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Exact and Approximate Recursive Calculations for Binary Markov Random Fields Defined on Graphs

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2012年第3期21卷 758-780页

作者： Tjelmeland, Hakon Austad, Haakon Michael Norwegian Univ Sci & Technol Dept Math Sci N-7491 Trondheim Norway

In this article, we propose computationally feasible approximations to binary Markov random fields (MRFs). The basis of the approximation is the forward-backward algorithm. The exact forward-backward algorithm is computationally feasible only for fields defined on small lattices. The forward part of the algorithm computes a series of joint marginal distributions by summing out each variable in turn. We represent these joint marginal distributions by interaction parameters of different orders. The approximation is defined by approximating to zero all interaction parameters that are sufficiently close to zero. In addition, an interaction parameter is approximated to zero whenever all associated lower-level interactions are (approximated to) zero. If sufficiently many interaction parameters are set to zero, the algorithm is computationally feasible both in terms of computation time and memory requirements. The resulting approximate forward part of the forward-backward algorithm defines an approximation to the intractable normalizing constant, and the corresponding backward part of the algorithm defines a computationally feasible approximation to the MRF. We present numerical examples demonstrating the quality of the approximation. The supplementary materials for this article, which are available online, include two appendices and R and C codes for the proposed recursive algorithms.

关键词： Approximate inference Approximate normalizing constant Autologistic model forward-backward algorithm Ising model Recursive computation

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Exact and efficient Bayesian inference for multiple changepoint problems

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STATISTICS AND COMPUTING 2006年第2期16卷 203-213页

作者： Fearnhead, P Univ Lancaster Dept Math & Stat Lancaster LA1 4YW England

We demonstrate how to perform direct simulation from the posterior distribution of a class of multiple changepoint models where the number of changepoints is unknown. The class of models assumes independence between the posterior distribution of the parameters associated with segments of data between successive changepoints. This approach is based on the use of recursions, and is related to work on product partition models. The computational complexity of the approach is quadratic in the number of observations, but an approximate version, which introduces negligible error, and whose computational cost is roughly linear in the number of observations, is also possible. Our approach can be useful, for example within an MCMC algorithm, even when the independence assumptions do not hold. We demonstrate our approach on coal-mining disaster data and on well-log data. Our method can cope with a range of models, and exact simulation from the posterior distribution is possible in a matter of minutes.

关键词： Bayes factor forward-backward algorithm model choice perfect simulation reversible jump MCMC well-log data

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Scalable Bayesian Inference for Coupled Hidden Markov and Semi-Markov Models

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2020年第2期29卷 238-249页

作者： Touloupou, Panayiota Finkenstadt, Barbel Spencer, Simon E. F. Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England

Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread ofEscherichia coliO157:H7 in *** this article are available online.

关键词： Coupled hidden Markov model Data augmentation Epidemics forward-backward algorithm Markov chain Monte Carlo methods

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Soft-output detector for partial response channels using vector quantization

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IEEE TRANSACTIONS ON MAGNETICS 2005年第10期41卷 2989-2991页

作者： Kurkoski, BM Siegel, PH Wolf, JK Univ Electrocommun Tokyo 1828585 Japan Univ Calif San Diego Ctr Magnet Recording Res La Jolla CA 92093 USA

An implementation of the Bahl-Cocke-Jelinek-Raviv algorithm for partial response detection which performs the usual forward and backward state metric recursions and the log-likelihood computation using only lookup tables is proposed. The state metrics are vector quantized, which requires fewer quantization points than the conventional approach of quantizing each state metric individually. This soft-output implementation is suitable for use in partial response systems using turbo equalization.

关键词： Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm forward-backward algorithm partial response channel turbo equalization

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Online machine health prognostics based on modified duration-dependent hidden semi-Markov model and high-order particle filtering

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2018年第1-4期94卷 1283-1297页

作者： Xiao, Qili Fang, Yilin Liu, Quan Zhou, Shujuan Wuhan Univ Technol Sch Informat Engn Wuhan 430070 Hubei Peoples R China Wuhan Univ Technol Key Lab Fiber Opt Sensing Technol & Informat Proc Minist Educ Wuhan 430070 Hubei Peoples R China

Accurate online health prognostics is considered as a significant part of the condition-based maintenance (CBM), and it contributes to reduce downtime and achieve the most reliable running condition for machinery equipment. In this paper, an online machine health prognostics approach is proposed based on the modified duration-dependent hidden semi-Markov model (MDD-HSMM) and the high-order particle filter (HOPF) method. In the MDD-HSMM, the health state transition probabilities and the observation probabilities are both defined not only as state dependent like traditional HSMM does, but also as duration dependent, which is more realistic to describe the state space model to model the mechanical failure propagation process. And a new forward-backward algorithm is developed to facilitate the training process and to reduce computational complexity of the proposed MDD-HSMM. Then, the HOPF method with an online update scheme is applied to recognize the health states and predict the residual useful lifetime (RUL) value of machine in real time, which is based on the health state space model established by the MDD-HSMM and the online sensing monitoring data. And, a sliding window with variable length, which represents the relationship between current state and several previous states, is applied to adjust the order of HOPF. Finally, a real case study is used to illustrate the prognostics performance of the proposed approach and the experiment results indicate that the proposed approach has higher effectiveness than conventional HSMM methods.

关键词： Online health prognostics Modified duration-dependent hidden semi-Markov model forward-backward algorithm High-order particle filter Residual useful lifetime assessment

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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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A GPU Implementation of a MAP Decoder for Synchronization Error Correcting Codes

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IEEE COMMUNICATIONS LETTERS 2013年第5期17卷 996-999页

作者： Briffa, Johann A. Univ Surrey Dept Comp Guildford GU2 7XH Surrey England

In this paper we present a parallel implementation of a MAP decoder for synchronization error correcting codes. For a modest implementation effort, we demonstrate a considerable decoding speedup, up to two orders of magnitude even on consumer GPUs. This enables the analysis of much larger codes and worse channel conditions than previously possible, and makes applications of such codes feasible for software implementations.

关键词： Insertion-deletion correction MAP decoder forward-backward algorithm CUDA GPU

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Inference in Hidden Markov Models with Explicit State Duration Distributions

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IEEE SIGNAL PROCESSING LETTERS 2012年第4期19卷 235-238页

作者： Dewar, Michael Wiggins, Chris Wood, Frank Columbia Univ Dept Stat New York NY 10027 USA Bitly Inc New York NY 10014 USA Columbia Univ Dept Appl Phys & Appl Math New York NY 10027 USA

In this letter, we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting of both discrete state-indicator and discrete state-duration random variables. In contrast to the implicit geometric state duration distribution possessed by the standard HMM, EDHMMs allow the direct parameterization and estimation of per-state duration distributions. As most duration distributions are defined over the positive integers, truncation or other approximations are usually required to perform EDHMM inference.

关键词： Bayesian explicit duration hidden Markov model Bayesian hidden semi-Markov model forward-backward algorithm Monte Carlo methods slice sampling

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Probabilistic methods of identifying genes in prokaryotic genomes: Connections to the FIMM theory

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BRIEFINGS IN BIOINFORMATICS 2004年第2期5卷 118-130页

作者： Azad, RK Borodovsky, M Georgia Inst Technol Sch Biol Atlanta GA 30332 USA Georgia Inst Technol Sch Biomed Engn Atlanta GA 30332 USA Georgia Inst Technol Ctr Bioinformat & Computat Biol Atlanta GA 30332 USA

In this paper, we review developments in probabilistic methods of gene recognition in prokaryotic genomes with the emphasis on connections to the general theory of hidden Markov models (HMM). We show that the Bayesian method implemented in GeneMark, a frequently used gene-finding tool, can be augmented and reintroduced as a rigorous forward-backward (FB) algorithm for local posterior decoding described in the HMM theory. Another earlier developed method, prokaryotic ***, uses a modification of the Viterbi algorithm for HMM with duration to identify the most likely global path through hidden functional states given the DNA sequence. GeneMark and *** programs are worth using in concert for analysing prokaryotic DNA sequences that arguably do not follow any exact mathematical model. The new extension of GeneMark using the FB algorithm was implemented in the software program ***. Given the DNA sequence, this program determines an a posteriori probability for each nucleotide to belong to coding or non-coding region. Also, for any open reading frame (ORF), it assigns a score defined as a probabilistic measure of all paths through hidden states that traverse the ORF as a coding region. The prediction accuracy of *** determined in our tests was compared favourably to the accuracy of the initial (standard) GeneMark program. Comparison to the prokaryotic *** has also demonstrated a certain, yet species-specific, degree of improvement in raw gene detection, ie detection of correct reading frame (and stop codon). The accuracy of exact gene prediction, which is concerned about precise prediction of gene start (which in a prokaryotic genome unambiguously defines the reading frame and stop codon, thus, the whole protein product), still remains more accurate in GeneMarks, which uses more elaborate HMM to specifically address this task.

关键词： prokoryotic gene prediction Markov model hidden Markov model forward-backward algorithm

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A sequential smoothing algorithm with linear computational cost

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BIOMETRIKA 2010年第2期97卷 447-464页

作者： Fearnhead, Paul Wyncoll, David Tawn, Jonathan Univ Lancaster Dept Math & Stat Lancaster LA1 4YF England

In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N-2) computational cost of most smoothers. The new method also overcomes some degeneracy problems in existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and by the analysis of an athletics dataset, that our new method also substantially outperforms the simple filter-smoother, the only other smoother with computational cost that is O(N).

关键词： Extreme value theory forward-backward algorithm Particle filtering Particle smoothing Two-filter formula

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