Although initially introduced and studied in the late 1960s and early 1970s, statistical methods of Markov source or hidden Markov modeling have become increasingly popular in the last several years. There are two strong reasons why this has occurred. First the models are very rich in mathematical structure and hence can form the theoretical basis for use in a wide range of applications. Sec-ond the models, when applied properly, work very well in practice for several important applications. In this paper we attempt to care-fully and methodically review the theoretical aspects of this type of statistical modeling and show how they have been applied to selected problems in machine recognition of speech. I.

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In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addressed. Using HMMs with Gaussian mixture state observation densities as an example, it is assumed that the prior densities for the HMM parameters can be adequately represented as a product of Dirichlet and normal-Wishart densities. The classical maximum likelihood estimation algorithms, namely the forward-backward algorithm and the segmental k-means algorithm, are expanded and MAP estimation formulas are developed. Prior density estimation issues are discussed for two classes of applications: parameter smoothing and model adaptation, and some experimental results are given illustrating the practical interest of this approach. Because of its adaptive nature, Bayesian learning is shown to serve as a unified approach for a wide range of speech recognition applications

Topological maps provide a useful abstraction for robotic navigation and planning. Although stochastic maps can theoretically be learned using the Baum-Welch algorithm, without strong prior constraint on the structure of the model it is slow to converge, requires a great deal of data, and is often stuck in local minima. In this paper, we consider a special case of hidden Markov models for robot-navigation environments, in which states are associated with points in a metric configuration space. We assume that the robot has some odometric ability to measure relative transformations between its configurations. Such odometry is typically not precise enough to suffice for building a global map, but it does give valuable local information about relations between adjacent states. We present an extension of the Baum-Welch algorithm that takes advantage of this local odometric information, yielding faster convergence to better solutions with less data.

Abstract—An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed in this paper. Index Terms—Baum–Petrie algorithm, entropy ergodic theorems, finite-state channels, hidden Markov models, identifiability, Kalman filter, maximum-likelihood (ML) estimation, order estimation, recursive parameter estimation, switching autoregressive processes, Ziv inequality. I.

This report is concerned with integrating connectionist networks into a hidden Markov model (HMM) speech recognition system, This is achieved through a statistical understanding of connectionist networks as probability estimators, first elucidated by Herve Bourlard. We review the basis of HMM speech recognition, and point out the possible benefits of incorporating connectionist networks. We discuss some issues necessary to the construction of a connectionist HMM recognition system, and describe the performance of such a system, including evaluations on the DARPA database, in collaboration with Mike Cohen and Horacio Franco of SRI International. In conclusion, we show that a connectionist component improves a state of the art HMM system. ii Part I INTRODUCTION Over the past few years, connectionist models have been widely proposed as a potentially powerful approach to speech recognition (e.g. Makino et al. (1983), Huang et al. (1988) and Waibel et al. (1989)). However, whilst connec...

This paper proposes a new covariance modeling technique for Gaussian Mixture Models. Specifically the inverse covariance (precision) matrix of each Gaussian is expanded in a rank-1 basis i.e., j = P j = k , 2 R; a k 2 R . A generalized EM algorithm is proposed to obtain maximum likelihood parameter estimates for the basis set fa k a k=1 and the expansion coefficients f g. This model, called the Extended Maximum Likelihood Linear Transform (EMLLT) model, is extremely flexible: by varying the number of basis elements from D = d to D = d(d + 1)=2 one gradually moves from a Maximum Likelihood Linear Transform (MLLT) model to a full-covariance model. Experimental results on two speech recognition tasks show that the EMLLT model can give relative gains of up to 35% in the word error rate over a standard diagonal covariance model, 30% over a standard MLLT model.

Hidden Markov models (hmms) and partially observable Markov decision processes (pomdps) provide a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office buildings, which are typical for robot navigation and planning. The work presented here describes a formal framework for incorporating readily available odometric information into both the models and the algorithm that learns them. By taking advantage of such information, learning hmms/pomdps can be made better and require fewer iterations, while being robust in the face of data reduction. That is, the performance of our algorithm does not significantly deteriorate as the training sequences provided to it become significantly shorter. Formal proofs for the convergence of the algorithm to a local maximum of the likelihood function are provided. Experimental results, obtained from both simulated and real robot data, demonstrate the effectiveness of the approach....

“Segmental hidden Markov models ” (SHMMs) are intended to overcome important speech-modelling limitations of the conventional-HMM approach by representing sequences (or segments) of features and incorporating the concept of trajectories to describe how features change over time. A novel feature of the approach presented in this paper is that extra-segmental variability between different examples of a sub-phonemic speech segment is modelled separately from intra-segmental variability within any one example. The extra-segmental component of the model is represented in terms of variability in the trajectory parameters, and these models are therefore referred to as “probabilistic-trajectory segmental HMMs ” (PTSHMMs). This paper presents the theory of PTSHMMs using a linear trajectory description characterized by slope and mid-point parameters, and presents theoretical and experimental comparisons between different types of PTSHMMs, simpler SHMMs and conventional HMMs. Experiments have demonstrated that, for any given feature set, a linear PTSHMM can substantially reduce the error rate in comparison with a conventional HMM, both for a connected-digit recognition task and for a phonetic classification task. Performance benefits have been demonstrated from incorporating a linear trajectory description and additionally from modelling variability in the mid-point parameter. c ○ 1999 British Crown Copyright/DERA 1.

In this paper a theoretical framework for Bayesian adaptive learning of discrete HMM and semi-continuous one with Gaussian mixture state observation densities is presented. Corresponding to the well-known Baum-Welch and segmental k-means algorithms respectively for HMM training, formulations of MAP (maximum aposteriori) and segmental MAP estimation of HMM parameters are developed. Furthermore, a computationally efficient method of the segmental quasi-Bayes estimation for semi-continuous HMM is also presented. The important issue of prior density estimation is discussed and a simplified method of moment estimate is given. The method proposed in this paper will be applicable to some problems in HMM training for speech recognition such as sequential or batch training, model adaptation, and parameter smoothing, etc.