MEAN FIELD IMPLEMENTATION OF BAYESIAN ICA

In this contribution we review the mean field approach to Bayesian independent component analysis (ICA) recently developed by the authors [1, 2]. For the chosen setting of additive Gaussian noise on the measured signal and Maximum Likelihood II estimation of the mixing matrix and the noise, the expected sufficient statistics are obtained from the two first posterior moments of the sources. These can be effectively estimated using variational mean field theory and its linear response correction. We give an application to feature extraction in neuro-imaging using a binary (stimuli/no stimuli) source paradigm. Finally, we discuss the possibilities of extending the framework to convolutive mixtures, temporal and ‘spatial’ source prior correlations, identification of common sources in mixtures of different media and ICA for density estimation.

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