Expectation-maximization algorithm

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... 

A special feature of the analysis of de Ligny et al. is that they have used an expectation maximization algorithm for handling missing data (see Chapter 6). Using the calculated model parameters, it is possible to provide predictions of the missing values. Moreover, error variances of these predictions are provided based on local linearizations of the model around the parameters. 

Hua, J., et aL (2007). SNiPer-HD Improved genotype ealling accuracy by an expectation-maximization algorithm for high-density SNP arrays. Bioinformatics, 23 57 63. 

Expectation-Maximization algorithm is the most suitable. Since the Expectation-Maximization algorithm uses the distribution calculated with the Twomey algorithm as initial values and optimizes it iteratively, the Expectation-Maximization distribution is expected to be more suitable. 

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. 

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 ... 

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). 

Lawrence, C. E., and Reilly, A. A. (1990) An expectation maximization (EM) algorithm for the identification and characterization of common sites in unaligned biopolymer sequences. Proteins 7, 41-51. 

Another method is Latent Semantic Analysis. This method creates a statistical word-usage model that permits comparisons of semantic similarity between pieces of textual information [3637]. An improved version is Probabilistic Latent Semantic Analysis (PLSA) [38]. This method explicitly models document topics. The Expectation Maximization [39] algorithm is then used to lit the model given a set of documents. Each document is defined in terms of a combination of topics based on the model-fitted conditional probabilities of word occurrences in each topic class. 

Population pharmacokinetics offered as a feature of a broader PK/PD application within an Enterprise (end-to-end, LIMS to report) solution population approach uses a parametric expectation-maximization (EM) algorithm to compute maximum likelihood estimates... 

Certain probabilistic models have a special structure in that there is missing data. If the missing data were not present, then optimization would be easy. For such problems, what is recommended is an algorithm known as the expectation-maximization (EM) algorithm. An excellent review of the algorithm can be found... 

Maximum-likelihood haplotype frequencies are estimated from the observed data using an expectation-maximization (EM) algorithm and standardized linkage disequilibrium values (D = D/D ax). and D values are shown as graphic maps (http // www.weU.ox.ac.uk/asthma/GOLD/docs/ldmax.html) and HAPLOVIEW program. 

The proposed approach is based on the computation of mixture models using the Expectation-Maximization (EM) algorithm (Dempster, Laird, Rubin 1977). Beside, side information is considered according to (Shental, Bar-Hillel, Hertz, Weinshall 2003). 

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