Sparse Gaussian ICA

TL;DR

This paper introduces a novel ICA method that can recover sparse mixing matrices even when the source components are Gaussian, by leveraging structured assumptions on the mixing matrix.

Contribution

It demonstrates that Gaussian ICA is feasible under sparsity assumptions on the mixing matrix, providing an efficient algorithm using only covariance information.

Findings

Successfully recovers the mixing matrix in Gaussian ICA scenarios.

Extends ICA applicability to cases with multiple Gaussian components.

Uses only covariance matrix, simplifying the data requirements.

Abstract

Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS where A is an unknown mixing matrix. Critically, all existing methods for ICA rely on and exploit strongly the assumption that S is not Gaussian as otherwise A becomes unidentifiable. In this paper, we show that in fact one can handle the case of Gaussian components by imposing structure on the matrix A. Specifically, we assume that A is sparse and generic in the sense that it is generated from a sparse Bernoulli-Gaussian ensemble. Under this condition, we give an efficient algorithm to recover the columns of A given only the covariance matrix of X as input even when S has several Gaussian components.