In this letter, we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting of both discrete state-indicator and discrete state-duration random variables. In contrast to the implicit geometric state duration distribution possessed by the standard HMM, EDHMMs allow the direct parameterization and estimation of per-state duration distributions. As most duration distributions are defined over the positive integers, truncation or other approximations are usually required to perform EDHMM inference.
A statistical speech synthesis system based on the hidden Markov model (HMM) was recently proposed. In this system, spectrum, excitation, and duration of speech are modeled simultaneously by context-dependent HMMs, and speech parameter vector sequences are generated from the HMMs themselves. This system defines a speech synthesis problem in a generative model framework and solves it based on the maximum likelihood (ML) criterion. However, there is an inconsistency: although state duration probability density functions (PDFs) are explicitly used in the synthesis part of the system, they have not been incorporated into its training part. This inconsistency can make the synthesized speech sound less natural. In this paper, we propose a statistical speech synthesis system based on a hidden semi-Markov model (HSMM), which can be viewed as an HMM with explicit state duration PDFs. The use of HSMMs can solve the above inconsistency because we can incorporate the state duration PDFs explicitly into both the synthesis and the training parts of the system. Subjective listening test results show that use of HSMMs improves the reported naturalness of synthesized speech. Many alternative models have been proposed to address some of the shortcomings of the hidden Markov model (HMM), which is currently the most popular approach to speech recognition. In particular, a variety of models that could be broadly classified as segment models have been described for representing a variable-length sequence of observation vectors in speech recognition applications. Since there are many aspects in common between these approaches, including the general recognition and training problems, it is useful to consider them in a unified framework. The paper describes a general stochastic model that encompasses most of the models proposed in the literature, pointing out similarities of the models in terms of correlation and parameter tying assumptions, and drawing analogies between segment models and HMMs. In addition, we summarize experimental results assessing different modeling assumptions and point out remaining open questions. This correspondence addresses several practical problems in implementing a forward-backward (FB) algorithm for an explicit-duration hidden Markov model. First, the FB variables are redefined in terms of posterior probabilities to avoid possible underflows that may occur in practice. Then, a forward recursion is used that is symmetric to the backward one and can reduce the number of logic gates required to implement on a field-programmable gate-array (FPGA) chip. We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior for the number of mixture components within each group. Given our desire to tie the mixture models in the various groups, we consider a hierarchical model, specifically one in which the base measure for the child Dirichlet processes is itself distributed according to a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessarily share atoms. Thus, as desired, the mixture models in the different groups necessarily share mixture components. We discuss representations of hierarchical Dirichlet processes ...  This tutorial provides an overview of the basic theory of hidden Markov models (HMMs) as originated by L.E. Baum and T. Petrie (1966) and gives practical details on methods of implementation of the theory along with a description of selected applications of the theory to distinct problems in speech recognition. Results from a number of original sources are combined to provide a single source of acquiring the background required to pursue further this area of research. The author first reviews the theory of discrete Markov chains and shows how the concept of hidden states, where the observation is a probabilistic function of the state, can be used effectively. The theory is illustrated with two simple examples, namely coin-tossing, and the classic balls-in-urns system. Three fundamental problems of HMMs are noted and several practical techniques for solving these problems are given. The various types of HMMs that have been studied, including ergodic as well as left-right models, are described. > The hierarchical Dirichlet process hidden Markov model (HDP-HMM) is a flexible, nonparametric model which allows state spaces of unknown size to be learned from data. We demonstrate some limitations of the original HDP-HMM formulation (, 2006), and propose a sticky extension which allows more robust learning of smoothly varying dynamics. Using DP mixtures, this formulation also allows learning of more complex, multimodal emission distributions. We further develop a sampling algorithm that employs a truncated approximation of the DP to jointly resample the full state sequence, greatly improving mixing rates. Via extensive experiments with synthetic data and the NIST speaker diarization database, we demonstrate the advantages of our sticky extension, and the utility of the HDP-HMM in real-world applications.