Can We Hear the Shape of a Maximum Entropy Potential From Spike Trains?

Rodrigo Cofre 1, * Bruno Cessac 1
* Auteur correspondant
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We consider a spike-generating stationary Markov process whose transition probabilities are known. We show that there is a canonicalpotential whose Gibbs distribution, obtained from the MaximumEntropy Principle (MaxEnt), is the equilibrium distribution of thisprocess. We provide a method to compute explicitly and exactly thispotential as a linear combination of spatio-temporal interactions.The method is based on the Hammersley Clifford decomposition andon periodic orbits sampling. An explicit correspondence between theparameters of MaxEnt model and the parameters of Markovianmodels like the Generalized-Linear Model can be established. Wealso provide numerical results.
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https://hal.inria.fr/hal-01095760
Contributeur : Bruno Cessac <>
Soumis le : mardi 16 décembre 2014 - 10:55:22
Dernière modification le : jeudi 3 mai 2018 - 13:32:58
Document(s) archivé(s) le : lundi 23 mars 2015 - 13:44:25

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Rodrigo Cofre, Bruno Cessac. Can We Hear the Shape of a Maximum Entropy Potential From Spike Trains?. Bernstein Conference 2015, Sep 2014, Goettingen, Germany. 〈http://www.bernstein-conference.de/〉. 〈hal-01095760〉

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