2018/04/02 by Nilin Abrahamsen, Philippe Rigollet, Abrahamsen, Nilin +1
Chemistry · Computer Science · #Blind Source Separation Techniques #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1804.00408
openalex publication_date 2018/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.