Skip to main content

Advertisement

Modeling spike-count dependence structures with multivariate Poisson distributions

Article metrics

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).

Figure 1
figure1

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.

References

  1. 1.

    Abbott LF, Dayan P: The effect of correlated variability on the accuracy of a population code. Neural Computation. 1999, 11: 91-101. 10.1162/089976699300016827.

  2. 2.

    Kawamura K: The structure of the multivariate Poisson distribution. Kodai Mathematical Journal. 1979, 2: 337-345. 10.2996/kmj/1138036064.

  3. 3.

    Nelsen RB: An Introduction to Copulas. 1998, New York: Springer-Verlag

  4. 4.

    Zohary E, Newsome WT: Responses of pairs of neurons in macaque MT/V5 as a function of motion coherence in stochastic dot stimuli. Neural Signal Archive, nsa2004.2. [http://www.neuralsignal.org]

Download references

Acknowledgements

This work was supported by BMBF grant 01GQ0410.

Author information

Correspondence to Arno Onken.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Keywords

  • Maximum Likelihood Estimation
  • Likelihood Estimation
  • Cumulative Distribution
  • Cumulative Distribution Function
  • Short Time Interval