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.

An expectation-maximization algorithm for probabilistic reconstructions of full-length isoforms from splice graphs

Abstract: Reconstructing full-length transcript isoforms from sequence fragments (such as ESTs) is a major interest and challenge for bioinformatic analysis of pre-mRNA alternative splicing. This problem has been formulated as finding traversals across the splice graph, which is a directed acyclic graph (DAG) representation of gene structure and alternative splicing. In this manuscript we introduce a probabilistic formulation of the isoform reconstruction problem, and provide an expectation-maximization (EM) algorithm for its maximum likelihood solution. Using a series of simulated data and expressed sequences from real human genes, we demonstrate that our EM algorithm can correctly handle various situations of fragmentation and coupling in the input data. Our work establishes a general probabilistic framework for splice graph-based reconstructions of full-length isoforms.

A Bayesian approach to joint feature selection and classifier design

Abstract: This paper adopts a Bayesian approach to simultaneously learn both an optimal nonlinear classifier and a subset of predictor variables (or features) that are most relevant to the classification task. The approach uses heavy-tailed priors to promote sparsity in the utilization of both basis functions and features; these priors act as regularizers for the likelihood function that rewards good classification on the training data. We derive an expectation- maximization (EM) algorithm to efficiently compute a maximum a posteriori (MAP) point estimate of the various parameters. The algorithm is an extension of recent state-of-the-art sparse Bayesian classifiers, which in turn can be seen as Bayesian counterparts of support vector machines. Experimental comparisons using kernel classifiers demonstrate both parsimonious feature selection and excellent classification accuracy on a range of synthetic and benchmark data sets.

Segmentation in Ultrasonic B -Mode Images of Healthy Carotid Arteries Using Mixtures of Nakagami Distributions and Stochastic Optimization

Abstract: The goal of this work is to perform a segmentation of the intimamedia thickness (IMT) of carotid arteries in view of computing various dynamical properties of that tissue, such as the elasticity distribution (elastogram). The echogenicity of a region of interest comprising the intima-media layers, the lumen, and the adventitia in an ultrasonic B-mode image is modeled by a mixture of three Nakagami distributions. In a first step, we compute the maximum a posteriori estimator of the proposed model, using the expectation maximization (EM) algorithm. We then compute the optimal segmentation based on the estimated distributions as well as a statistical prior for disease-free IMT using a variant of the exploration/selection (ES) algorithm. Convergence of the ES algorithm to the optimal solution is assured asymptotically and is independent of the initial solution. In particular, our method is well suited to a semi-automatic context that requires minimal manual initialization. Tests of the proposed method on 30 sequences of ultrasonic B-mode images of presumably disease-free control subjects are reported. They suggest that the semi-automatic segmentations obtained by the proposed method are within the variability of the manual segmentations of two experts.

On estimation and prediction for spatial generalized linear mixed models.

Abstract: We use spatial generalized linear mixed models (GLMM) to model non-Gaussian spatial variables that are observed at sampling locations in a continuous area. In many applications, prediction of random effects in a spatial GLMM is of great practical interest. We show that the minimum mean-squared error (MMSE) prediction can be done in a linear fashion in spatial GLMMs analogous to linear kriging. We develop a Monte Carlo version of the EM gradient algorithm for maximum likelihood estimation of model parameters. A by-product of this approach is that it also produces the MMSE estimates for the realized random effects at the sampled sites. This method is illustrated through a simulation study and is also applied to a real data set on plant root diseases to obtain a map of disease severity that can facilitate the practice of precision agriculture.

Vector quantization based on Gaussian mixture models

Abstract: We model the underlying probability density function of vectors in a database as a Gaussian mixture (GM) model. The model is employed for high rate vector quantization analysis and for design of vector quantizers. It is shown that the high rate formulas accurately predict the performance of model-based quantizers. We propose a novel method for optimizing GM model parameters for high rate performance, and an extension to the EM algorithm for densities having bounded support is also presented. The methods are applied to quantization of LPC parameters in speech coding and we present new high rate analysis results for band-limited spectral distortion and outlier statistics. In practical terms, we find that an optimal single-stage VQ can operate at approximately 3 bits less than a state-of-the-art LSF-based 2-split VQ.