Notes on methods based on maximum-likelihood estimation for learning the parameters of the mixture of Gaussians model

Authors:
Luis E. Ortiz;Leslie Kaelbling
Affiliations:
-;-
Venue:
Notes on methods based on maximum-likelihood estimation for learning the parameters of the mixture of Gaussians model
Year:
1999

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Abstract

In these notes, we present and review different methods based on maximum-likelihood estimation for learning the parameters of the mixture-of-Gaussians model. We describe a method based on the likelihood equations, traditional gradient-based methods (among them steepest ascent and gradient ascent), expectation-maximization (EM), conjugate gradient methods, and proposed accelerations of EM (among them Aitken acceleration or parameterized EM, and conjugate-gradient acceleration of EM). We describe all the methods in the context of the mixture-of-Gaussians model. We relate the methods presented through the generalized gradient-based formulation. None of the methods presented are theoretically dominant. We empirically analyze their performance on synthetic datasets and suggest cases in which particular methods perform better than others.