SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

INDEPENDENT COMPONENT ANALYSIS VIA NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION

Richard Samworth, Prof.

Date and Time: Feb 12, 2014 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

Independent Component Analysis (ICA) models are very popular semi- parametric models in which we observe independent copies of a random vec- tor X = AS, where A is a non-singular matrix and S has independent compo- nents. We propose a new way of estimating the unmixing matrix W = A^{-1} and the marginal distributions of the components of S using nonparamet- ric maximum likelihood. Specifically, we study the projection of the em- pirical 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.