Expectation maximization

Several numerical procedures for EADF evaluation have also been proposed. Morrison and Ross [19] developed the so-called CAEDMON (Computed Adsorption Energy Distribution in the Monolayer) method. Adamson and Ling [20] proposed an iterative approximation that needs no a priori assumptions. Later, House and Jaycock [21] improved that method and proposed the so-called HILDA (Heterogeneity Investigation at Loughborough by a Distribution Analysis) algorithm. Stanley et al. [22,23] presented two regularization methods as well as the method of expectation maximalization. 

Assuming the distribution models are accurate and that they model all the possible behaviors in the data set, Bayes s theorem says that pup2, and p3 are the probabilities that the unknown sample is a member of class 1, 2, or 3, respectively. The distributions are modeled using multivariate Gaussian functions in a method known as expectation maximization. ... 

Fallin D, Schork NJ. Accuracy of haplotype frequency estimation for biallelic loci via the expectation-maximization algorithm for unphased diploid genotype data. Am J Hum Genet 2000 67 947-959. 

This algorithm is well-known under the name expectation maximization algorithm (EM) (McLachlan and Pee 2000). Since the parameters /xr Xj, and pj are already needed in the E-step for computing the likelihoods, these parameters have to be... 

The expected maximal difference between two results obtained by repeated application of the analytical procedure to an identical test sample in different laboratories. The measure for the reproducibility (A) is the standard deviation... 

Expectation-maximize (EM), 154, 194 Expert pattern recognition, 31 Expressivity, 314... 

The most widely used and most effective general technique for estimating the mixture model parameters is the expectation maximization (EM) algorithm. " It finds (possibly suboptimally) values of the parameters using an iterative refinement approach similar to that given above for the k-means relocation method. The basic EM method proceeds as follows ... 

J.-A. Conchello, J.G. McNally, Past regularization technique for expectation maximization alogorithm for optical sectioning microscopy. SPIE Proc. 2655, 199-208 (1996)... 

NPEM is a program for performing non-para-metric expectation maximization. 

The concentration profile of benzene is, as expected, maximal at the surface of the catalyst pellet. With increasing time of operation benzene concentration becomes more uniform through the pellet giving a nearly flat concentration profile when the time on stream is about 100 min. The profiles depart more slowly from the initial profile (at t=0) when the empirical kinetic model for benzene hydrogenation is used. 

The above formulation of the two first problems seems to contain a considerable contradiction How can we determine optimal parameters without knowing the optimal hidden sequence Fortunately the solution is already available from the standard HMM framework The parameter optimization is carried out by the Expectation Maximization (EM) algorithm that iteratively determines the optimal parameters 0 via maximizing the expectation... 

A method close to the IT2S procedure is the expectation-maximization-like (EM) method presented by Mentre and Geomeni (36), which can be viewed as an extension of the IT2S procedure when both random and fixed effects are included in the model and for heteroscedastic errors known to a proportionality coefficient. This algorithm is implemented with the software P-PHARM (37). 

The training problem determines the set of model parameters given above for an observed set of wavelet coefficients. In other words, one first obtains the wavelet coefficients for the time series data that we are interested in and then, the model parameters that best explain the observed data are found by using the maximum likelihood principle. The expectation maximization (EM) approach that jointly estimates the model parameters and the hidden state probabilities is used. This is essentially an upward and downward EM method, which is extended from the Baum-Welch method developed for the chain structure HMM [43, 286]. 

Moses, A. M., Chiang, D. Y., and Eisen, M. B. (2004) Phylogenetic motif detection by expectation-maximization on evolutionary mixtures. Pac. Symp. Biocomput. 324-335. 

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