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Higher-Order Correlations and Cumulants

  • Chapter
Analysis of Parallel Spike Trains

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 7))

Abstract

Recent advances in electrophysiological and imaging techniques have highlighted the need for correlation measures that go beyond simple pairwise analyses. In this chapter, we discuss cumulant correlations as natural and intuitive higher-order generalizations of the covariance. In particular, we show how cumulant correlations fit to a frequently used additive model of correlation, an idea that mimics correlations among spike trains that originate from overlapping input pools. Finally, we compare the cumulant correlations to the interaction parameters of the well-known exponential family by computing the respective parameters for two different models. We find that the different frameworks measure entirely different aspects, so that populations can have higher-order correlations in one framework but none in the other.

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Author information

Authors and Affiliations

  1. Bernstein Center Freiburg, Albert-Ludwig University, Hansastrasse 9a, 79104, Freiburg, Germany

    Benjamin Staude

  2. Laboratory for Statistical Neuroscience, RIKEN Brain Science Institute, 2-1 Hirosawa, Wakoshi, Saitama, 351-0198, Japan

    Sonja Grün

  3. Bernstein Center Freiburg & Faculty of Biology, Albert-Ludwig University, Hansastrasse 9a, 79104, Freiburg, Germany

    Stefan Rotter

Authors
  1. Benjamin Staude
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  2. Sonja Grün
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  3. Stefan Rotter
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Corresponding author

Correspondence to Stefan Rotter .

Editor information

Editors and Affiliations

  1. Computational Neuroscience Group, RIKEN Brain Science Institute, Hirosawa 2-1, Saitama, 351-0198, Japan

    Sonja Grün

  2. Bernstein-Zentrum für Computational Neur, Neuroscience, Universität Freiburg, Hansastrasse 9A 9a, Freiburg, 79104, Germany

    Stefan Rotter

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Staude, B., Grün, S., Rotter, S. (2010). Higher-Order Correlations and Cumulants. In: Grün, S., Rotter, S. (eds) Analysis of Parallel Spike Trains. Springer Series in Computational Neuroscience, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5675-0_12

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