Estimation and Identification using Hidden Markov Models

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Author Index
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

Robust EM Algorithms For Markov Modulated Poisson Processes

Authors:

Robert J. Elliott, William P. Malcolm,

Volume: 1, Page 4678 Paper number 1419

Abstract:

In this article we consider robust filtering and smoothing for Markov Modulated Poisson Processes (MMPPs). Using the EM algorithm, these filters and smoothers can be applied to estimate the parameters of our model. Our dynamics do not involve stochastic integrals and our new formulae, in terms of time integrals, are easily discretized.

CD001419.PDF (From Author)

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Fault Detection in Hidden Markov Models: A Local Asymptotic Approach

Authors:

François LeGland, Laurent Mével,

Volume: 1, Page 4686 Paper number 1829

Abstract:

In this paper, the problem of detecting a change in the transition probability matrix of a hidden Markov chain is addressed, using the local asymptotic approach. The score function, evaluated at the nominal value, is used as the residual, and is expressed as an additive functional of the extended Markov chain consisting of the hidden state, the observation, the prediction filter and its gradient w.r.t. the parameter. The problem of residual evaluation is solved using available limit theorems on the extended Markov chain, which allow to replace the original detection problem by the simpler problem of detecting a change in the mean of a Gaussian r.v.

CD001829.PDF (From Author)

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Convergence Rates of the Maximum Likelihood Estimator of Hidden Markov Models

Authors:

Laurent Mével, Lorenzo Finesso,

Volume: 1, Page 4691 Paper number 1664

Abstract:

In this paper we consider the problem of the identification of a partially observed finite state Markov chain (or Hidden Markov Model, HMM), with continuous observations. Maximum Likelihood (ML) is the most popular approach to parameter estimation for this class of models. The asymptotic properties of the ML estimator (MLE) have already been investigated under a variety of conditions. Under the assumption of stationarity, Leroux has proved the almost sure consistency of the MLE, and Bykel, Ritov and Ryden have proved its asymptotic normality. More general results, encompassing both previous ones, have been given by Mevel. A new technique for the study of the convergence of HMM's has been developed. This technique is based on geometric ergodicity properties of the prediction filter and its derivatives, derived via results for products of random matrices. The main advantage is that convergence results for Hidden Markov Models can now be reduced to the analysis of a Markov process, with a properly defined state space. In this paper we apply the new technique to derive the almost sure rate of convergence of the MLE and give an example of application in the context of the model selection problem. As will be mentioned in the paper, these results extend easily to conditional least squares estimators.

CD001664.PDF (From Author)

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Reduced-Complexity Smoothing for Hidden Markov Models

Authors:

Louis Shue, Subhrakanti Dey,

Volume: 1, Page 4697 Paper number 1167

Abstract:

In this paper, we investigate approximate smoothing schemes for a class of hidden Markov models (HMM), namely, HMMs with underlying Markov chains that are nearly completely decomposable. The objective is to obtain substantial computational savings. Our algorithm can not only be used to obtain aggregate smoothed estimates, but can be used to obtain systematically approximate full-order smoothed estimates with computational savings, unlike many of the aggregation methods proposed earlier.

CD001167.PDF (From Author)

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On-Line Identification of Non-Minimum Phase Finite Impulse Response Linear Systems with Discrete Inputs via Hidden Markov Models

Authors:

Jason J. Ford,

Volume: 1, Page 4703 Paper number 1032

Abstract:

This paper considers adaptive estimation of noisy finite impulse response linear systems driven by stationary inputs from a discrete set. An equivalent hidden Markov model representations is presented which allows some powerful signal processing techniques to be applied to this estimation problem. A new adaptive estimation algorithm is presented and simulation studies illustrate the performance of the proposed algorithm.

CD001032.PDF (From Author)

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