A note on the iterative application of Bayes' rule

Spragins, J.

doi:10.1109/tit.1965.1053826

Cited by 64 publications

(16 citation statements)

References 7 publications

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“…and successively observed samples/blocks, which are served as the adaptation data to estimate the transformation parameters . The a posteriori density of satisfies the following recursive relation [11], [37]:…”

Section: A General Formulationmentioning

confidence: 99%

Online hierarchical transformation of hidden Markov models for speech recognition

Chien

1999

IEEE Trans. Speech Audio Process.

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This paper proposes a novel framework of online hierarchical transformation of hidden Markov model (HMM) parameters for adaptive speech recognition. Our goal is to incrementally transform (or adapt) all the HMM parameters to a new acoustical environment even though most of HMM units are unseen in observed adaptation data. We establish a hierarchical tree of HMM units and apply the tree to dynamically search the transformation parameters for individual HMM mixture components. In this paper, the transformation framework is formulated according to the approximate Bayesian estimate, which the prior statistics and the transformation parameters can be jointly and incrementally refreshed after each consecutive adaptation data is presented. Using this formulation, only the refreshed prior statistics and the current block of data are needed for online transformation. In a series of speaker adaptation experiments on the recognition of 408 Mandarin syllables, we examine the effects on constructing various types of hierarchical trees. The efficiency and effectiveness of proposed method on incremental adaptation of overall HMM units are also confirmed. Besides, we demonstrate the superiority of proposed online transformation to Huo's on-line adaptation [16] for a wide range of adaptation data.Index Terms-Approximate Bayesian estimate, EM algorithm, hidden Markov models, online hierarchical transformation, speaker adaptation, speech recognition.

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Section: A General Formulationmentioning

confidence: 99%

Online hierarchical transformation of hidden Markov models for speech recognition

Chien

1999

IEEE Trans. Speech Audio Process.

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“…Applying the Bayes theorem, we obtain a recursive expression for the a posteriori pdf of , given , as (4) Starting with the calculation of the posterior pdf from , a repeated use of (4) produces the sequence of densities , and so forth. This provides a basis of making recursive Bayesian inference of parameters [35]. Unfortunately, the implementation of this learning procedure for incremental CDHMM training raises some serious computational difficulties because of the nature of the missingdata problem caused by the underlying hidden processes, i.e., the state mixture component label sequence and the state sequence of the Markov chain for an HMM.…”

Section: Incremental Bayes Learningmentioning

confidence: 99%

“…Unfortunately, the implementation of this learning procedure for incremental CDHMM training raises some serious computational difficulties because of the nature of the missingdata problem caused by the underlying hidden processes, i.e., the state mixture component label sequence and the state sequence of the Markov chain for an HMM. It is well known that there exist no reproducing (natural conjugate) densities [35], [8], [12] for CDHMM. To illustrate this problem more clearly, let us begin with and consider what happens after a training utterance (sample) is observed.…”

Section: Incremental Bayes Learningmentioning

confidence: 99%

On-line adaptive learning of the continuous density hidden Markov model based on approximate recursive Bayes estimate

Huo

Lee²

1997

IEEE Trans. Speech Audio Process.

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“…Unfortunately, the Bayesian approach is computationally infeasible for most practical choices of p ( x I HI, w,). For the Bayesian scheme to be feasible, this unsupervised clustering problem has to be converted to a supervised one, since in this case, for most practical choices of p ( x I Hj,vj), a sufficient statistic vector exists for v (Spragins 1965). Based on this argument, Agrawala has proposed his "learning with a probabilistic teacher" scheme (Agrawala 1970).…”

Section: Learning With a Probabilistic Teachermentioning

confidence: 99%

“…However, for both algorithms, before training, the variances of all units are set to a fixed value 0, and thus, only the centers are to be trained. Hence, known to be a gaussian density (Spragins 1965), that is, s, = (c;, q)', (3.41) and (3.42) where the variance 0, reflects the confidence in C, as the estimate of c,.…”

Section: Pwta-ementioning

confidence: 99%

Probabilistic Winner-Take-All Learning Algorithm for Radial-Basis-Function Neural Classifiers

Osman

Fahmy

1994

Neural Computation

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This paper proposes a new adaptive competitive learning algorithm called "the probabilistic winner-take-all." The algorithm is based on a learning scheme developed by Agrawala within the statistical pattern recognition literature (Agrawala 1970). Its name stems from the fact that for a given input pattern once each competitor computes the probability of being the one that generated this pattern, the computed probabilities are utilized to probabilistically choose a winner. Then, only this winner is permitted to learn. The learning rule of the algorithm is derived for three different cases. Its properties are discussed and compared to those of two other competitive learning algorithms, namely the standard winner-take-all and the maximum-likelihood soft competition. Experimental comparison is also given. When all three algorithms are used to train the hidden layer of radial-basis-function classifiers, experiments indicate that classifiers trained with the probabilistic winner-take-all outperform those trained with the other two algorithms.

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A note on the iterative application of Bayes' rule

Cited by 64 publications

References 7 publications

Online hierarchical transformation of hidden Markov models for speech recognition

Online hierarchical transformation of hidden Markov models for speech recognition

On-line adaptive learning of the continuous density hidden Markov model based on approximate recursive Bayes estimate

Probabilistic Winner-Take-All Learning Algorithm for Radial-Basis-Function Neural Classifiers

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