Independent component analysis via nonparametric maximum likelihood estimation

Richard J. Samworth; Ming Yuan

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arXiv · 1206.0457

Independent component analysis via nonparametric maximum likelihood estimation

Richard J. Samworth·Ming Yuan

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Abstract

Independent Component Analysis (ICA) models are very popular semiparametric models in which we observe independent copies of a random vector $X = AS$, where $A$ is a non-singular matrix and $S$ has independent components. We propose a new way of estimating the unmixing matrix $W = A^{-1}$ and the marginal distributions of the components of $S$ using nonparametric maximum likelihood. Specifically, we study the projection of the empirical distribution onto the subset of ICA distributions having log-concave marginals. We show that, from the point of view of estimating the unmixing matrix, it makes no difference whether or not the log-concavity is correctly specified. The approach is further justified by both theoretical results and a simulation study.

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Richard J. Samworth, Ming Yuan. 2012-06-03. Independent component analysis via nonparametric maximum likelihood estimation. https://arxiv.org/abs/1206.0457

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