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Statistical Analysis of Sample-Size Effects in ICA

  • J. Michael Herrmann
  • Fabian J. Theis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4881)

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.

Keywords

Independent Component Analysis Fisher Information Independent Component Analysis Blind Source Separation Recovery Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • J. Michael Herrmann
    • 1
    • 2
  • Fabian J. Theis
    • 1
    • 3
  1. 1.Bernstein Center for Computational Neuroscience Göttingen 
  2. 2.Göttingen University, Institute for Nonlinear Dynamics 
  3. 3.Max Planck Institute for Dynamics and Self-Organization, Bunsenstraße 10, 37073 GöttingenGermany

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