Independent component analysis via nonparametric maximum likelihood estimation

2012/06/03 by Richard J. Samworth, Ming Yuan, Samworth, Richard J. +1 · 3 citations
Computer Science · Engineering · Mathematics · #62G07 #62G20 #Blind Source Separation Techniques #FOS: Mathematics #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1206.0457

openalex publication_date 2012/06/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Cited by

• Estimation of Independent Component Analysis Systems
• Nonparametric inference under shape constraints: past, present and future
• Independent vector analysis -- an introduction for statisticians

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