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  A non-stationary copula-based spike count model

Onken, A., Grünewälder, S., Munk, M., & Obermayer, K. (2010). A non-stationary copula-based spike count model. Poster presented at 7th Computational and Systems Neuroscience Meeting (COSYNE 2010), Salt Lake City, UT, USA.

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Onken, A, Author
Grünewälder, S, Author
Munk, MHJ1, 2, Author              
Obermayer, K, Author
Affiliations:
1Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: 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.

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 Dates: 2010-02
 Publication Status: Published in print
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 Identifiers: DOI: 10.3389/conf.fnins.2010.03.0024
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Title: 7th Computational and Systems Neuroscience Meeting (COSYNE 2010)
Place of Event: Salt Lake City, UT, USA
Start-/End Date: 2010-02-25 - 2010-02-28

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Title: Frontiers in Neuroscience
  Other : Front Neurosci
Source Genre: Journal
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Publ. Info: Lausanne, Switzerland : Frontiers Research Foundation
Pages: - Volume / Issue: 2010 (Conference Abstract: Computational and Systems Neuroscience 2010) Sequence Number: - Start / End Page: - Identifier: ISSN: 1662-4548
ISSN: 1662-453X
CoNE: https://pure.mpg.de/cone/journals/resource/1662-4548

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Title: 7th Computational and Systems Neuroscience Meeting (COSYNE 2010)
Source Genre: Proceedings
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Pages: - Volume / Issue: - Sequence Number: III-59 Start / End Page: 232 - 233 Identifier: -