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Topic: Expectation-Maximization

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Encyclopedia: Expectation-maximization algorithm EM alternates between performing an expectation (E) step, which computes the expected value of the latent variables, and a maximization (M) step, which computes the maximum likelihood estimates of the parameters given the data and setting the latent variables to their expectation. In statistical computing, an expectation-maximization (EM) algorithm is an algorithm for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables. is the value that maximizes (M) the expectation (E) of the complete data log-likelihood with respect to the conditional distribution of the latent data under the previous parameter value. www.nationmaster.com /encyclopedia/Expectation_maximization-algorithm   (1442 words)

Expectation-Maximization Maximization-Step: Assume the distribution to be correct and maximize the likelihood of the model (cluster parameter) with respect to the data. Expectation-Step: Assume the model (cluster parameters) to be correct and find the most likely distribution of the data with respect to the model. xenia.media.mit.edu /~schoner/presentations/INI98/sld014.htm   (44 words)

MAP Estimation of Target Manoeuvre Sequence with the Expectation-Maximization Algorithm The expectation maximization (EM) algorithm is first applied, resulting in a multi-pass estimator of the MAP sequence of inputs. The expectation step for each pass involves computation of state estimates in a bank of Kalman smoothers tuned to the possible manoeuvre sequences. The maximization computation is efficiently implemented using the Viterbi algorithm. www.ewh.ieee.org /soc/aes/taes/aes382/3820367.htm   (324 words)

Mixture Estimation using the EM Algorithm -- from Mathematica Information Center This package uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. expectation maximization (EM), parameter estimation, maximum likelihood estimation, mixture distribution Here the missing data are assumed to be the identities of the observations originating from each of the two distributions contributing to the mixture. library.wolfram.com /infocenter/MathSource/427   (123 words)

Expectation Maximization The generalized EM (GEM) algorithm is the same except that instead of requiring maximization in Step 3 it only requires that the estimate be improved. In the second step, called the maximization step, we set theta and phi to their mode conditioned on the expected sufficient statistics. In the first step, called the expectation step, we compute the expected sufficient statistics as follows. www.cs.brown.edu /research/ai/dynamics/tutorial/Documents/ExpectationMaximization.html   (1211 words)

LatestVersion.doc The Expectation Maximization algorithm is the most frequently used technique for estimating class conditional probability density functions (PDF) in both univariate and multivariate cases [23]. The proposed algorithm uses expectation maximization to along with the fuzzy k-means algorithm to generate optimum clusters. Instead of assigning cases or observations to clusters to maximize the differences in means for continuous variables, the EM clustering algorithm computes probabilities of cluster memberships based on one or more probability distributions. www.cse.unr.edu /~sara/LatestVersion.doc   (2093 words)

Expectation-Maximization Algorithm A maximization technique occuring in the statistical analysis of probablistic functions of Markov chains. An inequality and associated maximization technique in statistical estimation for probalistic functions of Markov processes. www.info.ucl.ac.be /~pdupont/pdupont/bib/em.html   (86 words)

EM Algorithm In the E-step, conditioned on the observation and current estimate of the parameters, the expectation of a complete-data log-likelihood function is computed; in the M-step, the parameters are updated so that the expectation is maximized. The hope is that maximization of this lower bound might be easier than direct maximization of the log-likelihood. The basic idea of the algorithm is that at each point, a lower bound of the log-likelihood, which is provided by the expectation of the complete-data log-likelihood function (according to Jensen's inequality), is computed and maximized. www.physics.brown.edu /physics/userpages/students/Jigang_Wang/emalgorithm.htm   (401 words)

Expectation-Maximization Theory Section 3.3 covers the interpretion the EM algorithm as the maximization of two quantities: the entropy and the expectation of complete-data likelihood. The M-step maximizes a likelihood function that is refined in each iteration by the E-step. The next section explains the traditional approach to deriving the EM algorithm and proving its convergence property. www.informit.com /articles/article.asp?p=363730   (1610 words)

Tony Jebara We present the CEM (Conditional Expectation Maximization) algorithm as an extension of the EM (Expectation Maximization) algorithm to conditional density estimation under missing data. A bounding and maximization process is given to specifically optimize conditional likelihood instead of the usual joint likelihood. The final result is a CEM algorithm that mirrors the EM algorithm where both estimate a variational lower bound on their respective incomplete objective functions, and both generate the same standard M-steps over complete likelihood for direct maximization. www.cs.columbia.edu /~jebara/cem.html   (275 words)

Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography The maximum likelihood (ML) expectation maximization (EM) approach in emission tomography has been very popular in medical imaging for several years. The new method is a natural extension of the EM for maximizing likelihood with concave priors. www.osti.gov /energycitations/product.biblio.jsp?osti_id=37337   (172 words)

From EM to CEM In this chapter, we discuss the extension of the EM (Expectation Maximization) algorithm for joint density estimation to conditional density estimation and derive the resulting CEM (Conditional Expectation Maximization) algorithm. In joint density estimation, the tried and true EM (expectation maximization) algorithm proceeds by maximizing likelihood over a training set. The missing unknown data components are estimated via the E-step and then a far simpler maximization over the complete data, the M-step, is performed. www.cs.columbia.edu /~jebara/htmlpapers/ARL/node48.html   (355 words)

Expectation-maximization algorithm - Wikipedia, the free encyclopedia EM alternates between performing an expectation (E) step, which computes the expected value of the latent variables, and a maximization (M) step, which computes the maximum likelihood estimates of the parameters given the data and setting the latent variables to their expectation. In statistical computing, an expectation-maximization (EM) algorithm is an algorithm for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables. The Baum-Welch algorithm is an example of an EM algorithm applied to hidden Markov models. en.wikipedia.org /wiki/Expectation-maximization_algorithm   (778 words)

Scaling EM (Expectation Maximization) Clustering to Large Databases Scaling EM (Expectation Maximization) Clustering to Large Databases Practical statistical clustering algorithms typically center upon an iterative refinement optimization procedure to compute a locally optimal clustering solution that maximizes the fit to data. These algorithms typically require many database scans to converge, and within each scan they require the access to every record in the data table. www.research.microsoft.com /scripts/pubs/view.asp?TR_ID=MSR-TR-98-35   (252 words)

help with coding expectation maximization needed. thanks - GIDForums The expectation maximization algorithm basically consists of 2 parts: the expectation step and the maximization step. In my lexicon, the term Expectation Maximization refers to one possible approach to solving a large class of statistical problems. This is to enable a system to learn about the network structure through training data, which are in most real world cases incomplete; hence the need to estimate the values of the missing data. www.gidforums.com /t-3467.html   (1909 words)

RECEIVER OPERATING CHARACTERISTIC (ROC) LITERATURE RESEARCH Receiver operating characteristic (ROC) analysis of images reconstructed with iterative expectation maximization algorithms. Maximizing diagnostic information from the dexamethasone suppression test: An approach to criterion selection using receiver operating characteristic analysis. An estimator of the cutoff point maximizing sum of sensitivity and specificity. splweb.bwh.harvard.edu:8000 /pages/ppl/zou/roc.html   (4448 words)

Conditional Expectation Maximization Computing this Q function forms the CE-step in the Conditional Expectation Maximization algorithm and it results in a simplified M-step. Note the absence of the logarithm of a sum and the decoupled models. The Q function adopts this form in Equation 7. vismod.media.mit.edu /pub/tech-reports/TR-522/node3.html   (209 words)

Nonparametric expectation maximization population modeling of ganciclovir. The use of the nonparametric expectation maximization (NPEM2) program to estimate pharmacokinetic parameters of ganciclovir in a group of patients with human immunodeficiency virus (HIV) and cytomegalovirus (CMV) infection was evaluated. A 10-point data set per patient obtained over 8 hours was analyzed. Preston SL; Drusano GL; Department of Pharmacy Practice, Albany College of Pharmacy, NY; 12208, USA. www.aegis.com /aidsline/1996/dec/M96C0816.html   (518 words)

Imaging On-Line Store The method operates globally on the pixel points using expectation maximization for fitting the body and surface vectors in the case of one highlight reflection. In the case of multiple highlights it is shown that it is possible to relax the method by fitting one surface vector to multiple highlights. A weighting value may be useful for classification of body and surface reflections in combination with other methods. www.imaging.org /store/epub.cfm?abstrid=8562   (258 words)

Expectation-Maximization as lower bound maximization - Minka (ResearchIndex) The Expectation Maximization Algorithm - Frank Dellaert College Abstract: The Expectation-Maximization algorithm given by Dempster et al (1977) has enjoyed considerable popularity for solving MAP estimation problems. Expectation-Maximization as lower bound maximization - Minka (ResearchIndex) citeseer.ist.psu.edu /minka98expectationmaximization.html   (309 words)

USU RTPC Laser Spectroscopy Csaba Gyulai has been working on a parallel implementation of the expectation maximization algorithm for the analysis of spectroscopy data. Gyulai, C., S. Bialkowski, G. Stiles, and L. Powers, A comparison of three multi-platform message-passing interfaces on an expectation maximization algorithm, Proc. The work was carried out by Marcellus Harper. www.engineering.usu.edu /ece/research/rtpc/projects/rt/laser.html   (255 words)

A General Decomposition Theorem that Extends the Baum-Welch and Expectation-Maximization Paradigm to Rational Forms The well-known Baum-Welch and expectation maximization (EM) algorithms do not apply to rational functions and are therefore limited to the simpler maximum-likelihood form of such models. We consider the problem of maximizing certain positive rational functions of a form that includes statistical constructs such as conditional mixture densities and conditional hidden Markov models. It extends the central inequality of Baum-Welch/EM and associated high-level algorithms to the rational case, and reduces to the standard inequality and algorithms for simpler problems. www.pnylab.com /pny/papers/gbw/main.html   (188 words)

3.9 Expectation-Maximization (EM) The algorithm is similar to the K-means procedure in that a set of parameters are re-computed until a desired convergence value is achieved. Here is a sample execution of the EM algorithm on a data set of 1179 gamma-ray bursts taken from the MFBMFR 3B catalog with attribute values Log T90, Log HR321, and Log Fluence. One measure of cluster quality is the likelihood that the data came from the dataset determined by the clustering. grb.mnsu.edu /grbts/doc/manual/Expectation_Maximization_EM.html   (983 words)

Multigrid Expectation Maximization Algorithm for PET using Wavelet Processing The MGEM algorithm implemented the Expectation Maximization (EM) algorithm on a set of reconstruction grids with different resolutions. The optimal multigrid expectation maximization algorithm (MGEM), a maximum likelihood (ML) method, has been applied to the problem of image reconstruction in positron emission tomography (PET). The algorithm begins with a coarse grid and continues iterating and switching grid-levels until the finest grid-level is reached in order to recover the high frequency components at the required resolution. www.njit.edu /old/ECE/dhawan/petrecon.html   (179 words)

Expectation-Maximization Algorithm A maximization technique occuring in the statistical analysis of probablistic functions of Markov chains. An inequality and associated maximization technique in statistical estimation for probalistic functions of Markov processes. An introduction to the Baum and EM algorithms for maximum likelihood estimation. www.info.ucl.ac.be /~pdupont/pdupont/bib/em.html   (86 words)

Talk:Expectation-maximization algorithm - Wikipedia, the free encyclopedia Given that it is hard to pin down people's motivations for liking or disliking an algorithm, perhaps we should drop the sentence from the article. But, based on what I heard at machine learning conferences, EM was preferred due to convergence. en.wikipedia.org /wiki/Talk:Expectation-maximization_algorithm   (332 words)

Journal of the American Statistical Association: Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. (expectation maximization; supplemental expectation maximization)@ HighBeam Research Over the past dozen or so years, the expectation maximization (EM) algorithm (Dempster, Laird and Rubin 1977, henceforth DLR) has become a remarkably popular tool in applied statistics and a common topic in many publications in statistics, so common in fact that articles often refer to it without citing any publication for it. A principal reason for this popularity is that it relies on flexible computing environments to find maximum likelihood estimates... Using EM to Obtain Asymptotic Variance - Covariance Matrices: The SEM Algorithm highbeam.com /library/doc0.asp?DOCID=1G1:11740707&...   (232 words)

Using evolutionary Expectation Maximization to estimate indel rates -- Holmes 21 (10): 2294 -- Bioinformatics Using evolutionary Expectation Maximization to estimate indel rates Using evolutionary Expectation Maximization to estimate indel rates -- Holmes 21 (10): 2294 -- Bioinformatics Bioinformatics Advance Access originally published online on February 24, 2005 bioinformatics.oxfordjournals.org /cgi/content/abstract/21/10/2294?rss=1   (271 words)

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