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- A. Onken,
S. Grünewälder, M. Munk, and K. Obermayer. Modeling Short-term
Noise Dependence of Spike Counts in Macaque Prefrontal Cortex.
.
In D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, editors, Advances
in Neural Information Processing Systems 21, pages 1233-1240. MIT
Press, 2009.
(PDF)
Correlations between spike counts are often used to analyze neural
coding. The noise is typically assumed to be Gaussian. Yet, this assumption
is often inappropriate, especially for low spike counts. In this study, we
present copulas as an alternative approach. With copulas it is possible to
use arbitrary marginal distributions such as Poisson or negative binomial
that are better suited for modeling noise distributions of spike counts.
Furthermore, copulas place a wide range of dependence structures at the
disposal and can be used to analyze higher order interactions. We develop a
framework to analyze spike count data by means of copulas. Methods for
parameter inference based on maximum likelihood estimates and for computation
of mutual information are provided. We apply the method to our data recorded
from macaque prefrontal cortex. The data analysis leads to three findings:
(1) copula-based distributions provide significantly better fits than
discretized multivariate normal distributions; (2) negative binomial margins
fit the data significantly better than Poisson margins; and (3) the
dependence structure carries 12% of the mutual information between stimuli
and responses.
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