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International Conference on Artificial Neural Networks

ICANN 2011: Artificial Neural Networks and Machine Learning – ICANN 2011 pp 205–212Cite as

Hermite Polynomials and Measures of Non-gaussianity

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6792))

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.

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Author information

Authors and Affiliations

  1. Dept of Mathematics and Statistics, University of Helsinki, Finland

    Jouni Puuronen & Aapo Hyvärinen

  2. Dept of Computer Science and HIIT, University of Helsinki, Finland

    Jouni Puuronen & Aapo Hyvärinen

Authors
  1. Jouni Puuronen
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  2. Aapo Hyvärinen
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Editor information

Editors and Affiliations

  1. Department of Information and Computer Science, Aalto University School of Science, P.O. Box 15400, 00076, Aalto, Finland

    Timo Honkela  & Samuel Kaski  & 

  2. School of Physics, Astronomy and Informatics, Department of Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100, Torun, Poland

    Włodzisław Duch

  3. Department of Statistical Science, University College London, 1-19 Torrington Place, WC1E 7HB, London, UK

    Mark Girolami

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© 2011 Springer-Verlag Berlin Heidelberg

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Puuronen, J., Hyvärinen, A. (2011). Hermite Polynomials and Measures of Non-gaussianity. In: Honkela, T., Duch, W., Girolami, M., Kaski, S. (eds) Artificial Neural Networks and Machine Learning – ICANN 2011. ICANN 2011. Lecture Notes in Computer Science, vol 6792. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21738-8_27

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  • DOI: https://doi.org/10.1007/978-3-642-21738-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21737-1

  • Online ISBN: 978-3-642-21738-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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