Large Deviations Properties of Maximum Entropy Markov Chains from Spike Trains

TL;DR

This paper explores the statistical properties and large deviation behaviors of maximum entropy Markov chains used to model neuronal spike trains, providing insights into their accuracy, convergence, and fluctuations.

Contribution

It applies large deviations theory to analyze the statistical fluctuations and properties of maximum entropy Markov chains in neuroscience modeling.

Findings

Explicit large deviation rate functions for simple models

Insights into fluctuations of correlations and irreversibility

Assessment of model distinguishability and convergence

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.