Parametric Estimation of Gibbs distributions as general Maximum-entropy models for the analysis of spike train statistics.

Juan Carlos Vasquez; Thierry Viéville; Bruno Cessac

inria-00574954, version 1

Parametric Estimation of Gibbs distributions as general Maximum-entropy models for the analysis of spike train statistics.

Juan Carlos Vasquez () ¹, Thierry Viéville () ², Bruno Cessac ()^a^, 1, 3

N° RR-7561 (2011)

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.

a – Université de Nice Sophia-Antipolis
1: NEUROMATHCOMP (INRIA Sophia Antipolis / Inria Rocquencourt)
INRIA – Université Nice Sophia Antipolis [UNS] – CNRS : UMR6621 – Ecole normale supérieure de Paris - ENS Paris
2: CORTEX (INRIA Lorraine - LORIA)
INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
3: Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]

inria-00574954, version 1
http://hal.inria.fr/inria-00574954
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From: Juan Carlos Vasquez <>
Submitted on: Wednesday, 9 March 2011 11:11:06
Updated on: Wednesday, 9 March 2011 15:25:05

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%% inria-00574954, version 1
%% http://hal.inria.fr/inria-00574954
@techreport{vasquez:inria-00574954,
    hal_id = {inria-00574954},
    url = {http://hal.inria.fr/inria-00574954},
    title = {{Parametric Estimation of Gibbs distributions as general Maximum-entropy models for the analysis of spike train statistics.}},
    author = {Vasquez, Juan Carlos and Vi{\'e}ville, Thierry and Cessac, Bruno},
    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.}},
    keywords = {Spike train analysis , Higher-order correlation , Statistical Physics , Gibbs Distributions , Maximum Entropy},
    language = {English},
    affiliation = {NEUROMATHCOMP - INRIA Sophia Antipolis / Inria Rocquencourt , CORTEX - INRIA Lorraine - LORIA , Laboratoire Jean Alexandre Dieudonn{\'e} - JAD},
    pages = {1-54},
    type = {Research Report},
    institution = {INRIA},
    number = {RR-7561},
    note = {This work corresponds to an extended and revisited version of a previous Arxiv preprint, submitted to HAL as http://hal.inria.fr/inria-00534847/fr/},
    year = {2011},
    month = Mar,
    pdf = {http://hal.inria.fr/inria-00574954/PDF/RR-7561.pdf},
}

%F inria-00574954, version 1
%0 Report
%U http://hal.inria.fr/inria-00574954
%2 SCCO:NEUR;INFO:INFO_IT;MATH:MATH_IT
%T Parametric Estimation of Gibbs distributions as general Maximum-entropy models for the analysis of spike train statistics.
%A Vasquez, Juan Carlos
%A Viéville, Thierry
%A Cessac, Bruno
%+ NEUROMATHCOMP - INRIA Sophia Antipolis / Inria Rocquencourt , CORTEX - INRIA Lorraine - LORIA , Laboratoire Jean Alexandre Dieudonné - JAD
%X 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.
%2 J.: Computer Applications/J.2: PHYSICAL SCIENCES AND ENGINEERING/J.2.7: Mathematics and statistics
%Z PACS: 05.10.-a , 87.19.lo , 87.19.lj MCS(2000): 37D35 , 37M25 , 37A30
%G English
%2 Research Report
%P 1-54
%8 2011-03-09
%2 http://enas.gforge.inria.fr/
%K Spike train analysis , Higher-order correlation , Statistical Physics , Gibbs Distributions , Maximum Entropy
%2 2010
%Z This work corresponds to an extended and revisited version of a previous Arxiv preprint, submitted to HAL as http://hal.inria.fr/inria-00534847/fr/
%Z RR-7561
%Z ERC NerVi, funded under the ERC 2008 IDEAS call French Ministery of Research fellowship to J.C. Vasquez.
%2 15032

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Parametric Estimation of Gibbs distributions as general Maximum-entropy models for the analysis of spike train statistics.

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