Independent component analysis via nonparametric maximum likelihood estimation

TL;DR

This paper introduces a nonparametric maximum likelihood approach for Independent Component Analysis (ICA) that estimates the unmixing matrix and component distributions, demonstrating robustness and theoretical validity.

Contribution

It proposes a novel nonparametric maximum likelihood method for ICA that projects empirical data onto log-concave distribution models, ensuring consistent unmixing matrix estimation.

Findings

Estimation of the unmixing matrix is robust to log-concavity misspecification.

The method is supported by theoretical guarantees.

Simulation results confirm practical effectiveness.

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.