A1094
Title: Some properties of ICA in infinite-dimensional settings
Authors: Marc Vidal - Ghent University, Max Planck Institute for Cognitive and Brain Sciences (Belgium) [presenting]
Ana Maria Aguilera - University of Granada (Spain)
Abstract: Independent component analysis (ICA) is discussed in a setting where infinitely many statistically independent components are allowed. A critical aspect of ICA models is the mixing operator, which turns out to be severely unidentified and ill-conditioned in the current framework. We elaborate on the notion of Hilbertian independence and separability to characterize this operator. Furthermore, it is shown how ICA based on kurtosis can be used to classify functions with near-perfect accuracy and explain the underlying principles of this phenomenon, which have a probabilistic interpretation by the Feldman-Hajek dichotomy. The usefulness of the methods is exemplified through neurophysiological data to identify cortical regions involved in depression disorder.
