Deterministically annealed design of hidden Markov model speech recognizers

Many conventional speech recognition systems are based on the use of hidden Markov models (HMM) within the context of discriminant-based pattern classification. While the speech recognition objective is a low rate of misclassification, HMM design has been traditionally approached via maximum likelihood (ML) modeling which is, in general, mismatched with the minimum error objective and hence suboptimal. Direct minimization of the error rate is difficult because of the complex nature of the cost surface, and has only been addressed recently by discriminative design methods such as generalized probabilistic descent (GPD). While existing discriminative methods offer significant benefits, they commonly rely on local optimization via gradient descent whose performance suffers from the prevalence of shallow local minima. As an alternative, we propose the deterministic annealing (DA) design method that directly minimizes the error rate while avoiding many poor local minima of the cost. DA is derived from fundamental principles of statistical physics and information theory. In DA, the HMM classifier's decision is randomized and its expected error rate is minimized subject to a constraint on the level of randomness which is measured by the Shannon entropy. The entropy constraint is gradually relaxed, leading in the limit of zero entropy to the design of regular nonrandom HMM classifiers. An efficient forward-backward algorithm is proposed for the DA method. Experiments on synthetic data and on a simplified recognizer for isolated English letters demonstrate that the DA design method can improve recognition error rates over both ML and GPD methods.