Ensemble Learning and Linear Response Theory for ICA
We propose a general Bayesian framework for performing independent component analysis (ICA) which relies on ensemble learning and linear response theory known from statistical physics. We apply it to both discrete and continuous sources. For the continuous source the underdetermined (overcomplete) case is studied. The naive mean-field approach fails in this case whereas linear response theory-which gives an improved estimate of covariances-is very efficient. The examples given are for sources without temporal correlations. However, this derivation can easily be extended to treat temporal correlations. Finally, the framework offers a simple way of generating new ICA algorithms without needing to define the prior distribution of the sources explicitly.