ML Estimation of a Stochastic Linear System with the EM Algorithm and Its Application to Speech Recognition

In this paper we present a nontraditional approach to the problem of estimating the parameters of a stochastic linear system. The method is based on the Expectation-Maximization algorithm and can be considered as the continuous analog of the Baum-Welch estimation algorithm for hidden Markov models. We use the algorithm for training the parameters of a dynamical system model that we propose for better representing the spectral dynamics of speech for recognition. We assume that the observed feature vectors of a phone segment are the output of a stochastic linear dynamical system, and we show how the evolution of the dynamics as a function of the segment length can be modeled using alternative assumptions. We show on a phoneme classification task using the TIMIT database that our approach is the first effective use of an explicit model for statistical dependence between frames of speech.