next up previous contents index
Next: Stochastic language modelling Up: System architecture for speech Previous: System architecture for speech

Bayes decision rule

 

Every approach to automatic speech recognition is faced with the problem of taking decisions in the presence of ambiguity and context, and of modelling the interdependence of these decisions at various levels. If it were possible to recognise phonemes  (or words) with a very high reliability, it would not be necessary to rely heavily on delayed decision techniques, error correcting techniques and statistical methods. In the near future, this problem of reliable and virtually error free phoneme  or word recognition  without using high-level knowledge is unlikely to be solved for large-vocabulary  continuous-speech  recognition.  As a consequence, the recognition system  has to deal with a large number of hypotheses about phonemes , words and sentences, and ideally has to take into account the ``high-level constraints'' as given by syntax , semantics and pragmatics . Given this state of affairs, statistical decision theory tells us how to minimise the probability of recognition errors [Bahl et al. (1983)].

The word sequence tex2html_wrap_inline45515 to be recognised from the sequence of acoustic observations tex2html_wrap_inline45517 is determined as that word sequence tex2html_wrap_inline45515 for which the posterior probability tex2html_wrap_inline45521 attains its maximum. The sequence of acoustic vectors tex2html_wrap_inline45523 over time t=1...T is derived from the speech signal in the preprocessing step of acoustic analysis. Statistical decision theory leads to the so-called Bayes decision rule, which can be written in the form:
eqnarray8710
where tex2html_wrap_inline45529 is the conditional probability, given the word sequence tex2html_wrap_inline45515, of observing the sequence of acoustic vectors tex2html_wrap_inline45517 and where tex2html_wrap_inline45535 is the prior probability of producing the word sequence tex2html_wrap_inline45515. The application of the Bayes decision rule to the speech recognition problem is illustrated in Figure 7.1.

 figure8717
Figure 7.1: Bayes decision rule for speech recognition 

The decision rule requires two types of probability distribution, which we refer to as stochastic knowledge sources,  along with a search strategy: 

 



next up previous contents index
Next: Stochastic language modelling Up: System architecture for speech Previous: System architecture for speech

EAGLES SWLG SoftEdition, May 1997. Get the book...