Entropy-based parametric estimation of spike train statistics

Juan Carlos Vasquez 1 Thierry Viéville 2 Bruno Cessac 1, 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
2 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 out the code" consists of inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This gives 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 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 only ?" A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.
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Preprints, Working Papers, ...
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https://hal.inria.fr/inria-00534847
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Submitted on : Wednesday, November 10, 2010 - 4:06:28 PM
Last modification on : Thursday, April 26, 2018 - 10:28:53 AM

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  • HAL Id : inria-00534847, version 1
  • ARXIV : 1003.3157

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Juan Carlos Vasquez, Thierry Viéville, Bruno Cessac. Entropy-based parametric estimation of spike train statistics. 2010. ⟨inria-00534847⟩

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