Higher-Order Correlations and Cumulants

  • Benjamin Staude
  • Sonja Grün
  • Stefan Rotter
Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 7)


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.


Spike Train Amplitude Distribution Pairwise Correlation Spike Count Exponential Parameter 
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 Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Bernstein Center FreiburgAlbert-Ludwig UniversityFreiburgGermany
  2. 2.Laboratory for Statistical NeuroscienceRIKEN Brain Science InstituteWakoshiJapan
  3. 3.Bernstein Center Freiburg & Faculty of BiologyAlbert-Ludwig UniversityFreiburgGermany

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