Independent Component Analysis Via Nonparametric Maximum Likelihood Estimation

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.
February 12 @ 12:30
12:30 pm (1h)

Discovery Building, Orchard View Room

Richard Samworth