Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.

A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography

Abstract: The maximum likelihood (ML) approach to estimating the radioactive distribution in the body cross section has become very popular among researchers in emission computed tomography (ECT) since it has been shown to provide very good images compared to those produced with the conventional filtered backprojection (FBP) algorithm. The expectation maximization (EM) algorithm is an often-used iterative approach for maximizing the Poisson likelihood in ECT because of its attractive theoretical and practical properties. Its major disadvantage is that, due to its slow rate of convergence, a large amount of computation is often required to achieve an acceptable image. Here, the authors present a row-action maximum likelihood algorithm (RAMLA) as an alternative to the EM algorithm for maximizing the Poisson likelihood in ECT. The authors deduce the convergence properties of this algorithm and demonstrate by way of computer simulations that the early iterates of RAMLA increase the Poisson likelihood in ECT at an order of magnitude faster that the standard EM algorithm. Specifically, the authors show that, from the point of view of measuring total radionuclide uptake in simulated brain phantoms, iterations 1, 2, 3, and 4 of RAMLA perform at least as well as iterations 45, 60, 70, and 80, respectively, of EM. Moreover, the authors show that iterations 1, 2, 3, and 4 of RAMLA achieve comparable likelihood values as iterations 45, 60, 70, and 80, respectively, of EM. The authors also present a modified version of a recent fast ordered subsets EM (OS-EM) algorithm and show that RAMLA is a special case of this modified OS-EM. Furthermore, the authors show that their modification converges to a ML solution whereas the standard OS-EM does not.

Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering

Abstract: Normal mixture models are widely used for statistical modeling of data, including cluster analysis. However maximum likelihood estimation (MLE) for normal mixtures using the EM algorithm may fail as the result of singularities or degeneracies. To avoid this, we propose replacing the MLE by a maximum a posteriori (MAP) estimator, also found by the EM algorithm. For choosing the number of components and the model parameterization, we propose a modified version of BIC, where the likelihood is evaluated at the MAP instead of the MLE. We use a highly dispersed proper conjugate prior, containing a small fraction of one observation's worth of information. The resulting method avoids degeneracies and singularities, but when these are not present it gives similar results to the standard method using MLE, EM and BIC.

Smoothing spline models for the analysis of nested and crossed samples of curves

Abstract: We introduce a class of models for an additive decomposition of groups of curves stratified by crossed and nested factors, generalizing smoothing splines to such samples by associating them with a corresponding mixed-effects model. The models are also useful for imputation of missing data and exploratory analysis of variance. We prove that the best linear unbiased predictors (BLUPs) from the extended mixed-effects model correspond to solutions of a generalized penalized regression where smoothing parameters are directly related to variance components, and we show that these solutions are natural cubic splines. The model parameters are estimated using a highly efficient implementation of the EM algorithm for restricted maximum likelihood (REML) estimation based on a preliminary eigenvector decomposition. Variability of computed estimates can be assessed with asymptotic techniques or with a novel hierarchical bootstrap resampling scheme for nested mixed-effects models. Our methods are applied to me...