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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.

In traditional speech recognition using Hidden Markov Models (HMMs), each state represents an acoustic portion of a phoneme. We explore the concept of an articulator based HMM, where each state represents a particular articulatory configuration [Erler 1996]. In this paper, we present a novel articulatory feature mapping and a new technique for model initialization. In addition, we use diphone modeling which allows context dependent training of transition probabilities. Our goal is to confirm that articulatory knowledge can assist speech recognition. We demonstrate this by showing that our mapping of articulatory configurations to phonemes performs better than random mappings. Furthermore, we demonstrate the practicality of the model by showing that, in combination with a standard model, a 12-21% relative word error rate decrease occurs relative to the standard model alone. 1. INTRODUCTION Hidden Markov Models (HMMs) are a popular approach for speech recognition. Commonly, a left-to-r...

Graphical models provide a promising paradigm to study both existing and novel techniques for automatic speech recognition. This paper first provides a brief overview of graphical models and their uses as statistical models. It is then shown that the statistical assumptions behind many pattern recognition techniques commonly used as part of a speech recognition system can be described by a graph – this includes Gaussian distributions, mixture models, decision trees, factor analysis, principle component analysis, linear discriminant analysis, and hidden Markov models. Moreover, this paper shows that many advanced models for speech recognition and language processing can also be simply described by a graph, including many at the acoustic-, pronunciation-, and language-modeling levels. A number of speech recognition techniques born directly out of the graphical-models paradigm are also surveyed. Additionally, this paper includes a novel graphical analysis regarding why derivative (or delta) features improve hidden Markov model-based speech recognition by improving structural discriminability. It also includes an example where a graph can be used to represent language model smoothing constraints. As will be seen, the space of models describable by a graph is quite large. A thorough exploration of this space should yield techniques that ultimately will supersede the hidden Markov model.

The performance of state-of-the-art speech recognition systems is still far worse than that of humans. This is partly caused by the use of poor statistical models. In a general statistical pattern classification task, the probabilistic models should represent the statistical structure unique to and distinguishing those objects to be classified. In many cases, however, model families are selected without verification of their ability to represent vital discriminative properties. For example, Hidden Markov Models (HMMs) are frequently used in automatic speech recognition systems even though they possess conditional independence properties that might cause inaccuracies when modeling and classifying speech signals. In this work, a new method for automatic speech recognition is developed where the natural statistical properties of speech are used to determine the probabilistic model. Starting from an HMM, new models are created by adding dependencies only if they are not already well captured by the HMM, and only if they increase the

Abstract—We propose a new model called a Pairwise Markov Chain (PMC), which generalizes the classical Hidden Markov Chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like Maximum A Posteriori (MAP), or Maximal Posterior Mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical Iterative Conditional Estimation (ICE) valid for of classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model. Index Terms—Bayesian restoration, hidden data, image segmentation, iterative conditional estimation, hidden Markov chain, pairwise Markov chain, unsupervised classification. 1

Since their inception over thirty years ago, hidden Markov models (HMMs) have have become the predominant methodology for automatic speech recognition (ASR) systems — today, most state-of-the-art speech systems are HMM-based. There have been a number of ways to explain HMMs and to list their capabilities, each of these ways having both advantages and disadvantages. In an effort to better understand what HMMs can do, this tutorial analyzes HMMs by exploring a novel way in which an HMM can be defined, namely in terms of random variables and conditional independence assumptions. We prefer this definition as it allows us to reason more throughly about the capabilities of HMMs. In particular, it is possible to deduce that there are, in theory at least, no theoretical limitations to the class of probability distributions representable by HMMs. This paper concludes that, in search of a model to supersede the HMM for ASR, we should rather than trying to correct for HMM limitations in the general case, new models should be found based on their potential for better parsimony, computational requirements, and noise insensitivity.

“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.

This thesis examines how artificial neural networks can benefit a large vocabulary, speaker independent, continuous speech recognition system. Currently, most speech recognition systems are based on hidden Markov models (HMMs), a statistical framework that supports both acoustic and temporal modeling. Despite their state-of-the-art performance, HMMs make a number of suboptimal modeling assumptions that limit their potential effectiveness. Neural networks avoid many of these assumptions, while they can also learn complex functions, generalize effectively, tolerate noise, and support parallelism. While neural networks can readily be applied to acoustic modeling, it is not yet clear how they can be used for temporal modeling. Therefore, we explore a class of systems called NN-HMM hybrids, in which neural networks perform acoustic modeling, and HMMs perform temporal modeling. We argue that a NN-HMM hybrid has several theoretical advantages over a pure HMM system, including better acoustic ...

... HMM conditional independence assumption in a principled way. Without increasing the number of states, the modeling power of an HMM is increased by including only those additional probabilistic dependencies (to the surrounding observation context) that are believed to be both relevant and discriminative. Conditional mutual information is used to determine both relevance and discriminability. Extended Gaussian-mixture HMMs and new EM update equations are introduced. In an isolated word speech database, results show an average 34% word error improvement over an HMM with the same number of states, and a 15% improvement over an HMM with a comparable number of parameters.