Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme

Abstract Learning techniques based on the Hidden Markov Model (HMM) assumption have proved efficient in various facets of speech analysis. The application of HMMs to speech unit modelling suffers, however, from one major deficiency; the implicit state occupancy distribution which is a geometric process is inadequate to model speech segment duration. To avoid this drawback, we propose to replace the underlying Markov chain by a semi-Markov chain, a more general framework where the state occupancy is explicitly modelled by an appropriate probability density function, in our case a gamma distribution. Due to particular dependency properties inside the semi-Markov chain, the direct adaptation of the Forward-Backward algorithm to the Hidden Semi-Markov Model (HSMM) assumption leads to rather complicated solutions for the training task. With the aim of simplification, we propose to adapt the Derin's scheme, originally developed in the field of image segmentation. One important characteristic of this scheme is its a-posteriori probability formalism which implicitly introduces a normalization at each step of the basic recursions. This allows us to solve in a rigorous and efficient manner the well known underflow problem in the training task. The re-estimation formulas for the HSMM parameters are derived according to a maximum likelihood criterion. Derin's algorithm for HSMMs is presented and a practical implementation is detailed. Results are given on a 130 isolated-word recognition task.