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Ch4-Hidden_Markov_Models

Ch4-Hidden_Markov_Models - Speech Recognition Hidden Markov...

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Speech Recognition Hidden Markov Models
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February 13, 2012 Veton Këpuska 2 Outline Introduction  Problem formulation  Forward-Backward algorithm  Viterbi search  Baum-Welch parameter estimation  Other considerations  Multiple observation sequences  Phone-based models for continuous speech recognition  Continuous density HMMs  Implementation issues 
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February 13, 2012 Veton Këpuska 3 Information Theoretic Approach to  ASR  Statistical Formulation of Speech Recognition A  – denotes the acoustic evidence (collection of feature  vectors, or data in general) based on which recognizer will  make its decision about which words were spoken. W  – denotes a string of words each belonging to a fixed  and known vocabulary. Speech Producer Acoustic Processor Linguistic Decoder Speaker's Mind Speech Ŵ Speaker Acoustic Channel Speech Recognizer A W
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February 13, 2012 Veton Këpuska 4 Information Theoretic Approach to  ASR Assume that  A  is a sequence of symbols taken from  some alphabet  A . W  – denotes a string of n words each belonging to a fixed  and known vocabulary  V . V ,..., , 2 1 = i m w w w w W A ,..., , 2 1 = i m a a a a A
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February 13, 2012 Veton Këpuska 5 Information Theoretic Approach to  ASR If P( W | A ) denotes the probability that the words  W  were  spoken, given that the evidence  A  was observed, then the  recognizer should decide in favor of a word string  Ŵ   satisfying: The recognizer will pick the most likely word string  given the observed acoustic evidence. ( 29 A W W W | max arg ˆ P =
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February 13, 2012 Veton Këpuska 6 Information Theoretic Approach to  ASR From the well known Bayes’ rule of probability theory: P( W ) – Probability that the word string  W  will be uttered P( A | W ) – Probability that when  W  was uttered the  acoustic evidence A will be observed P( A ) – is the average probability that  A  will be observed: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 A W W A A W| W W A A A W| P P P P P P P P | | = = ( 29 ( 29 ( 29 = ' ' ' | W W W A A P P P
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February 13, 2012 Veton Këpuska 7 Information Theoretic Approach to  ASR Since Maximization in: Is carried out with the variable A fixed (e.g., there is not  other acoustic data save the one we are give), it follows  from Baye’s rule that the recognizer’s aim is to find the  word string  Ŵ  that maximizes the product  P( A | W )P( W ) that is   ( 29 A W W W | max arg ˆ P = ( 29 ( 29 W A W W W P P | max arg ˆ =
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February 13, 2012 Veton Këpuska 8 Hidden Markov Models About Markov Chains: Let X 1 , X 2 , …, X n , … be a sequence of random variables taking their  values in the same finite alphabet  χ  = {1,2,3,…,c}. If nothing more is  said then Bayes’ formula applies:
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