{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch4-Hidden_Markov_Models

# Ch4-Hidden_Markov_Models - Speech Recognition Hidden Markov...

This preview shows pages 1–9. Sign up to view the full content.

Speech Recognition Hidden Markov Models

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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:
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}