Preprint Article Version 1 This version is not peer-reviewed

Large Deviations Properties of Maximum Entropy Markov Chains from Spike Trains

Version 1 : Received: 6 June 2018 / Approved: 7 June 2018 / Online: 7 June 2018 (11:06:22 CEST)

A peer-reviewed article of this Preprint also exists.

Cofré, R.; Maldonado, C.; Rosas, F. Large Deviations Properties of Maximum Entropy Markov Chains from Spike Trains. Entropy 2018, 20, 573. Cofré, R.; Maldonado, C.; Rosas, F. Large Deviations Properties of Maximum Entropy Markov Chains from Spike Trains. Entropy 2018, 20, 573.

Journal reference: Entropy 2018, 20, 573
DOI: 10.3390/e20080573

Abstract

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Subject Areas

computational neuroscience; spike train statistics; maximum entropy principle; large deviation theory; out-of-equilibrium statistical mechanics; thermodynamic formalism; entropy production

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