Markov Processes on Curves for Automatic Speech Recognition

We investigate a probabilistic framework for automatic speech recognition based on the intrinsic geometric properties of curves. In particular, we analyze the setting in which two variables-one continuous (x), one discrete (s)-evolve jointly in time. We suppose that the vector x traces out a smooth multidimensional curve and that the variable s evolves stochastically as a function of the arc length traversed along this curve. Since arc length does not depend on the rate at which a curve is traversed, this gives rise to a family of Markov processes whose predictions, Pr[s|x], are invariant to nonlinear warpings of time. We describe the use of such models, known as Markov processes on curves (MPCs), for automatic speech recognition, where x are acoustic feature trajectories and s are phonetic transcriptions. On two tasks--recognizing New Jersey town names and connected alpha-digits--we find that MPCs yield lower word error rates than comparably trained hidden Markov models.