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About 10,000 papers for “expectation-maximization algorithm”

Expectation-Maximization Algorithm

Jaroslav Vichr · Digital Repository (National Repository of Grey Literature) · 2013

EM (Expectation-Maximization) algorithm is an iterative method for finding maximum likelihood estimates in cases, when either complete data include missing values or assuming the existence of additional unobserved data points can lead to more simple formulation of the model. Each of its iterations consists of two parts. During the E step (expectation) we calculate the expected value of the log-likelihood function of the complete data, with respect to the observed data and the current estimate of the parameter. The M step (maximization) then finds new estimate, which will maximize the function obtained in the previous step and which will be used in the next iteration in step E. EM algorithm has important use in e.g. price and manage risk of the portfolio.

Cited by 0

Expectation Maximization Algorithm

Isobel Claire Gormley, Thomas Brendan Murphy · Encyclopedia of Statistics in Quality and Reliability · 2007

Abstract The expectation maximization (EM) algorithm is a powerful tool for finding maximum‐likelihood estimates in problems where the data are incomplete. Missing data may be an intrinsic feature of the problem or may be artificially imputed to ease estimation. The EM algorithm is an iterative algorithm that consists of two steps—an expectation step (E‐step) and a maximization step (M‐step). The output is a sequence of parameter estimates that converge to a maximum‐likelihood estimate. The implementation of the EM algorithm is illustrated using a finite mixture of exponential densities.

Cited by 75

Expectation maximization algorithm

Kechris, Katherina J, Zwet, Erik Van, Bickel, Peter J et al. · Figshare · 2011

<b>Copyright information:</b>Taken from "Detecting DNA regulatory motifs by incorporating positional trends in information content"Genome Biology 2004;5(7):R50-R50.Published online 24 Jun 2004PMCID:PMC463320.Copyright © 2004 Kechris et al.; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL. Differences between the fixed and variable change point model are labeled (F) and (V) respectively.

Cited by 0Open access

Expectation maximization algorithm

Kechris, Katherina J, Zwet, Erik Van, Bickel, Peter J et al. · Figshare · 2011

<b>Copyright information:</b>Taken from "Detecting DNA regulatory motifs by incorporating positional trends in information content"Genome Biology 2004;5(7):R50-R50.Published online 24 Jun 2004PMCID:PMC463320.Copyright © 2004 Kechris et al.; licensee BioMed Central Ltd. This is an Open Access article: verbatim copying and redistribution of this article are permitted in all media for any purpose, provided this notice is preserved along with the article's original URL. Differences between the fixed and variable change point model are labeled (F) and (V) respectively.

Cited by 0Open access

The Expectation Maximization Algorithm

Frank Dellaert College, Frank Dellaert · 2002

This note represents my attempt at explaining the EM algorithm (Hartley, 1958; Dempster et al., 1977; McLachlan and Krishnan, 1997). This is just a slight variation on Tom Minka&amp;apos;s tutorial (Minka, 1998), perhaps a little easier (or perhaps not). It includes a graphical example to provide some intuition. 1 Intuitive Explanation of EM EM is an iterative optimization method to estimate some unknown parameters #, given measurement data U. However, we are not given some &amp;quot;hidden&amp;quot; nuisance variables J, which need to be integrated out. In particular, we want to maximize the posterior probability of the parameters # given the data U, marginalizing over J: P (#, J|U) (1) The intuition behind EM is an old one: alternate between estimating the unknowns # and the hidden variables J. This idea has been around for a long time. However, instead of finding the best J # J given an estimate # at each iteration, EM computes a distribution over the space . One of the earliest papers on EM is (Hartley, 1958), but the seminal reference that formalized EM and provided a proof of convergence is the &amp;quot;DLR&amp;quot; paper by Dempster, Laird, and Rubin (Dempster et al., 1977). A recent book devoted entirely to EM and applications is (McLachlan and Krishnan, 1997), whereas (Tanner, 1996) is another popular and very useful reference. One of the most insightful explanations of EM, that provides a deeper understanding of its operation than the intuition of alternating between variables, is in terms of lowerbound maximization (Neal and Hinton, 1998; Minka, 1998). In this derivation, the E-step can be interpreted as constructing a local lower-bound to the posterior distribution, whereas the M-step optimizes the bound, thereby improving the estimate for the unknowns. This is demonstrated below for a s...

Cited by 0

The Expectation Maximization Algorithm

Dellaert, Frank · SMARTech Repository (Georgia Institute of Technology) · 2004

This note represents my attempt at explaining the EM algorithm. This is just a slight variation on Tom Minka's tutorial, perhaps a little easier (or perhaps not). It includes a graphical example to provide some intuition.

Cited by 64

The expectation-maximization algorithm

Todd K. Moon · IEEE Signal Processing Magazine · 1996

A common task in signal processing is the estimation of the parameters of a probability distribution function. Perhaps the most frequently encountered estimation problem is the estimation of the mean of a signal in noise. In many parameter estimation problems the situation is more complicated because direct access to the data necessary to estimate the parameters is impossible, or some of the data are missing. Such difficulties arise when an outcome is a result of an accumulation of simpler outcomes, or when outcomes are clumped together, for example, in a binning or histogram operation. There may also be data dropouts or clustering in such a way that the number of underlying data points is unknown (censoring and/or truncation). The EM (expectation-maximization) algorithm is ideally suited to problems of this sort, in that it produces maximum-likelihood (ML) estimates of parameters when there is a many-to-one mapping from an underlying distribution to the distribution governing the observation. The EM algorithm is presented at a level suitable for signal processing practitioners who have had some exposure to estimation theory.

Cited by 3,138

Quantum Expectation-Maximization Algorithm

Miyahara, Hideyuki, Aihara, Kazuyuki, Lechner, Wolfgang · arXiv (Cornell University) · 2019

Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the k-means algorithm has been proposed by Kerenidis, Landman, Luongo and Prakash. Based on their work, we propose a quantum expectation-maximization (EM) algorithm for Gaussian mixture models (GMMs). The robustness and quantum speedup of the algorithm is demonstrated. We also show numerically the advantage of GMM over k-means for non-trivial cluster data.

Cited by 0Open access