Flexible Bayesian Independent Component Analysis for Blind Source Separation

Abstract

Independent Component Analysis (ICA) is an important tool for extracting structure from data. ICA is traditionally performed under a maximum likelihood scheme in a latent variable model and in the absence of noise. Although extensively utilised, maximum likelihood estimation has well known drawbacks such as overfitting and sensitivity to local-maxima. In this paper, we propose a Bayesian learning scheme using the variational paradigm to learn the parameters of the model, estimate the source densities, and - together with Automatic Relevance Determination (ARD) - to infer the number of latent dimensions. We illustrate our method by separating a noisy mixture of images, estimating the noise and correctly inferring the true number of sources.