Robust estimation of Gaussian mixtures by $l_1$ penalization: an experimental study

Details Robust estimation of Gaussian mixtures by $l_1$ penalization: an experimental study Robust estimation of Gaussian mixtures by $l_1$ penalization: an experimental study

2009-01-29

arxiv.org/abs/0901.4752v1

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Many experiments in medicine and ecology can be conveniently modeled by finite Gaussian mixtures but face the problem of dealing with small data sets. We propose a robust version of the estimator based on self-regression and sparsity promoting penalization in order to estimate the components of Gaussian mixtures in such contexts. A space alternating version of the penalized EM algorithm is obtained and we prove that its cluster points satisfy the Karush-Kuhn-Tucker conditions. Monte Carlo experiments are presented in order to compare the results obtained by our method and by standard maximum likelihood estimation. In particular, our estimator is seen to perform well better than the maximum likelihood estimator.

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