Section: New Results

Spike trains statistics

Exact computation of the Maximum Entropy Potential of spiking neural networks models

Participants : Bruno Cessac [correspondent] , Rodrigo Cofre.

Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. But, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuro-mimetic models) provide a probabilistic mapping between stimulus, network architecture and spike patterns in terms of conditional probabilities. In this paper we build an exact analytical mapping between neuro-mimetic and Maximum Entropy models.

This work has been published in [18] and presented in [44] , [29] , [30] , [27] .

Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains

Participants : Bruno Cessac [correspondent] , Hassan Nasser.

We propose a numerical method to learn maximum entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers, [10] and [4], which proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows one to properly handle memory effects in spike statistics, for large-sized neural networks.

This work has been published in [25] and presented in [44] , [29] , [30] , [27] .