Making Use of Partial Knowledge About Hidden States in HMMs: An Approach Based on Belief Functions

This paper addresses the problem of parameter estimation and state prediction in hidden Markov models (HMMs) based on observed outputs and partial knowledge of hidden states expressed in the belief function framework. The usual HMM model is recovered when the belief functions are vacuous. Parameters are learned using the evidential expectation-maximization algorithm, a recently introduced variant of the expectation-maximization algorithm for maximum likelihood estimation based on uncertain data. The inference problem, i.e., finding the most probable sequence of states based on observed outputs and partial knowledge of states, is also addressed. Experimental results demonstrate that partial information about hidden states, when available, may substantially improve the estimation and prediction performances.