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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
A Predictive Approach to Model Selection
Seymour Geisser,William F. Eddy +1 more
TL;DR: In this article, a synthesis of Bayesian and sample-reuse approaches to the problem of high structure model selection geared to prediction is presented. But this approach is not suitable for high-dimensional models.
Journal ArticleDOI
On convergence properties of the em algorithm for gaussian mixtures
Lei Xu,Michael I. Jordan +1 more
TL;DR: The mathematical connection between the Expectation-Maximization (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite gaussian mixtures is built up and an explicit expression for the matrix is provided.
Proceedings Article
Ridge Regression Learning Algorithm in Dual Variables
TL;DR: A regression estimation algorithm which is a combination of the dual version of Ridge Regression is applied to the ANOVA enhancement of the infinitenode splines and the use of kernel functions, as used in Support Vector methods is introduced.