A Probabilistic Distance Measure for Hidden Markov Models

We propose a probabilistic distance measure for measuring the dissimilarity between pairs of hidden Markov models with arbitrary observation densities. The measure is based on the Kullback-Leibler number and is consistent with the reestimation technique for hidden Markov models. Numerical examples that demonstrate the utility of the proposed distance measure are given for hidden Markov models with discrete densities. We also discuss the effects of various parameter deviations in the Markov models on the resulting distance, and study the relationships among parameter estimates (obtained from reestimation), initial guesses of parameter values, and observation duration through the use of the measure.