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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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ReportDOI
Learning from Incomplete Data
TL;DR: A set of algorithms are described that handle clustering, classification, and function approximation from incomplete data in a principled and efficient manner that make two distinct appeals to the Expectation-Maximization principle.
Journal ArticleDOI
Asymptotic Analysis of Penalized Likelihood and Related Estimators
Dennis D. Cox,Finbarr O'Sullivan +1 more
TL;DR: In this paper, a general approach to the first order asymptotic analysis of penalized likelihood and related estimators is described, and the method gives expansions for the systematic and random error.
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On the Bernstein-von Mises Theorem with Infinite Dimensional Parameters
TL;DR: In this paper, the authors show that the posterior distribution of the parameter vector around the posterior mean of the posterior probability distribution of a variable is very close to the distribution around truth of the maximum likelihood estimate around truth.
Journal ArticleDOI
Hybrid Adaptive Splines
Zhen Luo,Grace Wahba +1 more
TL;DR: In this paper, an adaptive spline method for smoothing is proposed that combines features from both regression spline and smoothing spline approaches, which can be applied to many multivariate function estimation problems.
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Computation with infinite neural networks
TL;DR: For neural networks with a wide class of weight priors, it can be shown that in the limit of an infinite number of hidden units, the prior over functions tends to a gaussian process.