Parametric Estimation of Gibbs distributions as generalized maximum-entropy models for the analysis 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 propose a generalization of the existing maximum entropy models used for spike trains statistics analysis. We bring a simple method to estimate Gibbs distributions, generalizing existing approaches based on Ising model or one step Markov chains to arbitrary parametric potentials. Our method enables one to take into account memory effects in dynamics. It provides directly the "free-energy" density and the Kullback-Leibler divergence between the empirical statistics and the statistical model. It does not assume a specific Gibbs potential form and does not require the assumption of detailed balance. Furthermore, it allows the comparison of different statistical models and offers a control of finite-size sampling effects, inherent to empirical statistics, by using large deviations results. A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.
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Juan Carlos Vasquez, Thierry Viéville, Bruno Cessac. Parametric Estimation of Gibbs distributions as generalized maximum-entropy models for the analysis of spike train statistics.. [Research Report] RR-7561, INRIA. 2011, pp.54. ⟨inria-00574954v2⟩

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