Analysis of Parallel Spike Trains

Volume 7 of the series Springer Series in Computational Neuroscience pp 253-280

Higher-Order Correlations and Cumulants

  • Benjamin StaudeAffiliated withBernstein Center Freiburg, Albert-Ludwig University
  • , Sonja GrünAffiliated withLaboratory for Statistical Neuroscience, RIKEN Brain Science Institute
  • , Stefan RotterAffiliated withBernstein Center Freiburg & Faculty of Biology, Albert-Ludwig University Email author 

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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.