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This article is part of the supplement: Seventeenth Annual Computational Neuroscience Meeting: CNS*2008

Open Access Poster presentation

Modeling spike-count dependence structures with multivariate Poisson distributions

Arno Onken12* and Klaus Obermayer12

Author Affiliations

1 Bernstein Center for Computational Neuroscience, Berlin, 10115, Germany

2 Department of Electrical Engineering and Computer Science, Berlin Institute of Technology, Berlin, 10587, Germany

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BMC Neuroscience 2008, 9(Suppl 1):P127  doi:10.1186/1471-2202-9-S1-P127

The electronic version of this article is the complete one and can be found online at: http://www.biomedcentral.com/1471-2202/9/S1/P127


Published:11 July 2008

© 2008 Onken and Obermayer; licensee BioMed Central Ltd.

Poster presentation

Previous studies use multivariate Gaussian distributions as models of correlated spike-counts [1]. However, this approximation is not appropriate for short time intervals and fails to model realistic dependence structures. To eradicate these shortcomings, we propose alternative joint distributions that are marginally Poisson distributed and contain a broad range of dependence structures for count variables.

We apply two methods to generate multivariate Poisson distributions of dependent spike-counts. The first approach employs sums of hidden variables to introduce dependencies between the Poisson distributed counts [2]. The second approach introduces dependencies by means of copulas of several classes. Copulas are functions that couple marginal cumulative distribution functions to form a joint distribution function with the same margins [3].

The methods are evaluated on a data set of simultaneously measured spike-counts on 100 ms intervals of up to three neurons in macaque MT responding to stochastic dot stimuli [4]. Parameters are estimated by the inference-for margins method: first the margin likelihoods are separately maximized and then the coupling parameters are estimated given the parameterized margins. Resulting parameters are close to the maximum likelihood estimation with the advantage that the approach is also tractable for high dimensions. Goodness-of-fit is evaluated by cross-validation for the likelihoods. We find that a multivariate Poisson distribution with hidden variables provides the best overall fit to the data from [4] (see Figure 1).

thumbnailFigure 1. Likelihoods of the distribution fits to data from [4]. A. Empirical fractions of measured spike-counts for a representative neuron pair and white contour lines of the bivariate Poisson distribution with hidden variables. B. Log likelihoods for the discretized Gaussian, the multivariate Poisson distribution with hidden variables, and the best fitting copula at consecutive 100 ms time intervals after stimulus onset.

Acknowledgements

This work was supported by BMBF grant 01GQ0410.

References

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  2. Kawamura K: The structure of the multivariate Poisson distribution.

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    Neural Signal Archive, nsa2004.2 OpenURL