  We consider a multi-view learning problem known as group independent
component analysis (group ICA), where the goal is to recover shared independent
sources from many views. The statistical modeling of this problem requires to
take noise into account. When the model includes additive noise on the
observations, the likelihood is intractable. By contrast, we propose Adaptive
multiView ICA (AVICA), a noisy ICA model where each view is a linear mixture of
shared independent sources with additive noise on the sources. In this setting,
the likelihood has a tractable expression, which enables either direct
optimization of the log-likelihood using a quasi-Newton method, or generalized
EM. Importantly, we consider that the noise levels are also parameters that are
learned from the data. This enables sources estimation with a closed-form
Minimum Mean Squared Error (MMSE) estimator which weights each view according
to its relative noise level. On synthetic data, AVICA yields better sources
estimates than other group ICA methods thanks to its explicit MMSE estimator.
On real magnetoencephalograpy (MEG) data, we provide evidence that the
decomposition is less sensitive to sampling noise and that the noise variance
estimates are biologically plausible. Lastly, on functional magnetic resonance
imaging (fMRI) data, AVICA exhibits best performance in transferring
information across views.
