Voice Communication Between Humans and Machines (1994) / Chapter Skim
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Training and Search Methods for Speech Recognition
Training and Search Methods for Speech Recognition
Pages 199-214
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From page 199... ...
The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizes wishes to find the most probable utterance that could have caused the observed acoustic index string.
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The model of speech production of a sequence of words W is a concatenation of models of individual words wi making up the sequence W (see Figure 2~. We recall that the HMM of Figure 1 starts its operation in the initial state so and ends it when the final state SF iS reached.
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Essentially without loss of generality we will consider only a finite alphabet ~ of equivalence classes, so that O(W1' W2, · · · Wi_~) = 0i £ ~ A popular classifier example is: (the bigram model)
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There are three states and six transitions, t3 being a null transition. The transition probabilities satisfy constraints FIGURE3 Sample~ree- Am \ / /r t4 state hidden Markov t - model.
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The states of successive stages are connected by the nonnull transitions of the HMM because they take a unit of time to complete. The states within a stage are connected by the null transitions because these are accomplished instantaneously.
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Then it would seem intuitively reasonable to define the "counts" by (t' is restricted to nonnull transitions)
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, the counter of exactly one of the nonnull transitions is increased by 1 for each output, this same contribution is simply distributed by (8') among the various counters belonging to nonnull transitions.
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and M (s) are the sets of null and nonnull transitions leaving s, respectively: M¢s)
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As long as the text HMM contains a sufficient number of each of the elementary HMMs, the resulting estimation of the Pitt and Pa I t) parameters will be successful, and the HMMs 1i .' ,~ Pl~Ul<~; ~ Elementary hidden Markov model for the fenonic case.
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Consider the following basic problem: Given a fully specified HMM, find the sequence of transitions that were the most likely "cause" of given observed data A To solve the problem, we again use the trellis representation of the HMM output process (see Figure 4~.
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This statement must be interpreted literally we do not care what happens inside the HMM boxes. The slightly more complicated bigram language model [see Eq.
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~ 1 , 1 ~/ 1 1 ~/ 1 Or ~ ~/ ~ P(VN) ~/ \ HMM _ ~ _ of VN / / / / 1 FIGURE 6 Schematic structure of the hidden Markov model for a unigram language model.
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\ \ \_ \ rx \ ' ~ \ HMM of _ _ >. _ _ _ VN FIGURE 7 Schematic structure of the hidden Markov model for a bigram language model.
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trellis (see the third section of this paper) corresponding to Figure 7.
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The trace-back (see fourth section) from any of these final states, say, of word v at stage j, will lead to the initial state of the same word model, say at stage i.
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Paul, D B., "An Essential As Stack Decoder Algorithm for Continuous Speech Recognition with a Stochastic Language Model," 1992 International Conference on Acoustics, Speech, and Signal Processing, San Francisco, March 1992.
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