DE19755191A1 - Determining model-specific factors for assigning classes to test data in speech recognition - Google Patents

Abstract

The method uses a probability model to evaluate test data and assign them in different classes. Probability values of different models for the same class assignment are evaluated with model-specific factors and combined to form a total probability value. The model-specific factors are determined such that the total probability of assigning the training data to particular classes is a minimum compared to other classes, and erroneous classification of the training data is minimized.

Description

The invention relates to a method for determining model-specific factors for the combination different models in pattern recognition, especially in speech recognition.

The statistical speech recognition method uses Bayesian decision theory to construct recognizers with a minimal error rate [1]. According to this theory, an observation x must be classified in the class k (short x ∈ k,) if π (k | x) applies for a given posterior distribution:

The term log (π (k | x) / π (k '| x)) is referred to in the literature [1] as a discriminant function.

In the following, g (x, k, k ') is used for this.

If the decision rule (1) is projected onto the recognition of entire sentences, observed utterances x T | 1 = (x 1,..., X ^T ) of the length of time T in spoken word sequences w S | 1 = (w 1,... , w ^S ) of length S classified. However, the a-posteriori distribution π (w S | 1 | x T | 1) is unknown, because it describes the complex natural speech communication process of humans. It must therefore be approximated by a distribution p (w S | 1 | x T | 1). So far, acoustic, phonetic and grammatical modeling of language in the form of parametric probability distributions has proven to be the most powerful approximation method. The form of the distribution p (w S | 1 | x T | 1) is predetermined, the unknown parameters of the distribution are estimated on training data. The distribution p (w S | 1 | x T | 1) obtained is then used in the Bayesian decision rule. The utterance x T | 1 is then assigned to the word sequence w S | 1 for which the following applies:

By reshaping the discriminant function

the separation between the grammatical model (p (w S | 1) and the acoustic-phonetic model p (x T | 1w S | 1) is obtained in a natural way. The grammatical model p (w S | 1) describes the probability for the occurrence of the word sequence w S | 1 per se, the acoustic-phonetic model p (x T | 1 | w S | 1) evaluates the probability that the acoustic signal x T | 1 arises when the word sequence w S | 1 is said Both models can now be estimated separately, so that the limited amount of training data can be used optimally. By deviating the shape of the distribution p from the unknown distribution π, the decision rule (3) can be suboptimal, although the distribution p was estimated optimally motivates the use of discriminative methods. Discriminative methods optimize the distribution p directly with respect to the empirical error rate of the decision rule measured on training data. The simplest example of such a discriminatory tive optimization is the use of the so-called language model factor λ. (3) is modified as follows:

Experimental experience shows that the error rate of decision rule (4) decreases if λ <1 is chosen. The reason for this deviation from theory (i.e. λ = 1) obviously lies in the  incomplete or incorrect modeling of the probability of the compound event (w S | 1, x T | 1). The latter is inevitable because knowledge about the generating process of the event (w S | 1, x T | 1) increases is incomplete.

A variety of acoustic-phonetic and grammatical models of the language have been analyzed so far. The aim of these analyzes was to find the "best" model for the respective recognition task. However, all models determined in this way only give an incomplete representation of the real probability distribution, so that when using these models in pattern recognition, especially in speech recognition, erroneous detections in the sense of incorrect assignments to classes occur.

The object of the invention is to provide a modeling, in particular of the language, that of the real one Probability distribution comes as close as possible and yet with limited processing effort is applicable.

This object is achieved by the features specified in claim 1.

What is new about this approach is that no attempt is made to integrate the known properties of language into a single acoustic-phonetic distribution model and a single grammatical distribution model, which then become complex and difficult to train. The various acoustic-phonetic and grammatical properties are now in the form of the distributions p _j (w S | 1 | x T | 1), j = 1,. . ., M) modeled separately, trained and then in a distribution

integrated. The influence of the model p _j on the distribution p ^Π _{Λ} is determined by the coefficient λ _j .

The factor C (Λ) guarantees the fulfillment of the normalization condition for probabilities. The free coefficients Λ = (λ₁,..., Λ _M ) ^tr must be set so that the resulting discriminant function

has the lowest possible error rate.

This is the essence of the present invention.

There are various options for realizing this core idea, of which the following some are explained in more detail.

First, some terms, some of which have already been used, are clearly defined in summary.

• ⚫ Each word sequence w S | 1 is a class k, the length S can vary from class to class.
• ⚫ The expression x T | 1 is interpreted as observation x, the length T can vary from observation Observation may be different.
• ⚫ Training data are with (x _n , k _nr ), n = 1,. . ., N, r = 0,. . ., K, where N is the number of training acoustic observations x _n, k _n0 is the observation x _n corresponding correct class, and k _nr, r = 1,. . ., K are the K different faulty classes to _be rivaled.

It classifies the observation x into the class k according to the Bayesian decision rule (1) considered. The observation x is an acoustic realization of the class k. The following Explanation essentially refers to speech recognition, so that class k is always a word sequence symbolizes.  

Since the class k _n0 , which the training _observation x _n emitted, is known, the training _data (x _n , k _nr ), n = 1 _,. . ., N, r = 0,. . ., K an ideal empirical distribution (k | x) can be constructed. This distribution requires that the decision rule formed from it have a minimal error rate on the training data. When classifying whole word sequences k, one classification error (choice of the wrong word sequence k '≠ k) can lead to several word errors. The number of word errors between the incorrect class k 'and the correct class k is referred to as the Levenshtein distance L (k', k). The decision rule formed from the distribution (k | x) has a minimum word error rate if the following monotony property is fulfilled:

(k _nr | x _n ) <(k _{nr '} | x _n ) ⇔ L (k _nr , k _n0 ) <L (k _nr' , k _n0 ). (7)

From all possible distributions with this property, the following is chosen for the following explanation:

If the value µ in (8) is chosen to be very large, then the distribution (k _nr | x _n ) changes into the indicator function δ (k _nr , k _n0 ) ∈ {0, 1}. The latter is used in the classic discriminative training methods [8], [7] as an ideal empirical distribution for optimization. However, the indicator function has the disadvantage that it would lead to undefined logarithmic values if a decision rule of the form (1) were formed.

The ideal empirical distribution provides an optimal classifier on the given training data, but is not defined on unknown test data, since the correct class assignment is not given here. Therefore, with their help, it becomes a distribution

sought, which is defined on any independent test data and which has the lowest possible empirical error rate on the training data. Are the M given distribution models p ₁ (k | x),. . ., p _M (k | z) defined on any test data, this also applies to the distribution p ^Π _{Λ} (k | x). If the freely selectable coefficients Λ = (λ₁,..., Λ _M ) ^tr are determined such that p ^Π _{Λ} (k | x) has a minimal error rate on the training data, and if the training data are representative, then p ^Π _{Λ} (k | x) also provide an optimal decision rule on independent test data.

In order to actually minimize the empirical error rate of this distribution on the training data, two discriminative methods are considered:

• Bekannte the well-known GPD method ("Generalized Probabilistic Descent" [8] for direct minimization of the smoothed empirical error rate of the distribution p ^Π _{Λ} (k | x) on the training data. This method iteratively optimizes the free parameters of a distribution with respect to a differentiable one Error rate measure.
• ⚫ a new square mean method (minimization of the mean square distance of the discriminant functions of the distributions p ^Π _{Λ} (k | x) and (k | x)). Since (k | x) by definition has a minimal empirical error rate and since the discriminant function decides on the class assignment, the empirical error rate of p ^Π _{Λ} (k | x) on the training data must decrease by this method.

Both the GPD method and the square mean method optimize a criterion that the average error rate of the classifier approximated. However, the square mean method has over the GPD method has the advantage that it leads to a closed solution for the optimal coefficients Λ.  

First, the square mean method is considered.

Since the discriminant function (1) determines the quality of the classifier, the coefficients Λ are the mean square deviation

minimize the discriminant functions of the distributions p ^Π _{Λ} (k | x) and the empirical ideal distribution (k | x) .¹ The summation over r includes all rival classes in the criterion. That is, The distribution p ^Π _{Λ} is determined in such a way that on the training data (x _n , k _nr ) it has the same log-likelihood ratio between correct and incorrect hypothesis as the distribution. The minimization of D (Λ) leads to the following closed solution for the optimal coefficient vector Λ.

Λ = Q ^-1 P, (11)

With

and

Note that Q is the autocorrelation matrix of the discriminant functions of the given distribution models is. The vector P contains the relationship between the discriminant functions the predefined models and the discriminant function of the distribution.

Inserting (8) ultimately yields on the training data:

The word error rate L (k _nr , k _n0 ) of the hypotheses k _nr , r = 1 _,. . ., K linear in the coefficients λ ₁ ,. . ., λ _M a. Conversely, the ability of the distribution model p _i to discriminate goes beyond the discriminate function

linear in the coefficients λ ₁ ,. . ., λ _M a.

In this way, the coefficients can be determined directly.

Another way to determine these coefficients is to use the GPD method. With the GPD method [8], the smoothed empirical error rate L (Λ) can be:

minimize directly on the training data. ℓ (x _n , k _n0 , Λ) is a smoothed measure for the misclassification risk of observation x _n . The values A <0, B <0, η <0 determine the type of smoothing of the misclassification risk and must be specified appropriately.

If L (Λ) is minimized with respect to the coefficients Λ of the log-linear combination, then the coefficients λ _j , j = 1,. . ., M the following iteration equation with the step size ε:

Note that the coefficient vector Λ by means of the discriminant function

enters criterion L (Λ). If L (Λ) drops, then the discriminant function (17) due to (14) and (15) grow on average. This leads to a more optimal decision rule (cf. (1)).

Another way to determine the coefficients is to use the GIS method. In the previously described methods, the optimal coefficients Λ of the a-posterior distribution p ^Π _{Λ} (k | x) were sought. The analog log-linear distribution is then

Note that with (9) and (18) the following always applies:

In the continuous but limited space of the observations x, vector quantization is now carried out. Each training observation x _{n is assigned} a surrounding point set B _n with the volume V _n . The vector quantization enables the coefficients of the continuous distribution p ^Π _{Λ} (k, x) to be replaced by the coefficients Λ of the discrete distribution p ^Π _{Λ} (k _nr , x _n )

be approximated. Using the GIS method, the coefficients Λ of the discrete distribution p ^Π _{Λ} (k _nr , x _n ) on the training data (x _n , k _nr ), n = 1 _,. . ., N, r = 0,. . ., K optimized. The GIS procedure is intended to meet the following constraint:

where h (k _nr , x _n ) is the relative frequency of the event (k _nr , x _n ) on the training data. Since there can only be one correct word sequence k _n0 on the training _data for each characteristic x _n , the following applies to the relative frequency h (k _nr , x _n ):

To smooth the function h (k _nr , x _n ), you can also

start with (k _nr | x _n ) from (8).

The iteration equations for the probability p ^Π _{Λ} (k _nr , x _n ) are:

With

The result of the iterations results in the union probabilities p ^Π _{Λ} (k _nr , x _n ) ^(*) . With these probabilities and (20), the following linear system of equations results for the coefficients λ _j :

This system of equations has only M independent equations, since according to the GIS theorem [5] all association probabilities p ^Π _{Λ} (k _nr , x _n ) ^(*) , n = 1,. . ., N, r = 0,. . ., K of the distribution form (20) are sufficient. This gives a clear solution for the M coefficients λ _j , j = 1,. . ., M.

Claims (3)

1. Procedure for determining model-specific factors for the assignment of supplied test data to a training data sequence certain classes using several also from the Training data sequence determined probability models with which the test data are evaluated in order Determine probability values for assigning the same test data to different classes, and the probability values of different models for the same class assignment with the model-specific factors are combined to form an overall probability value, where the model-specific factors are determined so that the overall probability of the assignment of Training data for certain classes is a minimum compared to the assignment of the same training data to other classes and the misclassification of training data is minimized. 2. The method according to claim 1, wherein iterative intermediate step factors are formed and for each Iteration step the intermediate step factors for all models by one from the ratio of Probability value of each training date for the assignment to the correct class to the Probability values for the assignment to all other classes dependent value, separated for each Model being changed. 3. The method of claim 1, wherein for each model-specific factor, the normalized sum over all Classes and all training data of the ratio of the probability of assigning each Training date to the correct class for the probability of assigning this training date all other classes multiplied by a function indicating the word error rate.