A statistical discrimination measure for hidden Markov models based on divergence

This paper proposes and evaluates a new statistical discrimination measure for hidden Markov models (HMMs) extending the notion of divergence [1], a measure of average discrimination information originally defined for two probability density functions. The Average Divergence Distance (ADD) is proposed as a statistical discrimination measure between two HMMs, considering the transient behavior of these models. We show the analytical formulation of this discrimination measure, and demonstrate that this quantity is well defined for a left-to-right HMM topology with final non-emitting state, a standard model for basic acoustic units in Automatic Speech Recognition (ASR). Using experiments based on this discrimination measure, it is shown that ADD is a coherent way to evaluate the discrimination dissimilarity between acoustic models.