Continuously variable duration hidden Markov models for automatic speech recognition

S. E. Levinson

Research output: Contribution to journalArticlepeer-review


During the past decade, the applicability of hidden Markov models (HMM) to various facets of speech analysis has been demonstrated in several different experiments. These investigations all rest on the assumption that speech is a quasi-stationary process whose stationary intervals can be identified with the occupancy of a single state of an appropriate HMM. In the traditional form of the HMM, the probability of duration of a state decreases exponentially with time. This behavior does not provide an adequate representation of the temporal structure of speech. The solution proposed here is to replace the probability distributions of duration with continuous probability density functions to form a continuously variable duration hidden Markov model (CVDHMM). The gamma distribution is ideally suited to specification of the durational density since it is one-sided and only has two parameters which, together, define both mean and variance. The main result is a derivation and proof of convergence of re-estimation formulae for all the parameters of the CVDHMM. It is interesting to note that if the state durations are gamma-distributed, one of the formulae is non-algebraic but, fortuitously, has properties such that it is easily and rapidly solved numerically to any desired degree of accuracy. Other results are presented including the performance of the formulae on simulated data.

Original languageEnglish (US)
Pages (from-to)29-45
Number of pages17
JournalComputer Speech and Language
Issue number1
StatePublished - Jan 1 1986
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Human-Computer Interaction


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