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Statistical trajectory of an approximate EM algorithm for probabilistic image processing

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2007年第37期40卷 11285-11300页

作者： Tanaka, Kazuyuki Titterington, D. M. Tohoku Univ Grad Sch Informat Sci Aoba Ku Sendai Miyagi 9808579 Japan Univ Glasgow Dept Stat Glasgow G12 8QQ Lanark Scotland

We calculate analytically a statistical average of trajectories of an approximate expectation-maximization ( EM) algorithm with generalized belief propagation ( GBP) and a Gaussian graphical model for the estimation of hyperparameters from observable data in probabilistic image processing. A statistical average with respect to observed data corresponds to a configuration average for the random-field Ising model in spin glass theory. In the present paper, hyperparameters which correspond to interactions and external fields of spin systems are estimated by an approximate EM algorithm. A practical algorithm is described for gray-level image restoration based on a Gaussian graphical model and GBP. The GBP approach corresponds to the cluster variation method in statistical mechanics. Our main result in the present paper is to obtain the statistical average of the trajectory in the approximate EM algorithm by using loopy belief propagation and GBP with respect to degraded images generated from a probability density function with true values of hyperparameters. The statistical average of the trajectory can be expressed in terms of recursion formulas derived from some analytical calculations.

关键词： GENERALIZED BELIEF PROPAGATION GRAPHICAL MODELS HYPERPARAMETER ESTIMATION FREE-ENERGY RESTORATION MECHANICS CORRECTNESS CODES restoration Belief propagation Approximate Free energy expectation-maximisation algorithm Mechanics cluster variation method Image processing Probability density function Graphical models Codes trajectory RECURSIVE FUNCTIONS

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BINARY CLASSIFICATION BY STOCHASTIC NEURAL NETS

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1995年第2期6卷 488-491页

作者： NADAS, A IBM Research Division IBM Thomas J. Watson Research Center Yorktown Heights NY USA

We classify points in R(d) (feature vectors) by functions related to feedforward artificial neural networks (ANN's). These functions, dubbed ''stochastic neural nets,'' arise in a natural way from probabilistic as well as statistical considerations. The probabilistic idea is to define a classifying bit locally by using the sign of a hidden state-dependent noisy linear function of the feature vector as a new;d + 1st coordinate of the vector. This d + 1-dimensional distribution is approximated by a mixture distribution. The statistical idea-is that the approximating mixtures, and hence the a posteriori class probability functions (stochastic neural nets) defined by them, can be conveniently trained either by maximum likelihood or by a Bayes criterion through the use of an appropriate expectation-Maximization (EM) algorithm.

关键词： Probability functions Eigenvector maximum likelihood Stochastic expectation-maximisation algorithm Neural network

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hsmm - An R package for analyzing hidden semi-Markov models

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2010年第3期54卷 611-619页

作者： Bulla, Jan Bulla, Ingo Nenadic, Oleg Victoria Univ Wellington Sch Math Stat & Comp Sci Wellington 6140 New Zealand Univ Gottingen Inst Mikrobiol & Genet Abt Bioinformat D-37077 Gottingen Germany Univ Gottingen Inst Stat & Okonometrie D-37073 Gottingen Germany

Hidden semi-Markov models are a generalization of the well-known hidden Markov model. They allow for a greater flexibility of sojourn time distributions, which implicitly follow a geometric distribution in the case of a hidden Markov chain. The aim of this paper is to describe hsmm, a new software package for the statistical computing environment R. This package allows for the simulation and maximum likelihood estimation of hidden semi-Markov models. The implemented expectation Maximization algorithm assumes that the time spent in the last visited state is subject to right-censoring. it is therefore not subject to the common limitation that the last visited state terminates at the last observation. Additionally, hsmm permits the user to make inferences about the underlying state sequence via the Viterbi algorithm and smoothing probabilities. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Generalization expectation-maximisation algorithm Countries (nations) Viterbi algorithm Geometric distribution Software packages maximum likelihood estimation Hidden Markov models Markov chain Statistical Computing

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BAYESIAN RECONSTRUCTIONS FROM EMISSION TOMOGRAPHY DATA USING A MODIFIED EM algorithm

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1990年第1期9卷 84-93页

作者： GREEN, PJ UNIV DURHAM DURHAM DH1 3HPENGLAND

A novel method of reconstruction from single-photon emission computerized tomography data is proposed. This method builds on the expectation-maximization (EM) approach to maximum likelihood reconstruction from emission tomography data, but aims instead at maximum posterior probability estimation, which takes account of prior belief about smoothness in the isotope concentration. A novel modification to the EM algorithm yields a practical method. The method is illustrated by an application to data from brain scans.

关键词： Photon emission expectation-maximisation algorithm single photon emission computed tomography Maximum a posteriori estimation Bayesian inference Smoothness emission tomography

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Iterative data detection and channel estimation for space-time block coded continuous phase modulation over flat fading channels

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IET COMMUNICATIONS 2014年第13期8卷 2298-2307页

作者： Wang, Wenwen Abeysekera, Saman S. Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639790 Singapore

The problem of iterative data detection and channel estimation for space-time block coded continuous phase modulation (CPM) signals over quasi-static flat fading channels is studied in this study. Firstly, the combination of space-time block code with CPM is not as straightforward as with linear modulation schemes, because of the requirement of phase continuity and the associated inherent memory of CPM. Therefore a novel block construction method is proposed to insert a tail sequence into each block for ensuring the phase continuity. Secondly, at the receiver the expectation-maximisation algorithm is applied to channel estimation and the estimated channel information is used to evaluate a posteriori probability for data detection. The channel estimation and data detection work iteratively. Simulation results show that the spectral efficiency of transmission is improved by the proposed block construction method and that the proposed iterative receiver outperforms its non-iterative counterpart significantly.

关键词： fading channels continuous phase modulation space-time block codes channel estimation radio receivers expectation-maximisation algorithm CPM signals iterative receiver spectral efficiency posteriori probability channel information expectation-maximisation algorithm block construction method associated inherent memory phase continuity linear modulation schemes quasistatic flat fading channels space-time block coded continuous phase modulation channel estimation iterative data detection

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Using missing data methods in genetic studies with missing mutation status

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STATISTICS IN MEDICINE 1999年第4期18卷 473-485页

作者： Leong, T Lipsitz, SR Ibrahim, JG Dana Farber Canc Inst Dept Biostat Sci Boston MA 02115 USA Harvard Univ Sch Publ Hlth Dept Biostat Boston MA 02115 USA

Because of current techniques of determining gene mutation, investigators are now interested in estimating the odds ratio between genetic status (mutation, no mutation) and an outcome variable such as disease cell type (A, B). In this paper we consider the mutation of the RAS genetic family. To determine if the genes have mutated, investigators look at five specific locations on the RAS gene. RAS mutated is a mutation in at least one of the five gene locations and RAS non-mutated is no mutation in any of the five locations. Owing to limited time and financial resources, one cannot obtain a complete genetic evaluation of all five locations on the gene for all patients. We propose the use of maximum likelihood (ML) with a 2(6) multinomial distribution formed by cross-classifying the binary mutation status at five locations by binary disease cell type. This ML method includes all patients regardless of completeness of data, treats the locations not evaluated as missing data, and uses the EM algorithm to estimate the odds ratio between genetic mutation status and the disease type. We compare the ML method to complete case estimates, and a method used by clinical investigators, which excludes patients with data on less than five locations who have no mutations on these sites. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： Genes ras Likelihood Functions Multiple Myeloma Mutation Codon 基因 RAS 似然函数多发性骨髓瘤突变 Codons Computer Programming Languages Mutation expectation-maximisation algorithm Likelihood Functions Multiple Myeloma missing data ras Oncogene Clinical Investigators outcome variable Odds Ratio

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CAUSAL INFERENCE FOR TIME-VARYING TREATMENTS IN LATENT MARKOV MODELS: AN APPLICATION TO THE EFFECTS OF REMITTANCES ON POVERTY DYNAMICS

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ANNALS OF APPLIED STATISTICS 2022年第3期16卷 1962-1985页

作者： Tullio, Federico Bartolucci, Francesco Bank Italy Directorate Gen Econ Stat & Res Rome Italy Univ Perugia Dept Econ Perugia Italy

To assess the effectiveness of remittances on the poverty level of recipient households, we propose a causal inference approach that may be applied with longitudinal data and time-varying treatments. The method relies on the integration of a propensity score based technique, the inverse propensity weighting, with a general latent Markov (LM) framework. It is particularly useful when the outcome of interest is a characteristic that is not directly observable, and the analysis is focused on: (i) clustering units in a finite number of classes according to this latent characteristic and (ii) modelling the evolution of this characteristic across time depending on the received treatment. Parameter estimation is based on a two-step procedure. First, individual propensity score weights are computed accounting for predetermined covariates. Then, a weighted version of the standard LM model likelihood, based on such weights, is maximised by means of an expectation-maximisation algorithm or, alternatively, adopting a stepwise procedure. Finite-sample properties of the proposed estimators are studied by simulation. The application is focused on the effect of remittances on the poverty status of Ugandan households, based on a longitudinal survey spanning the period 2009-2014, and where manifest variables are indicators of deprivation. We find that remittances reduce the probability of falling into poverty, whereas they exert no impact on the probability of moving out of poverty.

关键词： Causal inference expectation-maximisation algorithm potential outcomes weighted maximum likelihood

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A hierarchical zero-inflated log-normal model for skewed responses

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STATISTICAL METHODS IN MEDICAL RESEARCH 2011年第3期20卷 175-189页

作者： Li, Ning Elashoff, David A. Robbins, Wendie A. Xun, Lin Univ Florida Dept Epidemiol & Biostat Coll Publ Hlth & Hlth Profess Gainesville FL 32610 USA Univ Calif Los Angeles Sch Publ Hlth Dept Biostat Los Angeles CA 90024 USA Univ Calif Los Angeles Sch Nursing Los Angeles CA 90024 USA

Although considerable attention has been given to zero-inflated count data, research on zero-inflated log-normal data is limited. In this article, we consider a study to examine human sperm cell DNA damage obtained from single-cell electrophoresis (COMET assay) experiment in which the outcome measures present a typical example of log-normal data with excess zeros. The problem is further complicated by the fact that each study subject has multiple outcomes at each of up to three visits separated by six-week intervals. Previous methods for zero-inflated log-normal data are based on either simple experimental designs, where comparison of means of zero-inflated log-normal data across different experiment groups is of primary interest, or longitudinal measurements, where only one observation is available for each subject at each visit. Their methods cannot be applied when multiple observations per visit are possible and both inter- and intra-subject variations are present. Our zero-inflated model extends the previous methods by incorporating a hierarchical structure using latent random variables to take into account both inter- and intra-subject variations in zero-inflated log-normal data. An EM algorithm has been developed to obtain the Maximum likelihood estimates of the parameters and their standard errors can be estimated by parametric bootstrap. The model is illustrated using the COMET assay data.

关键词： expectation-maximisation algorithm Spermatozoa maximum likelihood estimation Comet Assay Outcome Measures Hierarchical maximum likelihood

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A spatial Markovian framework for estimating regional and local dynamics of annual plants with dormancy

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THEORETICAL POPULATION BIOLOGY 2019年 127卷 120-132页

作者： Le Coz, Sebastian Cheptou, Pierre-Olivier Peyrard, Nathalie INRA UR 875 MIAT Chemin Borde Rouge F-31326 Castanet Tolosan France Univ Paul Valery Montpellier Univ Montpellier CNRS CEFE UMR 5175EPHE 1919Route Mende F-34293 Montpellier 05 France

Many species have a dormant stage in their life cycle, including seeds for plants. The dormancy stage influences the species dynamics but is often undetectable. One way to include dormancy is to model it as a hidden dynamical state within a Markovian framework. Models within this framework have already been proposed but with different limitations: only presence/absence observations are modelled, the dormancy stage is limited to one year, or colonisation from neighbouring patches is not taken into account. We propose a hidden Markov model that describes the local and regional dynamics of a species that can undergo dormancy with a potentially infinite dormancy time. Populations are modelled with abundance classes. Our model considers the colonisation process as the indistinguishable influence of neighbour non-dormant population states on a dormant population state in a patch. It would be expected that parameter estimation, hidden state estimation and prediction of the next non-dormant populations would have an exponential computational time in terms of the number of patches. However, we demonstrate that estimation, hidden state estimation and prediction are all achievable in a linear computational time. Numerical experiments on simulated data show that the state of dormant populations can easily be retrieved, as well as the state of future non-dormant populations. Our framework provides a simple and efficient tool that could be further used to analyse and compare annual plants dynamics like weed species survival strategies in crop fields. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Metapopulation Seed bank Hidden life stage Colonisation Prediction expectation-maximisation algorithm

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ON THE APPLICATION OF HIDDEN MARKOV-MODELS FOR ENHANCING NOISY SPEECH

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IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING 1989年第12期37卷 1846-1856页

作者： EPHRAIM, Y MALAH, D JUANG, BH AT&T BELL LABS DEPT SIGNAL PROC MURRAY HILL NJ 07974 USA

A maximum-a-posteriori approach for enhancing speech signals which have been degraded by statistically independent additive noise is proposed. The approach is based on statistical modeling of the clean speech signal and the noise process using long training sequences from the two processes. Hidden Markov models (HMMs) with mixtures of Gaussian autoregressive (AR) output probability distributions (PDs) are used to model the clean speech signal. The model for the noise process depends on its nature. The parameter set of the HMM model is estimated using the Baum or the EM (estimation-maximization) algorithm. The noisy speech is enhanced by reestimating the clean speech waveform using the EM algorithm. Efficient approximations of the training and enhancement procedures are examined. This results in the segmental k-means approach for hidden Markov modeling, in which the state sequence and the parameter set of the model are alternately estimated. Similarly, the enhancement is done by alternate estimation of the state and observation sequences. An approximate improvement of 4.0-6.0 dB in signal-to-noise ratio (SNR) is achieved at 10-dB input SNR.

关键词： expectation-maximisation algorithm statistical models (nuclear) Voice Signal Hidden Markov models Speech State estimation

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