Rate-adaptive Bayesian independent component analysis

Abstract

We consider independent component analysis (ICA) using a Bayesian approach. The latent sources are allowed to be block-wise independent while the underlying block structure is unknown. We consider prior distributions on the block structure, the mixing matrix and the marginal density functions of latent sources using a Dirichlet mixture and random series priors. We obtain a minimax-optimal posterior contraction rate of the joint density of the latent sources. This finding reveals that Bayesian ICA adaptively achieves the optimal rate of convergence according to the unknown smoothness level of the true marginal density functions and the unknown block structure. We evaluate the empirical performance of the proposed method by simulation studies.