Hermite polynomials and measures of non-gaussianity

Authors:
Jouni Puuronen;Aapo Hyvärinen
Affiliations:
Dept of Mathematics and Statistics, Dept of Computer Science and HIIT, University of Helsinki, Finland;Dept of Mathematics and Statistics, Dept of Computer Science and HIIT, University of Helsinki, Finland
Venue:
ICANN'11 Proceedings of the 21st international conference on Artificial neural networks - Volume Part II
Year:
2011

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Abstract

We first review some rigorous properties of the Hermite polynomials, and demonstrate their usefulness in estimating probability distributions as series from data samples. We then proceed to explain how these series can be used to obtain precise and robust measures of non-Gaussianity. Our measures of non-Gaussianity detect all kinds of deviations from Gaussianity, and thus provide reliable objective functions for ICA. With a linear computational complexity with respect to the sample size, our method is also suitable for large data sets.