Sparse Gaussian ICA
This addresses a fundamental limitation in ICA for data analysis, enabling application to scenarios with Gaussian components, though it relies on specific structural assumptions.
The paper tackles the problem of performing independent component analysis (ICA) when latent components are Gaussian, which traditionally makes the mixing matrix unidentifiable, by showing that recovery is possible under a sparse and generic mixing matrix assumption, and provides an efficient algorithm using only the covariance matrix of the data.
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.