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A generalized em algorithm FOR 3-D BAYESIAN RECONSTRUCTION FROM POISSON DATA USING GIBBS PRIORS

IEEE TRANSACTIONS ON MEDICAL IMAGING 1989年第2期8卷 194-202页

作者： HEBERT, T LEAHY, R Signal and Image Processing Institute. Department of Electrical Engineering-Systems University of Southern California Los Angeles CA USA

A generalized expectation-maximization (Gem) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model. For the M-step of the algorithm, a form of coordinate gradient ascent is derived. The algorithm reduces to the em maximum-likelihood algorithm as the Markov random-field prior tends towards a uniform distribution. Three different Gibbs function priors are examined. Reconstructions of 3-D images obtained from the Poisson model of single-photon-emission computed tomography are presented.

关键词： Three-Dimensional Images expectation-maximisation algorithm Markov algorithms Sim\'eon Denis Poisson generalized em algorithm Bayesian inference single photon emission computed tomography Gibbs function

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Efficient sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2025年 207卷

作者： Mclain, Alexander C. Zgodic, Anja Bondell, Howard Univ South Carolina Dept Epidemiol & Biostat 915 Greene St Columbia SC 29208 USA Univ Melbourne Sch Math & Stat 813 Swanston St Parkville Vic 3052 Australia

Bayesian variable selection methods are powerful techniques for fitting sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model parameters. A computationally efficient and powerful Bayesian approach is presented for sparse high-dimensional linear regression, requiring only minimal prior assumptions on parameters through plug-in empirical Bayes estimates of hyperparameters. The method employs a Parameter-Expanded Expectation-Conditional-Maximization (PX-ECM) algorithm to estimate maximum a posteriori (MAP) values of parameters via computationally efficient coordinate-wise optimization. The popular two-group approach to multiple testing motivates the E-step, resulting in a PaRtitiOned empirical Bayes Ecm (PROBE) algorithm for sparse high-dimensional linear regression. Both one-at-a-time and all-at-once optimization can be used to complete PROBE. Extensive simulation studies and analyses of cancer cell drug responses are conducted to compare PROBE's empirical properties with those of related methods. Implementation is available through the R package probe.

关键词： Approximate Bayesian computation generalized em algorithm High-dimensional linear regression Sparsity Variable selection

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A nonlinear quantile regression for accelerated destructive degradation testing data

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IISE TRANSACTIONS 2025年第6期57卷 621-638页

作者： Bae, Suk Joo Lim, Munwon Hanyang Univ Dept Ind Engn Seoul South Korea

Traditional regression approaches to Accelerated Destructive Degradation test (ADDT) data have modeled the mean curve as being representative. However, maximum likelihood estimates of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear Quantile Regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the tau th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

关键词： Accelerated destructive degradation test asymmetric Laplace distribution bootstrap estimator generalized em algorithm order statistic estimator

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Fitting the Erlang mixture model to data via a Gem-CMM algorithm

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHemATICS 2018年 343卷 189-205页

作者： Gui, Wenyong Huang, Rongtan Lin, X. Sheldon Xiamen Univ Sch Math Sci Xiamen Peoples R China Univ Toronto Dept Stat Sci Toronto ON M5S 3G3 Canada

The Erlang mixture model with common scale parameter is flexible and analytically tractable. As such, it is a useful model to fit insurance loss data and to calculate quantities of interest for insurance risk management. In this paper, we propose a generalized expectation-maximization (Gem) algorithm along with a clusterized method of moments (CMM) to estimate the model parameters. The Gem algorithm not only estimates the mixing weights and scale parameter of the model but also estimates the shape parameters of the model using a local search method. The CMM method enables to produce quality initial estimates for the Gem algorithm. As a result, the proposed approach provides an efficient algorithm that can fit the model to the body and the tail of truncated and censored loss data well and converges fast. We examine the performance of the proposed approach through several simulation studies and apply it to fit the Erlang mixture model to two real loss data sets. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Erlang mixture model Insurance loss data generalized em algorithm Clusterized method of moments Local search method

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Quantile Regression via the em algorithm

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2014年第10期43卷 2162-2172页

作者： Zhou, Ying-Hui Ni, Zhong-Xin Li, Yong Shanghai Univ Sch Econ Shanghai 200444 Peoples R China Renmin Univ Hanqing Adv Inst Econ & Finance Beijing 100872 Peoples R China

The three-parameter asymmetric Laplace distribution (ALD) has received increasing attention in the field of quantile regression due to an important feature between its location and asymmetric parameters. On the basis of the representation of the ALD as a normal-variance-mean mixture with an exponential mixing distribution, this article develops em and generalized em algorithms, respectively, for computing regression quantiles of linear and nonlinear regression models. It is interesting to show that the proposed em algorithm and the MM (Majorization-Minimization) algorithm for quantile regressions are really the same in terms of computation, since the updating formula of them are the same. This provides a good example that connects the em and MM algorithms. Simulation studies show that the em algorithm can successfully recover the true parameters in quantile regressions.

关键词： Normal-variance-mean mixture. Asymmetric Laplace distribution generalized inverse Gaussian distribution MM algorithm generalized em algorithm

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Analysis of structural equation models with censored or truncated data via em algorithm

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1998年第1期27卷 33-46页

作者： Tang, ML Lee, SY Chinese Univ Hong Kong Dept Stat Shatin NT Hong Kong

In this article, we delineate the analysis of structural equation models with censored data or truncated data with the number of unmeasured subjects under the framework of the generalized censoring mechanism (GCM), one of the most popular non-ignorable missing mechanisms. An em algorithm for maximum-likelihood estimation in structural equation models with censored data will be presented. By reformulating the censored-data problem into non-ignorable missing-data problem, the maximization procedure is shown to be simplified. A simulated data set will be used as an illustrative example. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： structural equation models non-ignorable missing mechanism generalized censoring mechanism (GCM) maximum-likelihood estimation generalized em algorithm censored data truncated data

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Robust global identification of linear parameter varying systems with generalised expectation-maximisation algorithm

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IET CONTROL THEORY AND APPLICATIONS 2015年第7期9卷 1103-1110页

作者： Yang, Xianqiang Lu, Yaojie Yan, Zhibin Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin 150080 Heilongjiang Peoples R China Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2G6 Canada Harbin Inst Technol Nat Sci Res Ctr Harbin 150080 Heilongjiang Peoples R China

In this study, a robust approach to global identification of linear parameter varying (LPV) systems in an input-output setting is proposed. In practice, the industrial process data are often contaminated with outliers. In order to handle outliers in process modelling, the robust LPV modelling problem is formulated and solved in the scheme of generalised expectation-maximisation (Gem) algorithm. The measurement noise is taken to follow the Student's t-distribution instead of using the conventional Gaussian distribution, in this algorithm. The extent of robustness of the proposed approach is adaptively adjusted by optimising the degrees of freedom parameter of the Student's t-distribution iteratively through the maximisation step of the Gem algorithm. The numerical example is provided to demonstrate the effectiveness of the proposed approach.

关键词： expectation-maximisation algorithm Degree of freedom outliers linear parameter varying system generalized em algorithm Student\'s t-distribution Gaussian distribution Robustness Noise measurement

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Bayesian image reconstruction in SPECT using higher order mechanical models as priors

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IEEE TRANSACTIONS ON MEDICAL IMAGING 1995年第4期14卷 669-680页

作者： Lee, SJ Rangarajan, A Gindi, G SUNY STONY BROOK DEPT ELECT ENGN STONY BROOK NY 11794 USA YALE UNIV DEPT COMP SCI NEW HAVEN CT 06520 USA SUNY STONY BROOK DEPT RADIOL STONY BROOK NY 11794 USA

While the ML-em algorithm for reconstruction for emission tomography is unstable due to the ill-posed nature of the problem. Bayesian reconstruction methods overcome this instability by introducing prior information, often in the form of a spatial smoothness regularizer. More elaborate forms of smoothness constraints may be used to extend the role of the prior beyond that of a stabilizer in order to capture actual spatial information about the object. Previously proposed forms of such prior distributions were based on the assumption of a piecewise constant source distribution. Here, we propose an extension to a piecewise linear model-the weak plate-which is more expressive than the piecewise constant model. The weak plate prior not only preserves edges but also allows for piecewise ramplike regions in the reconstruction. Indeed, for our application in SPECT, such ramplike regions are observed in ground-truth source distributions in the form of primate autoradiographs of rCBF radionuclides. To incorporate the weak plate prior in a MAP approach, we model the prior as a Gibbs distribution and use a Gem formulation for the optimization. We compare quantitative performance of the ML-em algorithm, a Gem algorithm with a prior favoring piecewise constant regions, and a Gem algorithm with our weak plate prior. Pointwise and regional bias and variance of ensemble image reconstructions are used as indications of image quality. Our results show that the weak plate and membrane priors exhibit improved bias and variance relative to ML-em techniques.

关键词： emission tomography Piecewise expectation-maximisation algorithm image reconstruction generalized em algorithm MECHANICAL MODEL single photon emission computed tomography

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Kernel eigenvoice speaker adaptation

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IEEE TRANSACTIONS ON SPEECH AND AUDIO PROCESSING 2005年第5期13卷 984-992页

作者： Mak, B Kwok, JT Ho, S Hong Kong Univ Sci & Technol Dept Comp Sci Hong Kong Hong Kong Peoples R China

Eigenvoice-based methods have been shown to be effective for fast speaker adaptation when only a small amount of adaptation data, say, less than 10 s, is available. At the heart of the method is principal component analysis (PCA) employed to find the most important eigenvoices. In this paper, we postulate that nonlinear PCA using kernel methods may be even more effective. The eigenvoices thus derived will be called kernel eigenvoices (KEV), and we will call our new adaptation method kernel eigenvoice speaker adaptation. However, unlike the standard eigenvoice (EV) method, an adapted speaker model found by the kernel eigenvoice method resides in the high-dimensional kernel-induced feature space, which, in general, cannot be mapped back to an exact preimage in the input speaker supervector space. Consequently, it is not clear how to obtain the constituent Gaussians of the adapted model that are needed for the computation of state observation likelihoods during the estimation of eigenvoice weights and subsequent decoding. Our solution is the use of composite kernels in such a way that state observation likelihoods can be computed using only kernel functions without the need of a speaker-adapted model in the input supervector space. In this paper, we investigate two different composite kernels for KEV adaptation: direct sum kernel and tensor product kernel. In an evaluation on the TIDIGITS task, it is found that KEV speaker adaptation using both forms of coma posite Gaussian kernels are equally effective, and they outperform a speaker-independent model and adapted models found by EV, MAP, or MLLR adaptation using 2.1 and 4.1 s of speech. For example, with 2.1 s of adaptation data, KEV adaptation outperforms the speaker-independent model by 27.5%, whereas EV, MAP, or MLLR adaptation are not effective at all.

关键词： composite kernels eigenvoice speaker adaptation generalized em algorithm kernel eigenvoice speaker adaptation kernel principal component analysis

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l₁-penalization for mixture regression models

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TEST 2010年第2期19卷 209-256页

作者： Staedler, Nicolas Buehlmann, Peter van de Geer, Sara ETH Seminar Stat CH-8092 Zurich Switzerland

We consider a finite mixture of regressions (FMR) model for high-dimensional inhomogeneous data where the number of covariates may be much larger than sample size. We propose an l(1)-penalized maximum likelihood estimator in an appropriate parameterization. This kind of estimation belongs to a class of problems where optimization and theory for non-convex functions is needed. This distinguishes itself very clearly from high-dimensional estimation with convex loss-or objective functions as, for example, with the Lasso in linear or generalized linear models. Mixture models represent a prime and important example where non-convexity arises. For FMR models, we develop an efficient em algorithm for numerical optimization with provable convergence properties. Our penalized estimator is numerically better posed (e.g., boundedness of the criterion function) than unpenalized maximum likelihood estimation, and it allows for effective statistical regularization including variable selection. We also present some asymptotic theory and oracle inequalities: due to non-convexity of the negative log-likelihood function, different mathematical arguments are needed than for problems with convex losses. Finally, we apply the new method to both simulated and real data.

关键词： Adaptive Lasso Finite mixture models generalized em algorithm High-dimensional estimation Lasso Oracle inequality

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