Sparse Priors on the Mixing Matrix in Independent Component Analysis

In independent component analysis, prior information on the distributions of the independent components is often used; some weak information is in fact necessary for succesful estimation. In contrast, prior information on the mixing matrix is usually not used. This is because it is considered that the estimation should be completely blind as to the form of the mixing matrix. Nevertheless, it could be possible to nd forms of prior information that are suuciently general to be useful in a wide range of applications. In this paper, we argue that prior information on the sparsity of the mixing matrix could be a constraint general enough to merit attention. Moreover, we show that the computational implementation of such sparsifying priors on the mixing matrix is very simple since in many cases they can be expressed as conjugate priors. The property of being conjugate priors means that essentially the same algorithm can be used as in ordinary ICA.