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Recent developments in expectation‐maximization methods for analyzing complex data

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The expectation–maximization (EM) algorithm is highly popular in computational statistics because it possesses a number of desirable properties such as reliable global convergence, numerical stability, and simplicity of implementation. More complex data are now increasingly prevalent across many application areas in a wide scope of scientific fields. These data could exhibit a hierarchical or longitudinal structure and involve atypical and/or asymmetric observations. The application of the EM algorithm in the analysis of these complex data presents significant challenges to existing EM methods. It is because the models developed often lead to intractable expectation‐steps or complicated maximization‐steps in order to model the correlation between hierarchical data and/or the skewness of asymmetric observations. This paper discusses recent advanced developments in EM methods to overcome these barriers in handling complex problems. WIREs Comput Stat 2013, 5:415–431. doi: 10.1002/wics.1277 This article is categorized under: Statistical and Graphical Methods of Data Analysis > EM Algorithm Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods
Clustering solutions (clusters denoted by dots, circles, and crosses) obtained from different sets of initial values: (a) final likelihood = −5750.8; (b) final likelihood = −5860.4.
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Pairwise two‐dimensional contours of the fitted skew t mixture model. Reprinted with permission from Ref 8. Copyright 2009 IEEE.
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Clustering solutions using a mixture of linear mixed models (five clusters). (a) Cluster 1 (24 genes), (b) Cluster 2 (305 genes), (c) Cluster 3 (426 genes), (d) Cluster 4 (1511 genes), and (e) Cluster 5 (960 genes).
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Averaged expression profiles: Cluster 1 (dotted line, 24 genes); Cluster 2 (dashed line, 305 genes); Cluster 3 (dotted‐x line, 426 genes); Cluster 4 (dotted‐o line, 1511 genes); Cluster 5 (solid line, 960 genes).
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Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods
Statistical and Graphical Methods of Data Analysis > EM Algorithm

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