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Preprints, Working Papers, ... Year : 2010

Entropy-based parametric estimation of spike train statistics

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.

Dates and versions

inria-00534847 , version 1 (10-11-2010)

Identifiers

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

Cite

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