The emalgorithm is a widely applicable algorithm for modal estimation but often criticized for its slow convergence. A new hybrid accelerator named Apx-em is proposed for speeding up the convergence of emalgorithm, ...
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The emalgorithm is a widely applicable algorithm for modal estimation but often criticized for its slow convergence. A new hybrid accelerator named Apx-em is proposed for speeding up the convergence of emalgorithm, which is based on both Linearly Preconditioned Nonlinear Conjugate Gradient (PNCG) and px-em algorithm. The intuitive idea is that, each step of the px-em algorithm can be viewed approximately as a generalized gradient just like the emalgorithm, then the linearly PNCG method can be used to accelerate the emalgorithm. Essentially, this method is an adjustment of the Aemalgorithm, and it usually achieves a faster convergence rate than the Aemalgorithm by sacrificing a little simplicity. The convergence of the Apx-em algorithm, includes a global convergence result for this method under suitable conditions, is discussed. This method is illustrated for factor analysis and a random-effects model. (C) 2020 Elsevier B.V. All rights reserved.
This em review article focuses on parameter expansion, a simple technique introduced in the px-em algorithm to make em converge faster while maintaining its simplicity and stability. The primary objective concerns the...
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This em review article focuses on parameter expansion, a simple technique introduced in the px-em algorithm to make em converge faster while maintaining its simplicity and stability. The primary objective concerns the connection between parameter expansion and efficient inference. It reviews the statistical interpretation of the px-em algorithm, in terms of efficient inference via bias reduction, and further unfolds the px-em mystery by looking at px-em from different perspectives. In addition, it briefly discusses potential applications of parameter expansion to statistical inference and the broader impact of statistical thinking on understanding and developing other iterative optimization algorithms.
We develop optimal adaptive design of radar waveform polarizations for a target in compound-Gaussian clutter. We present maximum likelihood estimates of the target's scattering matrix and clutter parameters using ...
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We develop optimal adaptive design of radar waveform polarizations for a target in compound-Gaussian clutter. We present maximum likelihood estimates of the target's scattering matrix and clutter parameters using a parameter-expanded expectation-maximization (px-em) algorithm. We compute the Cramer-Rao bound (CRB) on the target's scattering matrix. To design the polarization, we propose an algorithm that minimizes a CRB function. We propose also suboptimal versions of this algorithm and illustrate the performance as well as compare our algorithm with numerical examples. (c) 2008 Elsevier B.V. All rights reserved.
A finite mixture model using the multivariate t distribution has been well recognized as a robust extension of Gaussian mixtures. This paper presents an efficient px-em algorithm for supervised learning of multivariat...
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Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms;these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Me...
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Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms;these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Metropolis algorithms can sometimes be slow. We examine solutions that involve reparameterization and over-parameterization. We begin with parameter expansion using working parameters, a strategy developed for the emalgorithm. This strategy can lead to algorithms that are much less susceptible to becoming stuck near zero values of the variance parameters than are more standard algorithms. Second, we consider a simple rotation of the regression coefficients based on an estimate of their posterior covariance matrix. This leads to a Gibbs algorithm based on updating the transformed parameters one at a time or a Metropolis algorithm with vector jumps;either of these algorithms can perform much better (in terms of total CPU time) than the two standard algorithms: one-at-a-time updating of untransformed parameters or vector updating using a linear regression at each step. We present an innovative evaluation of the algorithms in terms of how quickly they can get away from remote areas of parameter space, along with some more standard evaluation of computation and convergence speeds. We illustrate our methods with examples from our applied work. Our ultimate goal is to develop a fast and reliable method for fitting a hierarchical linear model as easily as one can now fit a nonhierarchical model, and to increase understanding of Gibbs samplers for hierarchical models in general.
Logistic random-effects models are often employed in the analysis of correlated binary data. However, fitting these models is challenging, since the marginal distribution of the response variables is analytically intr...
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Logistic random-effects models are often employed in the analysis of correlated binary data. However, fitting these models is challenging, since the marginal distribution of the response variables is analytically intractable. Often, the random effects are treated as missing data for constructing traditional data augmentation algorithms. We create a novel alternative data augmentation scheme that simplifies the likelihood-based inference for logistic random-effects models. We cast the random-effects model in a 'survival framework', where each binary response is the censoring indicator for a survival time that is treated as additional missing data. Under this augmentation framework, the conditional expectations are free of unknown regression parameters. Such a construction has a particular advantage that, in the case of discrete covariates, the score equations for regression parameters have analytical solutions. Consequently, one does not need to resort to a search algorithm in estimating the regression parameters. We further create a parameter expansion scheme for logistic random-effects models under this survival data augmentation framework. The proposed data augmentation is illustrated when the random-effects distribution follows a multivariate Gaussian and multivariate t-distribution. The performance of the method is assessed through simulation studies and a real data analysis.
A finite mixture model using the Student's t distribution has been recognized as a robust extension of normal mixtures. Recently, a mixture of skew normal distributions has been found to be effective in the treatm...
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A finite mixture model using the Student's t distribution has been recognized as a robust extension of normal mixtures. Recently, a mixture of skew normal distributions has been found to be effective in the treatment of heterogeneous data involving asymmetric behaviors across subclasses. In this article, we propose a robust mixture framework based on the skew t distribution to efficiently deal with heavy-tailedness, extra skewness and multimodality in a wide range of settings. Statistical mixture modeling based on normal, Student's t and skew normal distributions can be viewed as special cases of the skew t mixture model. We present analytically simple em-type algorithms for iteratively computing maximum likelihood estimates. The proposed methodology is illustrated by analyzing a real data example.
Generalized linear mixed models (GLMM) are useful in many longitudinal data analyses. In the presence of informative dropouts and missing covariates, however, standard complete-data methods may not be applicable. In t...
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Generalized linear mixed models (GLMM) are useful in many longitudinal data analyses. In the presence of informative dropouts and missing covariates, however, standard complete-data methods may not be applicable. In this article, we consider a likelihood method and an approximate method for GLMM with informative dropouts and missing covariates. The methods are implemented by Monte-Carlo emalgorithms combined with Gibbs sampler. The approximate method may lead to inconsistent estimators but is computationally more efficient than the likelihood method. The two methods are evaluated via a simulation study for longitudinal binary data, and appear to perform reasonably well. A dataset on mental distress is analyzed in details.
Nonlinear mixed-effects (NLME) models are popular in many longitudinal studies, including human immunodeficiency virus (HIV) viral dynamics, pharmacokinetic analyses, and studies of growth and decay. In practice, cova...
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Nonlinear mixed-effects (NLME) models are popular in many longitudinal studies, including human immunodeficiency virus (HIV) viral dynamics, pharmacokinetic analyses, and studies of growth and decay. In practice, covariates in these studies often contain missing data, and so standard complete-data methods are not directly applicable. In this article we propose Monte Carlo parameter-expanded (px)-emalgorithms for exact and approximate likelihood inferences for NLME models with missing covariates when the missing-data mechanism is ignorable. We allow arbitrary missing-data patterns and allow the covariates to be categorical, continuous, and mixed. The px-em algorithm maintains the simplicity and stability of the standard emalgorithm and may converge much faster than em. The approximate method is computationally more efficient and may be preferable to the exact method when the exact method exhibits convergence problems, such as slow convergence or nonconvergence. It becomes an exact method for linear mixed-effects models and certain NLME models with missing covariates. We also discuss several sampling methods and convergence of the Monte Carlo (px) emalgorithms. We illustrate the methods using a real data example from the study of HIV viral dynamics and compare the methods via a simulation study.
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