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Convergence analyses and comparisons of Markov chain Monte Carlo algorithms in digital communications

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2002年第2期50卷 255-270页

作者： Chen, R Liu, JS Wang, XD Univ Illinois Dept Informat & Decis Sci Chicago IL USA Harvard Univ Dept Stat Cambridge MA 02138 USA Columbia Univ Dept Elect Engn New York NY 10027 USA

Recently, Markov chain Monte Carlo (MCMC) methods have been applied to the design of blind Bayesian receivers in a number of digital communications applications. The salient features of these MCMC receivers include the following: a) They are optimal in the sense of achieving minimum symbol error rate;b) they do not require the knowledge of the channel states, nor do they explicitly estimate the channel by employing training signals or decision-feedback;and c) they are well suited for iterative (turbo) processing in coded systems. In this paper, we investigate the convergence behaviors of several MCMC algorithms (both existing and new ones) in,digital communication applications. The geometric convergence property of these algorithms is established by considering only the chains or the marginal chains corresponding to the transmitted digital symbols, which take values from a finite discrete set. We then focus on three specific applications, namely, the MCMC decoders in AWGN channels, ISI channels, and CDMA channels. The convergence rates for these algorithms are computed for small simulated datasets. Different convergence behaviors are observed. It is seen that differential encoding, parameter constraining, collapsing, and grouping are efficient ways of accelerating the convergence of the MCMC algorithms, especially in the presence of channel phase ambiguity.

关键词： Bayesian receiver duality eigenvalue forward-backward algorithm Gibbs sampler Metropolis algorithm transition function

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High-order extensions of the double chain Markov model

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STOCHASTIC MODELS 2002年第2期18卷 193-227页

作者： Berchtold, A Univ Lausanne Inst Appl Math SSP BFSH2 CH-1015 Lausanne Switzerland Univ Washington Seattle WA 98195 USA

The Double Chain Markov Model is a fully Markovian model for the representation of time-series in random environments. In this article, we show that it can handle transitions of high-order between both a set of observations and a set of hidden states. In order to reduce the number of parameters, each transition matrix can be replaced by a Mixture Transition Distribution model. We provide a complete derivation of the algorithms needed to compute the model. Three applications, the analysis of a sequence of DNA, the song of the wood pewee, and the behavior of young monkeys show that this model is of great interest for the representation of data that can be decomposed into a finite set of patterns.

关键词： double chain Markov model (DCMM) high-order transitions mixture transition distribution model (MTD) forward-backward algorithm Baum-Welch algorithm viterbi algorithm DNA pewee behavior

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Hidden Gauss-Markov models for signal classification

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2002年第6期50卷 1355-1367页

作者： Ainsleigh, PL Kehtarnavaz, N Streit, RL USN Undersea Warfare Ctr Newport RI 02841 USA Univ Texas Dept Elect Engn Richardson TX 75080 USA

Continuous-state hidden Markov models (CS-HMMs) are developed as a tool for signal classification. Analogs of the Baum, Viterbi, and Baum-Welch algorithms are formulated for this class of models. The CS-HMM algorithms are then specialized to hidden Gauss-Markov models (HGMMs) with linear Gaussian state-transition and output densities. A new Gaussian refactorization lemma is used to show that the Baum and Viterbi algorithms for HGMMs are implemented by two different formulations of the fixed-interval Kalman smoother. The measurement likelihoods obtained from the forward pass of the HGMM Baum algorithm and from the Kalman-filter innovation sequence are shown to be equal. A direct link between the Baum-Welch training algorithm and an existing expectation-maximization (EM) algorithm for Gaussian models is demonstrated. A new expression for the cross covariance between time-adjacent states in HGMMs is derived from the off-diagonal block of the conditional joint covariance matrix. A parameter invariance structure is noted for the HGMM likelihood function. CS-HMMs and HGMMs are extended to incorporate mixture densities for the a priori density of the initial state. Application of HGMMs to signal classification is demonstrated with a three-class test simulation.

关键词： Baum-Welch algorithm continuous-state HMM EM algorithm fixed-interval smoother forward-backward algorithm hidden Markov model Kalman filter maximum likelihood classification mixture density

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Multicomponent signal classification using the PMHT algorithm

Multicomponent signal classification using the PMHT algorith...

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5th International Conference on Information Fusion (FUSION 2002)

作者： Ainsleigh, P Luginbuhl, T USN Undersea Warfare Ctr Newport RI 02841 USA

ISBN: (纸本)0972184414

The probabilistic multi-hypothesis tracking (PMHT) algorithm is extended for application to classification. The PMHT model is reformulated as a bank of continuous-state hidden Harkov models, allowing for supervised learning of the class-conditional probability density models, and for likelihood evaluation of multicomponent signals.

关键词： classification probablistic multi-hypothesis tracking PMHT hidden Markov model HMM continuous-state HMM EM algorithm forward-backward algorithm

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Confidence measures for large vocabulary continuous speech recognition

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 2001年第3期9卷 288-298页

作者： Wessel, F Schlüter, R Macherey, K Ney, H Rhein Westfal TH Aachen Lehrstuhl Informat 6 D-52056 Aachen Germany

In this paper, we present several confidence measures for large vocabulary continuous speech recognition. We propose to estimate the confidence of a hypothesized word directly as its posterior probability, given all acoustic observations of the utterance. These probabilities are computed on word graphs using a forward-backward algorithm. We also study the estimation of posterior probabilities on N-best lists instead of word graphs and compare both algorithms in detail. In addition, we compare the posterior probabilities with two alternative confidence measures, i.e., the acoustic stability and the hypothesis density. We present experimental results on five different corpora: the Dutch ARISE 1k evaluation corpus, the German Verbmobil '98 7k evaluation corpus, the English North American Business '94 20k and 64k development corpora, and the English Broadcast News '96 65k evaluation corpus, We show that the posterior probabilities computed on word graphs outperform all other confidence measures. The relative reduction in confidence error rate ranges between 19% and 35% compared to the baseline confidence error rate.

关键词： confidence measures forward-backward algorithm N-best lists posterior probabilities speech recognition word graphs

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MAP symbol decoding in channels with error bursts

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第5期47卷 1832-1838页

作者： Turin, W AT&T Labs Res Shannon Lab Florham Pk NJ 07932 USA

In this paper, we analyze the forward-backward algorithm for the maximum a posteriori (MAP) decoding of information transmitted over channels with memory and propose a suboptimal forward-only algorithm, We assume that both the information source and channel are described using hidden Markov models (HMMs), The algorithm lends itself to parallel implementation and pipelining. We apply the algorithm to MAP decoding of symbols which were trellis-code modulated and transmitted over channels with error bursts.

关键词： forward-backward algorithm hidden Markov models maximum aposteriori (MAP) decoding

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Automatic recognition and understanding of spoken language - A first step toward natural human-machine communication

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PROCEEDINGS OF THE IEEE 2000年第8期88卷 1142-1165页

作者： Juang, BH Furui, S Lucent Technol Inc Murray Hill NJ 07974 USA Tokyo Inst Technol Tokyo 1528552 Japan

The promise of a powerful computing device to help people in productivity as well as in recreation can only be realized with proper human-machine communication. Automatic recognition and understanding of spoken language is the first and probably the most important step toward natural human-machine interaction. Research in this fascinating field in the past few decades has produced remarkable results, leading to many exciting expectations as well as new challenges. In this paper, we summarize the development of the spoken language technology from both a vertical (the chronology) and a horizontal (the spectrum of technical approaches) perspective. We highlighted the introduction of statistical methods in dealing with language-related problems as it represents a paradigm shift in the research field of spoken language processing. Statistical methods are designed to allow the machine to learn, directly from data, structure regularities in the speech signal for the purpose of automatic speech recognition and understanding. Today, research results in spoken language processing have led to a number of successful applications ranging from dictation software for personal computers and telephone-call processing systems for automatic call routing to automatic subcaptioning for television broadcast. We analyze the technical successes that support these applications. Along with an assessment of the state-of-the-art in this board technical field, we also discuss the limitations of the current technology can be presented as the basis to inspire future advances.

关键词： acoustic modeling acoustic-phonetics articulation automatic recognition and understanding Bayes risk cepstral distance continuous speech recognition detection-based approach dialogue systems discriminative training dynamic programming finite state machine forward-backward algorithm generalized phone models grammar hidden Markov models human-machine communication isolated word recognition language modeling language structure linear prediction maximum a posteriori maximum-likelihood estimation noise perplexity probability distribution of speech pronunciation modeling robustness search algorithms short-time spectral analysis signal analysis speech dictation speech distortion speech representations spoken language processing technology statistical language processing statistical pattern recognition

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Source localization and time delay estimation using constrained least squares and best path smoothing

Source localization and time delay estimation using constrai...

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Conference on Advanced Signal Processing algorithms, Architectures, and Implementations IX

作者： Tung, TL Yao, K Reed, CW Hudson, RE Chen, D Chen, J Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

ISBN: (纸本)0819432938

The problem of source localization from arrival time delay estimates requires a computationally costly iterative solution of a set of nonlinear equations. Most known methods assume that the propagation speed is known. In this paper, we provide several effective source localization and propagation velocity estimation methods which only use measurements of the relative arrival time delays between sensors. The formulae for source localization and propagation speed estimation are derived based on least squares, total least squares, bounded data uncertainty, and constrained least squares methods. Statistical performance of these methods are compared via computer simulation. In addition, in order to avoid time delay ambiguity problems and obtain smoother time delays, two time delay smoothing methods based on the forward backward algorithm and the Viterbi algorithm are also proposed. Field experiment results based on these techniques are also presented.

关键词： time delay smoothing source localization forward-backward algorithm Viterbi algorithm least squares total least squares bounded data uncertainty constrained least squares

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ESTIMATION FOR PARTIALLY OBSERVED MARKOV-PROCESSES

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STOCHASTIC HYDROLOGY AND HYDRAULICS 1995年第1期9卷 33-47页

作者： THOMPSON, ME KASEKE, TN UNIV WATERLOO DEPT STAT & ACTUARIAL SCIWATERLOOON N2L 3G1CANADA

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X(n), n greater than or equal to 0) or (X(t), t greater than or equal to 0) for which the parameters are of interest and physically meaningful, and an observable process (Y-n, n greater than or equal to 0) or (Y-t, t greater than or equal to 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations;the Y process may be the X process observed with a noise component;the X process might constitute a random environment for the Y process, as with hidden Markov models;the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed usually at a discrete sample of time points.

关键词： HIDDEN MARKOV MODELS MAXIMUM LIKELIHOOD ESTIMATION EM algorithm MARTINGALE ESTIMATING FUNCTION forward-backward algorithm MONTE CARLO FILTERING NASH CASCADE MODEL RAINFALL RUNOFF MODELING

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Baum's forward-backward algorithm revisited

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Pattern Recognition Letters 1985年第6期3卷 369-373页

作者： Devijver, Pierre A Philips Research Laboratory B-1170 Brussels Avenue Van Becelaere 2 Belgium

In this note, we examine the forward-backward algorithm from the computational viewpoint of the underflow problem inherent in Baum's (1972) original formulation. We demonstrate that the conversion of Baum's computation of joint likelihoods into the computation of posterior probabilities results in essentially the same algorithm, except for the presence of a scaling factor suggested by Levinson et al. (1983) on rather heuristic grounds. The resulting algorithm is immune to the underflow problem, and Levinson's scaling method is given a theoretical justification. We also investigate the relationship between Baum's algorithm and the recent algorithms of Askar and Derin (1981) and Devijver (1984). © 1985.

关键词： forward-backward algorithm Hidden Markov chains maximum a posteriori probability estimation maximum likelihood estimation

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