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

Rodrigo Cofre 1, * Bruno Cessac 1 
* Corresponding author
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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Contributor : Bruno Cessac Connect in order to contact the contributor
Submitted on : Tuesday, December 16, 2014 - 10:55:22 AM
Last modification on : Thursday, August 4, 2022 - 4:58:17 PM
Long-term archiving on: : Monday, March 23, 2015 - 1:44:25 PM


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  • HAL Id : hal-01095760, version 1


Rodrigo Cofre, Bruno Cessac. Can We Hear the Shape of a Maximum Entropy Potential From Spike Trains?. Bernstein Conference 2015, Sep 2014, Goettingen, Germany. . ⟨hal-01095760⟩



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