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We consider a multi-view learning problem known as group independentcomponent analysis (group ICA), where the goal is to recover shared independentsources from many views. The statistical modeling of this problem requires totake noise into account. When the model includes additive noise on theobservations, the likelihood is intractable. By contrast, we propose AdaptivemultiView ICA (AVICA), a noisy ICA model where each view is a linear mixture ofshared independent sources with additive noise on the sources. In this setting,the likelihood has a tractable expression, which enables either directoptimization of the log-likelihood using a quasi-Newton method, or generalizedEM. Importantly, we consider that the noise levels are also parameters that arelearned from the data. This enables sources estimation with a closed-formMinimum Mean Squared Error (MMSE) estimator which weights each view accordingto its relative noise level. On synthetic data, AVICA yields better sourcesestimates than other group ICA methods thanks to its explicit MMSE estimator.On real magnetoencephalograpy (MEG) data, we provide evidence that thedecomposition is less sensitive to sampling noise and that the noise varianceestimates are biologically plausible. Lastly, on functional magnetic resonanceimaging (fMRI) data, AVICA exhibits best performance in transferringinformation across views.

Adaptive Multi-View ICA: Estimation of noise levels for optimal inference