Statistical analysis of sample-size effects in ICA

Authors:
J. Michael Herrmann;Fabian J. Theis
Affiliations:
University of Edinburgh, Scotland, UK and Bernstein Center for Computational Neuroscience Göttingen and Göttingen University, Institute for Nonlinear Dynamics;Computational Modeling in Biology, IBI, GSF, Munich, Germany and Bernstein Center for Computational Neuroscience Göttingen and Max Planck Institute for Dynamics and Self-Organization, Gö ...
Venue:
IDEAL'07 Proceedings of the 8th international conference on Intelligent data engineering and automated learning
Year:
2007

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Abstract

Independent component analysis (ICA) solves the blind source separation problem by evaluating higher-order statistics, e.g. by estimating fourth-order moments. While estimation errors of the kurtosis can be shown to asymptotically decay with sample size according to a square-root law, they are subject to two further effects for finite samples. Firstly, errors in the estimation of kurtosis increase with the deviation from Gaussianity. Secondly, errors in kurtosis-based ICA algorithms increase when approaching the Gaussian case. These considerations allow us to derive a strict lower bound for the sample size to achieve a given separation quality, which we study analytically for a specific family of distributions and a particular algorithm (fastICA). We further provide results from simulations that support the relevance of the analytical results.