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- A. Onken, S. Grünewälder,
and K. Obermayer. Correlation coefficients are insufficient for analyzing
spike count dependencies.
.
In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta,
editors, Advances in Neural Information Processing Systems 22,
pages 1383-1391. MIT Press, 2009.
(PDF)
The linear correlation coefficient is typically used to
characterize and analyze dependencies of neural spike counts. Here, we show
that the correlation coefficient is in general insufficient to characterize
these dependencies. We construct two neuron spike count models with
Poisson-like marginals and vary their dependence structure using copulas. To
this end, we construct a copula that allows to keep the spike counts
uncorrelated while varying their dependence strength. Moreover, we employ a
network of leaky integrate-and-fire neurons to investigate whether weakly
correlated spike counts with strong dependencies are likely to occur in real
networks. We find that the entropy of uncorrelated but dependent spike count
distributions can deviate from the corresponding distribution with
independent components by more than 25 % and that weakly correlated but
strongly dependent spike counts are very likely to occur in biological
networks. Finally, we introduce a test for deciding whether the dependence
structure of distributions with Poisson-like marginals is well characterized
by the linear correlation coefficient and verify it for different
copula-based models.
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