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A non-stationary copula-based spike count model

Arno Onken1, 2*, Steffen Grünewälder3, Matthias H. Munk4 and Klaus Obermayer1
  • 1 Technische Universität Berlin, Germany
  • 2 BCCN, Germany
  • 3 University College London, United Kingdom
  • 4 MPI for Biological Cybernetics, Germany

Recently, detailed dependencies of spike counts were successfully modeled with the help of copulas [1, 2, 3]. Copulas can be used to couple arbitrary single neuron distributions to form joint distributions with various dependencies. This approach has so far been restricted to stationary spike rates and dependencies. It is known, however, that spike counts of recorded neurons can exhibit non-stationary behavior within trials. In this work, we extend the copula approach to capture non-stationary rates and dependence strengths which are on the order of several hundred milliseconds. We use Poisson marginals for the single neuron statistics and several copula families with and without tail dependencies to couple these marginals. The rates of the Poisson marginals and the dependence strengths of the copula families are time-dependent and fitted to overlapping 100 ms time bins using the inference for margins procedure. To reduce the model complexity we then use regularized least-squares fits of polynomial basis functions for the time-dependent rates and dependence strengths. The approach is applied to data that were recorded from macaque prefrontal cortex during a visual delayed match-to-sample task. Spike trains were recorded using a micro-tetrode array and post-processed using a PCA-based spike sorting method. We compare the cross-validated log likelihoods of the non-stationary models to the corresponding stationary models that have the same marginals and copula families. We find that taking non-stationarities into account increases the likelihood of the test set trials. The approach thereby widens the applicability of detailed dependence models of spike counts. This work was supported by BMBF grant 01GQ0410.

References

1. A. Onken, S. Grünewälder, M. H. J. Munk, and K. Obermayer. Analyzing short-term noise dependencies of spike-counts in macaque prefrontal cortex using copulas and the flashlight transformation. PLoS Computational Biology, in press.

2. A. Onken, S. Grünewälder, M. H. J. 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, 2009.

3. P. Berkes, F. Wood, and J. Pillow. Characterizing neural dependencies with copula models. In D. Koller, D. Schuurmans, Y. Bengio, and L. Bottou, editors, Advances in Neural Information Processing Systems 21, pages 129-136, 2009.

Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010.

Presentation Type: Poster Presentation

Topic: Poster session III

Citation: Onken A, Grünewälder S, Munk MH and Obermayer K (2010). A non-stationary copula-based spike count model. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00243

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Received: 04 Mar 2010; Published Online: 04 Mar 2010.

* Correspondence: Arno Onken, Technische Universität Berlin, Berlin, Germany, aonken@cs.tu-berlin.de