output unit 10 can generate a vector time series from the combined HMM, as in the case of generating a vector time series from one HMM described above.

  When the vector time series is generated from the combined HMM of FIG. 21, a vector time series of three periods of the vector time series of the periodic trajectory can be obtained. It is possible to obtain a minute vector time series.

That is, after the state probability P _i (t) is obtained for the combined HMM in FIG. 21 in the state probability estimation unit 3 (FIG. 3), the state S of HMM # 2 is included in the state probability P _i (t). Only the state probabilities P _{i ′} (t) corresponding to _{1 to} S _N are extracted. Then, the vector time series generation unit 4 outputs a vector time series obtained from the state probability P _{i ′} (t) as one period, and generates a periodic orbit vector time series by repeating this. It becomes possible.

Here, in the coupled HMM of FIG. 21, the state S _N of HMM # 1 to the state S of HMM # 2 are affected by the influence of HMM # 1 on the left side of HMM # 2 and HMM # 3 on the right side of HMM # 2. _{Since the} vector time series obtained over ₁ and the vector time series obtained from state S _N of HMM # 2 to state S ₁ of HMM # 3 change smoothly, the state of HMM # 2 Even in a vector time series obtained by repeating outputting a vector time series obtained from the state probabilities P _{i ′} (t) corresponding to S _{1 to} S _N as one period, the state S _{N of} HMM # 2 The portion obtained from state to state S ₁ changes smoothly.

  Next, the processing of the speech synthesizer in FIG. 1 in the case where the HMMs are combined to generate a periodic trajectory vector time series will be described with reference to the flowchart in FIG.

  In step S61, the selection unit 2 in FIG. 1 selects one HMM used for speech synthesis from the HMMs stored in the HMM storage unit 1, proceeds to step S62, and copies the one HMM. The same three HMMs # 1, # 2, and # 3 are obtained. Further, the selection unit 2 combines the three HMMs # 1, # 2, and # 3 in that order, thereby obtaining the combined HMM shown in FIG. Then, the selection unit 2 supplies the combined HMM to the state probability estimation unit 3 and the vector time series generation unit 4, and proceeds from step S62 to step S63.

In step S63, the state probability estimation unit 3 performs state probability estimation processing for estimating the state probability P _i (t) for each time t at a predetermined interval for each state S _i of the combined HMM supplied from the selection unit 2. Then, the process proceeds to step S64, and only the state probabilities P _{i ′} (t) corresponding to the states S _{1 to} S _N of HMM # 2 are obtained from the state probabilities P _i (t) obtained as a result of the state probability estimation process. The extracted time is supplied to the vector time series generation unit 4 and the process proceeds to step S65.

In step S65, the vector time series generation unit 4 performs the vector time series generation process with the state probability P _{i ′} (t) from the state probability estimation unit 3 and the HMM # of the combined HMMs supplied from the selection unit 2. 2 and outputting a vector time series for one period obtained as a result, and the process proceeds to step S66.

  In step S66, the inverse filter 5 obtains and outputs an audio signal by filtering the vector time series output from the vector time series generation unit 4, and the process proceeds to step S67.

  In step S67, the vector time series generation unit 4 determines whether or not the vector time series output has been repeated a predetermined number of times, for example, a predetermined number of times, and has been repeatedly performed a predetermined number of times. If it is determined that there is not, the process returns to step S65, and the same processing is repeated thereafter. In the second and subsequent steps S65, the vector time series generation process may be performed again, but the vector time series output in the first step S65 is stored without performing the vector time series generation process. The vector time series may be output.

  On the other hand, if it is determined in step S67 that the vector time-series output has been repeated a predetermined number of times, the process ends.

In FIG. 21, the same three HMMs # 1, # 2, and # 3 are combined, but the same four or more HMMs may be combined. In this case, state probabilities P _{i ′} (corresponding to one or more HMMs excluding the first HMM and the last HMM are obtained from the state probabilities P _i (t) obtained by combining the four or more HMMs. It is only necessary to extract (extract) t) and generate a vector time series using the state probability P _{i ′} (t).

Next, in the above-described case, the total duration T of Equation (8), which is the sum of the expected durations d _i of the states S _i of the HMM, is expressed as the length of the vector time series output from the HMM ( The number of vectors in the vector time series) is used. The length of the vector time series output from the HMM is, for example, the operation of the operation unit (not shown) by the user or the vector time series output unit 10 in FIG. It can be adjusted according to the request from the application.

The adjustment of the length of the vector time series output from the HMM is performed by, for example, calculating the expected value d _i of the duration used when obtaining the expected transition time t _i (and the inverse expected transition time t _i ′) This can be done by adjusting according to (25).

・・・（２５）

... (25)

In the equation (25), when the coefficient α is 1.0, the expected value d _i of the duration time remains the value (E [n]) obtained by the equation (7). Further, in the equation (25), when the coefficient α is set to a value larger than 1.0, the expected duration d _i is larger than the value obtained in the equation (7), and conversely, the coefficient α is set to 1.0. If the value is smaller than the expected value d _i , the expected duration d _i is smaller than the value obtained by equation (7).

By adjusting the expected value d _i of the duration according to, for example, Equation (25), the total duration T obtained by Equation (8), that is, the length of the vector time series output from the HMM is adjusted. It will be α times the case where α is not performed (when α is 1.0).

The coefficient α in the equation (25) can be the same value for all the states S _{i of} the HMM or can be changed for each state S _i . That is, for example, α = 0.7 is used to adjust the expected value d ₁ of the duration of state S ₁ , and α = 1.5 is used to adjust the expected value d _N of the duration of state S _N , for example. Etc. are possible. When the coefficient α in Expression (25) is changed for each state S _{i of} the HMM, the length of the vector time series output from the HMM can be partially adjusted.

  Next, in the above, the vector time series output unit 10 in FIG. 1 uses one HMM (including the combined HMM) to generate a vector time series output from the HMM. For example, using a plurality of HMMs, a vector time series obtained by mixing (synthesizing) vector time series output from each of the plurality of HMMs, that is, a vector time series output from each of the plurality of HMMs, It is possible to generate a vector time series.

  Here, the vector time series obtained by mixing the vector time series output from each of the plurality of HMMs is obtained by mixing (combining) the plurality of HMMs into one HMM, and then from the HMM (hereinafter referred to as a combined HMM as appropriate). It can be considered to be an output vector time series.

  Note that a synthetic HMM is different from an HMM that simply connects (couples) the states of a plurality of HMMs, such as a coupled HMM. That is, if the HMM can be represented by a point on the xy coordinate system, the synthetic HMM intuitively, for example, when two points on the xy coordinate system are given, the two points are It is an HMM represented by an arbitrary point on a straight line passing through two points representing two HMMs, as can be used to represent an arbitrary point on the straight line passing through the two points.

  FIG. 23 uses two HMM # 1 and # 2 to generate an intermediate vector time series that is a mixture of the vector time series output from HMM # 1 and the vector time series output from HMM # 2. It is a figure explaining the method to do.

In FIG. 23, HMM # 1 is a left-to-right type HMM composed of N + 2 states S ₀ , S ₁ , S ₂ ,..., S _N , S _{N + 1.} Reference numeral 2 denotes a left-to-right type HMM composed of M + 2 states S ′ ₀ , S ′ ₁ , S ′ ₂ ,..., S ′ _M , S ′ _{M + 1} .

  Now, HMM # 1 (vector time series output from) and HMM # 2 (vector time series output from) are mixed at a ratio of β: 1−β.

  Here, β is appropriately referred to as a mixing coefficient hereinafter. Further, the mixing coefficient β is a value in the range of 0.0 <= β <= 1.0.

  When the mixing coefficient β = 1.0, the same vector time series as that generated using only HMM # 1 must be generated. When the mixing coefficient β = 0.0, only HMM # 2 is generated. A vector time series identical to the vector time series generated by using must be generated. If the mixing coefficient β is greater than 0 and less than 1, it is generated using the vector time series generated using HMM # 1 and HMM # 2 according to the value of the mixing coefficient β. An intermediate vector time series that is mixed with the vector time series must be generated.

Therefore, first, HMM # we expected value d ₁ of the duration of each state S _i of 1, d _2, · · ·, a d _N, wherein together determined by (7), the HMM # 2 of each state S _'j Expected values d ′ ₁ , d ′ ₂ ,..., D _M of the duration time are obtained by Expression (7).

The overall duration of HMM # 1 (the length of the vector time series generated using HMM # 1) T is the expected value of the duration of each state S _i of HMM # 1 as shown in Equation (26). This is the sum of d ₁ , d ₂ ,..., d _N.

・・・（２６）

... (26)

Similarly, (vector time series is generated by using the HMM # 2 length) total duration of HMM # 2 T ', as shown in equation (27), the HMM # 2 each state S' of the _j the duration of the expected value _{d '1, d' 2,} ···, the sum of d _M.

・・・（２７）

... (27)

  The total duration T of HMM # 1 in equation (26) and the total duration T ′ of HMM # 2 in equation (27) do not necessarily match. Therefore, an intermediate vector time series in which a vector time series of length T generated using HMM # 1 and a vector time series of length T ′ generated using HMM # 2 is mixed ( Hereinafter, it will be a problem how to determine the length T ″ of the mixed vector time series as appropriate. For example, the length T ″ is determined according to the equation (28) based on the mixing coefficient β.

・・・（２８）

... (28)

  The length of the vector time series having a length of T generated using HMM # 1 and the vector time series having a length of T ′ generated using HMM # 2 is obtained by Expression (28). To adjust (match) to the mixed vector time series length T ″, the coefficient is generated using HMM # 2 and the coefficient γ that adjusts the length of the vector time series generated using HMM # 1. A coefficient γ ′ for adjusting the length of the vector time series is obtained by Expression (29) and Expression (30), respectively.

・・・（２９）

... (29)

・・・（３０）

... (30)

Then, the expected values d ₁ , d ₂ ,..., D _N of the durations of the respective states S _i of HMM # 1 are expressed as γ × d ₁ , γ × d ₂ ,. adjusted to γ × d _N. Similarly, the expected values d ′ ₁ , d ′ ₂ ,..., D _M of the respective states S ′ _j of HMM # 2 are also expressed as γ ′ × d ′ ₁ , γ ′ using the coefficient γ ′. × d ′ ₂ ,..., Γ ′ × d ′ _M

  As a result of the above, the overall duration of HMM # 1 is γ × T (= T ''), and the overall duration of HMM # 2 is γ '× T' (= T ''). The length T ″ of the mixed vector time series of (28) is obtained.

As described above, each state of HMM # 1 is set such that the total duration of HMM # 1 and the total duration of HMM # 2 are the length T ″ of the mixed vector time series of Equation (28). expected value d ₁ of the duration of S _i, d _2, ···, a d _N, respectively _{γ × d 1, γ × d} 2, ···, while adjusting the gamma × d _N, of HMM # 2 The expected values d ′ ₁ , d ′ ₂ ,..., D _M of the states S ′ _j are respectively expressed as γ ′ × d ′ ₁ , γ ′ × d ′ ₂ ,. 'After adjusting to _M , for HMM # 1, use the expected duration value after adjustment γ × d _i to obtain the state probability, and for HMM # 2, also after adjusting the expected duration value γ × The state probability is obtained using d' _j .

Here, the state probability obtained for HMM # 1 is represented as P _i (t), and the state probability obtained for HMM # 2 is represented as P ′ _j (t).

For HMM # 1, the state probability P _i (t) at time t = 1, 2,..., T '' is obtained for each state S _i (i = 1, 2,..., N). For HMM # 2, for each state S ′ _j (j = 1, 2,..., M), the state probability P ′ _j ( t) is required.

The state probability P _i (t) of HMM # 1 represents the probability that the states S ₁ , S ₂ , S ₃ ,..., S _{N of} HMM # 1 output a vector at time t. The state probability P ′ _j (t) represents the probability that the states S ′ ₁ , S ′ ₂ , S ′ ₃ ,..., S ′ _M of the HMM # 2 output a vector at time t.

That is, the probability that the state S ₁ , S ₂ , S ₃ ,..., S _{N of} HMM # 1 outputs a vector at time t is P ₁ (t), P ₂ (t), P _{3, respectively.} (t), · · ·, a P _N (t), the probability of HMM # 2 states _{S '1, S' 2,} S '3, ···, S' M outputs a vector, respectively, P ′ ₁ (t), P ′ ₂ (t), P ′ ₃ (t),..., P ′ _M (t).

The vector x _{t at} time t of the mixed vector time series is a ratio β: 1−β according to the mixing coefficient β between the vector output from the HMM # 1 and the vector output from the HMM # 2 at the time t. And is given by equation (31).

・・・（３１）

... (31)

Here, in Expression (31), μ _i is an average vector obtained from the output probability density function defined in the state S _i of HMM # 1, and μ ′ _j is the state S ′ _j of HMM # 2. An average vector obtained from a defined output probability density function.

According to the equation (31), the vector x _t is obtained for each of the times t = 1, 2,..., T ″, so that the vector time series x ₁ , x _{2 of} length T ″ is obtained. , ..., x _{T ''} can be obtained.

From equation (5), the summation ΣP _i (t) of the state probability P _i (t) over the states S _{1 to} S _N of the HMM # 1 and the state over the states S _{1 to} S _M of the HMM # 2 The summation ΣP′j (t) of the probability P ′ _j (t) is 1, and therefore, the mixing coefficient β, the state probability P _i (t), P ′ _j (t) in the equation (31). With respect to, equation (32) holds.

・・・（３２）

... (32)

According to Expression (31) and Expression (32), the vector x _t at the time t of the mixed vector time series is a vector obtained by linearly combining the average vectors output from all the states of HMM # 1 and HMM # 2. The weight used for the linear combination is adjusted by the mixing coefficient β, the state probability P _i (t), and the state probability P ′ _j (t).

In the above case, the description has been made assuming that the mixing coefficient β satisfies the expression 0.0 <= β <= 1.0. However, even when the value of the mixing coefficient β is negative, the mixing coefficient β is larger than 1.0. Even if it exists, Formula (32) is materialized. Therefore, the vector x _t can be obtained from the equation (31) by adopting an arbitrary value of the mixing coefficient β. When the mixing coefficient β is a value satisfying the expression 0.0 <= β <= 1.0, the vector time series output from the combined HMM corresponding to the inner dividing point of HMM # 1 and # 2 is obtained. Can do. Further, when the mixing coefficient β is a negative value such as −1.0, for example, or a value larger than 1.0 such as 1.5, for example, the external division of HMM # 1 and # 2 A vector time series output from the combined HMM corresponding to the points can be obtained.

  Here, the generation of the mixed vector time series as described above can be performed regardless of whether the number of states N of HMM # 1 and the number of states M of HMM # 2 match or not. .

  Further, in the above-described case, the total duration T of HMM # 1 in Expression (26) obtained using the expected value of the duration as it is and the total duration T ′ of HMM # 2 in Expression (27) are obtained. The length T ″ of the mixed vector time series is determined according to the equation (28). The length T ″ of the mixed vector time series is determined by, for example, the HMM # 1 according to the equation (25), for example. It is also possible to adjust the expected value of the duration time of # 2 and # 2 and determine using the total duration time of HMM # 1 and # 2 obtained using the expected value of the duration time after the adjustment.

  In the above case, the two HMM # 1 and # 2 are mixed (the vector time series output from HMM # 1 and the vector time series output from HMM # 2 are mixed). It is also possible to mix three or more HMMs.

  Next, with reference to the flowchart of FIG. 24, the state probability estimation process performed in the state probability estimation part 3 of FIG. 11 when mixing HMM as mentioned above is demonstrated. Here, it is assumed that two HMM # 1 and # 2 are mixed, and the two HMM # 1 and # 2 are read from the HMM storage unit 1 by the selection unit 2 (FIG. 1), and the state probability It is assumed that it is supplied to the estimation unit 3.

The duration length calculation unit 21 receives the supply of HMM # 1 and # 2 from the selection unit 2 (FIG. 1), and uses the state transition probability a _ij of the HMM # 1 from the selection unit 2 in step S71. The expected value d _i (= E [n]) of the duration n of each state S _i of HMM # 1 represented by (7) is calculated, and the state transition probability a ′ of HMM # 2 from the selection unit 2 _{Using ij} , the expected value d ′ _j (= E [n]) of the duration n of each state S ′ _j of HMM # 2 represented by Expression (7) is calculated, and the process proceeds to step S72.

At step S72, the duration calculator 21, HMM expected value d _i of duration n of each state S _i of the # 1, HMM # 2 'of the expected value d duration n of _{j' j} each state S And adjust.

In other words, the duration calculation unit 21 determines the total duration of the HMM # 1 (the length of the vector time series generated using the HMM # 1) T according to the equation (26), The sum of expected values d ₁ , d ₂ ,..., D _N of the duration of S _{i is obtained} , and the total duration of HMM # 2 (the vector time series generated using HMM # 2 Length) T ′ is obtained by taking the sum of expected values d ′ ₁ , d ′ ₂ ,..., D _M of the durations of the states S ′ _j of HMM # 2 in accordance with equation (27). .

  Further, the duration calculation unit 21 uses the total duration T of HMM # 1, the total duration T ′ of HMM # 2, and the mixing coefficient β, and HMM # 1 and # 2 according to Expression (28). The length T ″ of the mixed vector time series output from the combined HMM obtained by mixing is obtained.

  Here, the mixing coefficient β can be set in advance, for example. Further, the mixing coefficient β is obtained by, for example, operating the operation unit (not shown) by the user, or the vector time series output unit 10 configured by the state probability estimation unit 3 and the vector time series generation unit 4 of FIG. Can be given from the application to use.

  When the duration time calculating unit 21 obtains the length T ″ of the mixed vector time series, a coefficient for adjusting the length of the vector time series generated using the HMM # 1 based on the length T ″. γ is obtained according to Equation (29), and a coefficient γ ′ for adjusting the length of the vector time series generated using HMM # 2 is obtained according to Equation (30).

Then, the duration calculation unit 21 uses the coefficient γ to calculate γ × d ₁ , γ using the expected values d ₁ , d ₂ ,..., D _N of the durations of the states S _i of the HMM # 1. × d _2, · · ·, as well as adjusting the γ × d _N, HMM # 'expected value d of the duration of _{j' 1} each state S of 2, d _'2, · · ·, d _M also, the coefficient gamma To adjust to γ ′ × d ′ ₁ , γ ′ × d ′ ₂ ,..., Γ ′ × d ′ _M.

Thereafter, the duration length calculator 21 adjusts the expected value of the duration of each state S _i of the HMM # 1 after adjustment γ × d ₁ , γ × d ₂ ,..., Γ × d _N and the HMM The value γ ′ × d ′ ₁ , γ ′ × d ′ ₂ ,..., Γ ′ × d ′ _M after adjustment of the expected value of the duration of each state S ′ _{j in} # 2 is calculated as an expected transition time calculation unit. 22 and proceeds from step S72 to step S73.

In step S73, the expected transition time calculation unit 22 adjusts the expected values of the durations of the states S _i of the HMM # 1 from the duration length calculation unit 21 γ × d ₁ , γ × d ₂ ,. ..., using a gamma × d _N, the expected transition time t _i, obtains an inverse expected transition time t _i ', the expected transition time t _i, and supplies the forward transition probability determining unit 23F, reverse expected transition The time t _i ′ is supplied to the backward transition probability determining unit 23B, and the process proceeds to step S74.

In step S74, the forward transition probability determining unit 23F uses the expected transition time t _i from the expected transition time calculating unit 22 to obtain the forward transition probability q _i (t) of Expression (9), and the forward state probability calculating unit 24F. , The backward transition probability determination unit 23B obtains the backward transition probability r _i (t) of Equation (10) using the reverse expected transition time t _i ′ from the expected transition time calculation unit 22, and the backward state probability The voltage is supplied to the calculation unit 24B and proceeds to step S75.

In step S75, the forward state probability calculation unit 24F uses the forward transition probability q _i (t) from the forward transition probability determination unit 23F to obtain the forward state probability Pf _i (t) of Expression (13), and the state probability The backward state probability calculation unit 24B supplies the backward state probability Pb _i (t) of Expression (17) using the backward transition probability r _i (t) from the backward transition probability determination unit 23B. Obtained and supplied to the state probability calculation unit 25, the process proceeds to step S76.

In step S76, the state probability calculation unit 25 uses the forward state probability Pf _i (t) from the forward state probability calculation unit 24F and the backward state probability Pb _i (t) from the backward state probability calculation unit 24B. The state probability P _i (t) of equation (19), that is, each state S _i (i = 1, 2,..., N) of HMM # 1 is changed to each time t (= 1, 2,. A state probability P _i (t) that is a probability of outputting a vector at T ″ (= γ × T)) is obtained.

The processing in steps S73 to S76 is performed in the same manner for HMM # 2, and thus the state probability calculation unit 25 causes the state probability P _i (t) of Expression (19) for HMM # 2, ie, the HMM. Each state S _j (j = 1,2, ..., N) of # 2 outputs a vector at each time t (= 1,2, ..., T '' (= γ '× T')) The state probability P ′ _j (t), which is the probability of

Then, the state probability calculation unit 25 uses the state probability P _i (t) for HMM # 1 and the state probability P ′ _j (t) for HMM # 2 as the vector time-series generation unit 4 (FIG. 1). ) To finish the state probability estimation process.

  Next, a vector time series generation process performed by the vector time series generation unit 4 in FIG. 13 when mixing HMMs as described above will be described with reference to the flowchart in FIG. Here, similarly to the case of FIG. 24, two HMM # 1 and # 2 are mixed, and the two HMM # 1 and # 2 are mixed by the selection unit 2 (FIG. 1) by the HMM storage unit. 1 and is supplied to the vector time series generation unit 4.

The vector time series generation unit 4 is supplied with HMM # 1 and # 2 from the selection unit 2 (FIG. 1), and the state probability estimation unit 3 (FIG. 1) performs the state probability estimation process of FIG. Thus, the state probability P _i (t) for HMM # 1 and the state probability P ′ _j (t) for HMM # 2 are supplied.

The expected value acquisition unit 31 receives the supply of HMM # 1 and # 2 from the selection unit 2 (FIG. 1), and outputs the probability probability function b _i (x) of the HMM # 1 supplied from the selection unit 2 in step S81. From the expected value of the vector x according to the probability distribution represented by the output probability density function b _i (x) in the HMM # 1 from the selection unit 2, the output probability density function b ₁ (x), b ₂ (x), .., B _N (x) are defined for each state S ₁ , S ₂ ,..., S _N and supplied to the expected value calculation unit 32.

That is, the expectation value acquisition unit 31 has each state in which the output probability density functions b ₁ (x), b ₂ (x),..., B _N (x) are defined in the HMM # 1 from the selection unit 2. For S ₁ , S ₂ ,..., S _N , the mean vector μ ₁ that defines the normal distribution represented by the output probability density function b ₁ (x), b ₂ (x), ..., b _N (x) , Μ ₂ ,..., Μ _N are obtained and supplied to the expected value calculation unit 32.

Similarly, the expected value acquisition unit 31 also outputs the output probability density functions b ′ ₁ (x), b ′ ₂ (x),..., B ′ _M for the HMM # 2 from the selection unit 2 in the HMM # 2. For each state S ′ ₁ , S ′ ₂ ,..., S ′ _M in which (x) is defined, output probability density functions b ′ ₁ (x), b ′ ₂ (x),. Mean vectors μ ′ ₁ , μ ′ ₂ ,..., Μ ′ _M that define the normal distribution represented by “ _M (x) are obtained and supplied to the expected value calculation unit 32.

Then, the process proceeds from step S81 to step S82, where the expected value calculation unit 32 determines the state probability P _i (t) for HMM # 1 from the state probability estimation unit 3 (FIG. 1) and the state probability P for HMM # 2. ' _j (t) and the mean vector μ ₁ , μ ₂ ,..., μ _N for HMM # 1 supplied from the expected value acquisition unit 31 and the state probability estimation unit 3 HMM # 1 state probabilities P ₁ (t), P ₂ (t),..., P _N (t) at time t, that is, parentheses in the first term on the right side of equation (31) The summation calculation result ΣP _i (t) · μ _i is obtained as the expected value of the vector output from the HMM # 1 at time t.

Similarly, the expected value calculation unit 32 supplies the average vectors μ ′ ₁ , μ ′ ₂ ,..., Μ ′ _M for HMM # 2 supplied from the expected value acquisition unit 31 and the state probability estimation unit 3. Product-sum operation with the state probabilities P ′ ₁ (t), P ′ ₂ (t),..., P ′ _M (t) of the HMM # 2 at the time t to be performed, that is, the right side of the expression (31) Summation calculation in parentheses in the second term is performed, and the product-sum operation result ΣP ′ _j (t) · μ ′ _j is obtained as an expected value of the vector output from HMM # 2 at time t.

In step S82, the expected value calculation unit 32 calculates the expected value ΣP _i (t) · μ _{i of the} vector x output from the HMM # 1 for each time t = 1, 2,. When the expected value ΣP ′ _j (t) · μ ′ _{j of the} vector x output from HMM # 2 is obtained, the process proceeds to step S83, and is output from HMM # 1 at time t according to equation (31). The ratio of the expected value ΣP _i (t) · μ _i of the vector x and the expected value ΣP ' _j (t) · μ' _{j of the} vector x output from the HMM # 2 to the ratio β: 1 The mixed vector time series x ₁ , x ₂ ,..., x _T is obtained by mixing at −β and the total duration T ″. Then, the expected value calculation unit 32 proceeds from step S83 to step S84, outputs the mixed vector time series x ₁ , x ₂ ,..., X _T and ends the vector time series generation process.

As described above, at each time t, the state probability P _i (t) that is the probability that each state S _i of the HMM outputs a vector is introduced, and the HMM outputs based on the state probability P _i (t) By calculating the expected value of the vector x analytically, the vector time series x ₁ , x ₂ , ..., x _T is generated, so that time series data that changes smoothly can be easily obtained. In addition, it is possible to easily adjust the length of the vector time series output from the HMM, the time interval, and other characteristics by adjusting the time interval for obtaining the state probability P _i (t).

  Also, generation of vector time series from combined HMMs that combine multiple HMMs, generation of periodic vector time series, and vector time series from combined HMMs that mix multiple HMMs (mixed vector time series) ) Can be easily generated.

That is, for example, the time when transition from one state to another state (expected transition time t _i , reverse expected transition time t ′ _i ) is a predetermined probability distribution, for example, according to a normal distribution, The probability P _i (t) is estimated, but since the variance of the normal distribution (the variance σ ^{2 in} equation (9) and the variance σ ′ ^{2 in} equation (10)) can be adjusted, The characteristics of the output vector time series can be easily adjusted.

Furthermore, for example, the time interval for estimating the state probability P _i (t) can be adjusted not only to 1 but also to 0.1 etc., so that the time between vectors in the vector time series output from the HMM can be adjusted by the adjustment. The interval can be easily adjusted.

In addition, for example, by estimating the state probability P _i (t) for each state of the combined HMM as a new state transition probability model obtained by combining a plurality of HMMs, it is output from each of the plurality of HMMs. A vector time series in which vector time series are arranged can be easily generated.

Furthermore, for example, the same three HMM # 1, # 2, for binding HMM that combines # 3, to estimate the state probabilities P _i (t), of its state probability P _i (t), HMM # By extracting only the state probabilities P _{i ′} (t) corresponding to each state of 2 and generating a vector time series based on the state probabilities P _{i ′} (t), a periodic vector time series is obtained. Can be easily generated.

Also, for example, the state probability P _i (t) of HMM # 1 and the state probability P ′ _j (t) of HMM # 2, the length of the vector time series output by HMM # 1, and the output of HMM # 2 HMM # 1 state probability P _i (t) and HMM # 1 state output as average data μ _i HMM # 2 by generating a vector time series based on the state probability P ′ _j (t) of HMM # 2 and the average vector μ ′ _j as representative data output by the state of HMM # 2. It is possible to easily obtain a mixed vector time series output by the combined HMM obtained by mixing 1 and HMM # 2. That is, it is possible to easily obtain the vector time series output by the combined HMM that is neither HMM # 1 nor # 2.

  Next, the series of processes described above can be performed by hardware or software. When a series of processing is performed by software, a program constituting the software is installed in a general-purpose computer or the like.

  Therefore, FIG. 26 shows a configuration example of an embodiment of a computer in which a program for executing the series of processes described above is installed.

  The program can be recorded in advance in a hard disk 105 or a ROM 103 as a recording medium built in the computer.

  Alternatively, the program is stored temporarily on a removable recording medium 111 such as a flexible disk, a CD-ROM (Compact Disc Read Only Memory), a MO (Magneto Optical) disk, a DVD (Digital Versatile Disc), a magnetic disk, or a semiconductor memory. It can be stored permanently (recorded). Such a removable recording medium 111 can be provided as so-called package software.

  The program is installed in the computer from the removable recording medium 111 as described above, or transferred from the download site to the computer wirelessly via a digital satellite broadcasting artificial satellite, LAN (Local Area Network), The program can be transferred to a computer via a network such as the Internet, and the computer can receive the program transferred in this way by the communication unit 108 and install it in the built-in hard disk 105.

  The computer includes a CPU (Central Processing Unit) 102. An input / output interface 110 is connected to the CPU 102 via the bus 101, and the CPU 102 operates an input unit 107 including a keyboard, a mouse, a microphone, and the like by the user via the input / output interface 110. When a command is input as a result, the program stored in a ROM (Read Only Memory) 103 is executed accordingly. Alternatively, the CPU 102 also transfers from a program stored in the hard disk 105, a program transferred from a satellite or a network, received by the communication unit 108 and installed in the hard disk 105, or a removable recording medium 111 attached to the drive 109. The program read and installed in the hard disk 105 is loaded into a RAM (Random Access Memory) 104 and executed. Thus, the CPU 102 performs processing according to the above-described flowchart or processing performed by the configuration of the above-described block diagram. Then, the CPU 102 outputs the processing result from the output unit 106 configured with an LCD (Liquid Crystal Display), a speaker, or the like, for example, via the input / output interface 110, or from the communication unit 108 as necessary. Transmission and further recording on the hard disk 105 are performed.

  Here, in this specification, the processing steps for describing a program for causing a computer to perform various types of processing do not necessarily have to be processed in time series according to the order described in the flowchart, but in parallel or individually. This includes processing to be executed (for example, parallel processing or processing by an object).

  Further, the program may be processed by a single computer, or may be processed in a distributed manner by a plurality of computers. Furthermore, the program may be transferred to a remote computer and executed.

  In the present embodiment, the case where the vector time series output unit 10 that outputs a vector time series is applied to a speech synthesizer has been described. Various systems that take time series signals as input and perform processing according to the time series signals, for example, by driving an actuator (motor) according to a motor signal that is a time series signal, It can be applied to a robot that moves a part corresponding to a leg.

  The “vector” in the present embodiment includes a one-dimensional vector, that is, a scalar quantity.

  Furthermore, the embodiments of the present invention are not limited to the above-described embodiments, and various modifications can be made without departing from the gist of the present invention.

It is a block diagram which shows the structural example of one Embodiment of the speech synthesizer to which this invention is applied. It is a figure which shows the example of left-to-right type HMM. It is a flowchart explaining the process of a speech synthesizer. It is a figure which shows the example of the method of the state transition in left-to-right type HMM. FIG. 10 is a diagram showing a normal distribution in which an average value is an expected transition time t _i and a variance is σ ² according to a transition time t. It is a figure which shows the relationship between forward transition probability q _i (t) and the state of HMM. It is a figure which shows the relationship between backward transition probability r _i (t) and the state of HMM. It is the figure which showed the forward state probability Pf _i (t) typically. It is the figure which showed backward state probability Pb _i (t) typically. FIG. 6 is a diagram schematically showing a state probability P _i (t). 3 is a block diagram illustrating a configuration example of a state probability estimation unit 3. FIG. It is a flowchart explaining a state probability estimation process. FIG. 3 is a block diagram illustrating a configuration example of a vector time series generation unit 4. It is a flowchart explaining a vector time series production | generation process. It is a figure which shows the learning data used for the learning of HMM in simulation. It is a figure which shows the one-dimensional vector time series produced | generated from HMM by simulation. FIG. 6 is a diagram showing a state probability P _i (t) obtained when the step size at time t is 1 and a state probability P _i (t) obtained when the step size at time t is 0.1. It is a figure which shows the joint HMM which couple | bonded two HMM # 1 and # 2. It is a flowchart explaining the process of the speech synthesizer when combining HMMs to generate a vector time series. FIG. 10 is a diagram showing an HMM that has given a transition from a state S _N immediately before the end state S _{N + 1} to a state S ₁ immediately after the initial state S ₀ . It is a figure which shows the coupling | bonding HMM which couple | bonded the same three HMM # 1, # 2, # 3 in the order. It is a flowchart explaining the process of the speech synthesizer when generating a vector time series of a periodic trajectory. It is a figure explaining the method to produce | generate the intermediate | middle vector time series which mixed the vector time series output from HMM # 1, and the vector time series output from HMM # 2. It is a flowchart explaining the state probability estimation process performed in the state probability estimation part 3 in the case of mixing HMM. It is a flowchart explaining the vector time series production | generation process performed in the vector time series production | generation part 4 in the case of mixing HMM. It is a block diagram which shows the structural example of one Embodiment of the computer to which this invention is applied.

Explanation of symbols

  1 HMM storage unit, 2 selection unit, 3 state probability estimation unit, 4 vector time series generation unit, 5 inverse filter, 10 vector time series output unit, 21 duration length calculation unit, 22 expected transition time calculation unit, 23F forward transition Probability determining unit, 23B backward transition probability determining unit, 24F forward state probability calculating unit, 24B backward state probability calculating unit, 25 state probability calculating unit, 31 expected value acquiring unit, 32 expected value calculating unit, 101 bus, 102 CPU, 103 ROM, 104 RAM, 105 hard disk, 106 output unit, 107 input unit, 108 communication unit, 109 drive, 110 input / output interface, 111 removable recording medium

Claims (11)

In a data output device that outputs time-series data,
State probability that estimates the state probability that the state outputs data for each time of a predetermined interval for each state of the HMM defined by the state transition probability that the state transitions and the probability distribution of the data that each state outputs An estimation means;
Based on the state probability and the average value of the data according to the probability distribution, time-series data generating means for obtaining data for each time of a predetermined interval output by the HMM and outputting as time-series data ,
The state probability estimation means, for each state of the HMM,
Using the state transition probability of self-transition, find the value corresponding to the expected value of the number of times that self-transition occurs as the expected value of the duration of self-transition,
A recurrence formula using the normal distribution, assuming that the transition time of transition from one state to another state follows a normal distribution whose average value is the expected transition time obtained by adding the expected value of the duration. The value corresponding to the probability that the state transition starts from the state at each time is obtained as the state probability at each time,
The time series data generation means is a data output device for obtaining data output by the HMM at each time by linear combination of the average values of the data weighted by the state probabilities of the respective states . The data output device according to claim 1 , wherein
The dispersion of normal distribution, the data output device is determined based on the expected value of the duration in which the self-transition continues. The data output device according to claim 1 , wherein
Data output device that adjust the variance of the normal distribution. The data output device according to claim 1, wherein
A data output device for determining an interval of time at which the state probability estimating means estimates the state probability. The data output device according to claim 1, wherein
It said state probability estimation means, for each state of a new HMM obtained by combining a plurality of HMM, the data output apparatus for estimating the state probability. The data output device according to claim 1, wherein
It said state probability estimating means, first the three identical HMM, for each state of the new HMM obtained by combining the second and third HMM, estimates the state probability,
The time-series data generation means is based on the state probability for each state of the second HMM out of the state probabilities estimated by the state probability estimation means, and an average value of data according to the probability distribution A data output device for obtaining data for each time of a predetermined interval output by the HMM . The data output device according to claim 1, wherein
The state probability estimating means includes
For each of the first and second HMMs, first and second coefficients for adjusting the sum of the expected values of the duration time to the same predetermined time are obtained.
Adjusting the expected value of the duration of the first HMM by the first coefficient, and adjusting the expected value of the duration of the second HMM by the second coefficient;
For each of the first and second HMMs, using the expected value of the duration after adjustment, obtain the state probability at each time;
The time-series data generating means, said probability mean value of the data according to the distribution of the said state probability of the first HMM first HMM, and wherein said state probability of the second HMM second HMM A data output device for obtaining the time-series data based on an average value of data according to the probability distribution . The data output device according to claim 7 , wherein
The state probability estimation means is configured to calculate a sum of expected values of the durations of the first HMM and the durations of the second HMM based on a mixing ratio of the first and second HMMs. A data output device for obtaining the first and second coefficients using an addition value obtained by adding the sum of expected values according to the mixing ratio as the predetermined time . The data output device according to claim 1, wherein
The time-series data is a time-series vector. In the data output method for outputting time series data,
State probability that estimates the state probability that the state outputs data for each time of a predetermined interval for each state of the HMM defined by the state transition probability that the state transitions and the probability distribution of the data that each state outputs An estimation step;
Said state probability, on the basis of the average value of the data according to the probability distribution, obtains the data for each time of a predetermined interval HMM outputs, viewed contains a series data generating step when outputting a data of the time series,
In the state probability estimation step, for each state of the HMM,
Using the state transition probability of self-transition, find the value corresponding to the expected value of the number of times that self-transition occurs as the expected value of the duration of self-transition,
A recurrence formula using the normal distribution, assuming that the transition time of transition from one state to another state follows a normal distribution whose average value is the expected transition time obtained by adding the expected value of the duration. The value corresponding to the probability that the state transition starts from the state at each time is obtained as the state probability at each time,
The time series data generation step is a data output method for obtaining data output by the HMM at each time by linear combination of the average values of the data weighted by the state probabilities of the respective states . In a program for causing a computer to execute data output processing for outputting time-series data,
State probability that estimates the state probability that the state outputs data for each time of a predetermined interval for each state of the HMM defined by the state transition probability that the state transitions and the probability distribution of the data that each state outputs An estimation means ;
Time-series data generating means for obtaining data for each time of a predetermined interval output by the HMM based on the state probability and the average value of the data according to the probability distribution, and outputting as time-series data
And a program to make the computer function,
The state probability estimation means, for each state of the HMM,
Using the state transition probability of self-transition, find the value corresponding to the expected value of the number of times that self-transition occurs as the expected value of the duration of self-transition,
A recurrence formula using the normal distribution, assuming that the transition time of transition from one state to another state follows a normal distribution whose average value is the expected transition time obtained by adding the expected value of the duration. The value corresponding to the probability that the state transition starts from the state at each time is obtained as the state probability at each time,
The time-series data generation means is a program for obtaining data output by the HMM at each time by linear combination of the average values of the data weighted by the state probabilities of the respective states .

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