Independent Component Analysis via Nonparametric Maximum Likelihood

• Activity Number: 209
• Type: Invited
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Richard Samworth*+ and Ming Yuan
• Companies: University of Cambridge and University of Wisconsin-Madison
• Keywords: Independent Component Analysis ; Nonparametric maximum likelihood ; Log-concavity

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.