Postnonlinear independent component analysis by variational Bayesian learning

Abstract. Post-nonlinear (PNL) independent component analysis (ICA) is a generalisation of ICA where the observations are assumed to have been generated from independent sources by linear mixing followed by component-wise scalar nonlinearities. Most previous PNL ICA algorithms require the post-nonlinearities to be invertible functions. In this paper, we present a variational Bayesian approach to PNL ICA that also works for non-invertible post-nonlinearities. The method is based on a gener-ative model with multi-layer perceptron (MLP) networks to model the post-nonlinearities. Preliminary results with a difficult artificial example are encouraging.