Hidden Markov models based on multi-space probability distribution for pitch pattern modeling

This paper discusses a hidden Markov model (HMM) based on multi-space probability distribution (MSD). The HMMs are widely-used statistical models to characterize the sequence of speech spectra and have successfully been applied to speech recognition systems. From these facts, it is considered that the HMM is useful for modeling pitch patterns of speech. However, we cannot apply the conventional discrete or continuous HMMs to pitch pattern modeling since the observation sequence of the pitch pattern is composed of one-dimensional continuous values and a discrete symbol which represents "unvoiced". MSD-HMM includes discrete HMMs and continuous mixture HMMs as special cases, and further can model the sequence of observation vectors with variable dimension including zero-dimensional observations, i.e., discrete symbols. As a result, MSD-HMMs can model pitch patterns without heuristic assumption. We derive a reestimation algorithm for the extended HMM and show that it can find a critical point of the likelihood function.