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.

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 this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how information-theoretic criterion functions can be used to induce sparse, discriminative, and classconditional network structures that yield an optimal approximation to the class posterior probability, and therefore are useful for the classification task. Using a new structure learning heuristic, the resulting models are tested on a medium-vocabulary isolated-word speech recognition task. It is demonstrated that these discriminatively structured dynamic Bayesian multinets, when trained in a maximum likelihood setting using EM, can outperform both HMMs and other dynamic Bayesian networks with a similar number of parameters. 1 Introduction While Markov chains are sometimes a useful model for sequences, such simple independence assumptions can lead...

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.

Recent advances in automatic speech recognition are accomplished by designing a plug-in maximum a posteriori decision rule such that the forms of the acoustic and language model distributions are specified and the parameters of the assumed distributions are estimated from a collection of speech and language training corpora. Maximum-likelihood point estimation is by far the most prevailing training method. However, due to the problems of unknown speech distributions, sparse training data, high spectral and temporal variabilities in speech, and possible mismatch between training and testing conditions, a dynamic training strategy is needed. To cope with the changing speakers and speaking conditions in real operational conditions for high-performance speech recognition, such paradigms incorporate a small amount of speaker and environment specific adaptation data into the training process. Bayesian adaptive learning is an optimal way to combine

Due to the difficulty of character segmentation in cursive handwriting recognition, much recent research has turned to segmentation free approaches of word recognition. While techniques of feature extraction for presegmented characters have been thoroughly explored in the literature, an evaluation of features for use with segmentation during recognition techniques remains sparse. The main purpose of this thesis is to provide a comparison of a number of feature extraction techniques applied to the domain of legal amount recognition in bank checks. An experimental system using Hidden Markov Models and a horizontally sliding window is described. Results are presented for the recognition of the entire legal field using a variety of features. Of the experiments presented here, the best results were obtained by concatenating the feature vectors from the present, previous, and next window...

Abstract — We present a method for performing mode classification of real-time streams of GPS surface position data. Our approach has two parts: an algorithm for robust, unconstrained fitting of hidden Markov models (HMMs) to continuousvalued time series, and SensorGrid technology that manages data streams through a series of filters coupled with a publish/subscribe messaging system. The SensorGrid framework enables strong connections between data sources, the HMM time series analysis software, and users. We demonstrate our approach through a web portal environment through which users can easily access data from the SCIGN and SOPAC GPS networks in Southern California, apply the analysis method, and view results. Ongoing real-time mode classifications of streaming GPS data are displayed in a map-based visualization interface. I.

A Hidden Markov Model Toolbox is presented within the Scilab environement. In this toolbox popular methods for the resolution of HMM problems are incorporated. These methods cover the training and recognition phases. Models may be used with discrete and continuous observations. This toolbox includes conventional methods as well as extensions. 1. Introduction Hidden Markov models (HMM) have been widely applied in automatic speech recognition. In this field, signals are encoded as temporal variation of short time power spectrum [12]. HMM applications are now being extended to many fields such as pattern recognition, signal processing, modeling and control of dynamic systems. They are well suited for the classification of one or two dimensional signals. A HMM is a double stochastic process with one underlying process that is not observable but may be estimated through a set of processes that produce a sequence of observations. They may be used for the treatment of problems where informat...

We present an application of hidden Markov models (HMMs) to analysis of geode-tic time series in Southern California. Our model fitting method uses a regularized version of the deterministic annealing expectation-maximization algorithm to en-sure that model solutions are both robust and of high quality. Using the fitted models, we segment the daily displacement time series collected by 127 stations of the Southern California Integrated Geodetic Network (SCIGN) over a two year period. Segmentations of the series are based on statistical changes as identified by the trained HMMs. We look for correlations in state changes across multi-ple stations that indicate region-wide activity. We find that although in one case a strong seismic event was associated with a spike in station correlations, in all other cases in the study time period strong correlations were not associated with any seismic event. This indicates that the method was able to identify more subtle signals associated with aseismic events or long-range interactions between smaller events.

We present a novel structured variational inference algorithm for probabilistic speech separation. The algorithm