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- A. Onken and
K. Obermayer. A Frank mixture copula family for modeling higher-order
correlations of neural spike counts.
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In Journal of Physics: Conference Series, volume 197, page 012019
(10pp), 2009.
(HTTP)
In order to evaluate the importance of higher-order correlations in
neural spike count codes, flexible statistical models of dependent
multivariate spike counts are required. Copula families, parametric
multivariate distributions that represent dependencies, can be applied to
construct such models. We introduce the Frank mixture family as a new copula
family that has separate parameters for all pairwise and higher-order
correlations. In contrast to the Farlie-Gumbel-Morgenstern copula family that
shares this property, the Frank mixture copula can model strong correlations.
We apply spike count models based on the Frank mixture copula to data
generated by a network of leaky integrate-and-fire neurons and compare the
goodness of fit to distributions based on the Farlie-Gumbel-Morgenstern
family. Finally, we evaluate the importance of using proper single neuron
spike count distributions on the Shannon information. We find notable
deviations in the entropy that increase with decreasing firing rates.
Moreover, we find that the Frank mixture family increases the log likelihood
of the fit significantly compared to the Farlie-Gumbel-Morgenstern family.
This shows that the Frank mixture copula is a useful tool to assess the
importance of higher-order correlations in spike count codes.
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