Evaluation and improvement of the HMM by state-space modeling

Analytical modeling of speech production is not an easy task, in part because of the rapidly time-varying nature of speech signals. The hidden Markov model (HMM) is widely used for the stochastic modeling of time-varying signals, and it has been most applied in the area of speech production and recognition.; Most current HMM research has focused on its applications. On the other hand, studies of the theoretical aspects of the HMM are relatively few. This is due to the difficulties of analyzing a model that is inherently probabilistic and recursive in nature. However, if the fundamentals of the HMM are approached from a different direction, it is possible to obtain useful analyses of the HMM which contribute to its use in speech technologies.; The main objective of this dissertation is to revisit and further investigate three fundamental HMM problems related to speech recognition using a novel mathematical formulation. Rather than the conventional representation of the HMM as a scalar recursive algorithm, the HMM will be represented using a vector-matrix formulation. It will be shown that the HMM can be represented as a state-space model. The conventional Baum-Welch (time-varying) model as well as an “approximate” time-invariant model will be studied in detail in the context of this new formulation. A more thorough theoretical and empirical investigation of this approximate model is presented in this dissertation. In particular, the spoken-digit recognition problem will be the focus of applied studies.; Some useful results and techniques using the time-invariant approximation of the HMM are addressed and analyzed. In addition, new state-search techniques using clustering, and novel set-membership identification techniques are developed as the basis for a novel HMM training approach. The new training results in HMM state assignments corresponding to acoustically meaningful segmentation of the speech, rather than adherence to the conventional maximum likelihood criterion. The results of new search techniques are compared to those of the Viterbi search.