Parametric Estimation of spike train statistics

Bruno Cessac 1, 2 Juan Carlos Vasquez 1 Thierry Viéville 3
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
3 CORTEX - Neuromimetic intelligence
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This provides us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators . A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed, minimizing the relative entropy, yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding ? A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.
Type de document :
Communication dans un congrès
Eighteenth Annual Computational Neuroscience Meeting CNS*2009, 2009, Berlin, Germany. 2009
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https://hal.inria.fr/inria-00407913
Contributeur : Thierry Viéville <>
Soumis le : lundi 27 juillet 2009 - 19:45:11
Dernière modification le : jeudi 26 avril 2018 - 10:28:53

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  • HAL Id : inria-00407913, version 1

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Bruno Cessac, Juan Carlos Vasquez, Thierry Viéville. Parametric Estimation of spike train statistics. Eighteenth Annual Computational Neuroscience Meeting CNS*2009, 2009, Berlin, Germany. 2009. 〈inria-00407913〉

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