Open AccessJournal Article
A gentle tutorial of the em algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models
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In this paper, the authors describe the EM algorithm for finding the parameters of a mixture of Gaussian densities and a hidden Markov model (HMM) for both discrete and Gaussian mixture observation models.Abstract:
We describe the maximum-likelihood parameter estimation problem and how the ExpectationMaximization (EM) algorithm can be used for its solution. We first describe the abstract form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) finding the parameters of a hidden Markov model (HMM) (i.e., the Baum-Welch algorithm) for both discrete and Gaussian mixture observation models. We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical rigor.read more
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References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
The Nature of Statistical Learning Theory
TL;DR: Setting of the learning problem consistency of learning processes bounds on the rate of convergence ofLearning processes controlling the generalization ability of learning process constructing learning algorithms what is important in learning theory?
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TL;DR: Presenting a method for determining the necessary and sufficient conditions for consistency of learning process, the author covers function estimates from small data pools, applying these estimations to real-life problems, and much more.
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The Fractal Geometry of Nature
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.