Random versus maximum entropy models of neural population activity

TL;DR

This study compares maximum entropy models to random models in describing retinal neuron activity, finding maximum entropy generally provides a better fit, especially as population size increases, but struggles with strong correlations.

Contribution

It systematically evaluates the effectiveness of maximum entropy models against random models in neural data, highlighting conditions where maximum entropy excels or fails.

Findings

Maximum entropy models better approximate neural activity than random models.

The advantage of maximum entropy increases with larger neural populations.

Strong correlations in data reduce the effectiveness of maximum entropy models.

Abstract

The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions underlying maximum entropy are intuitive and appealing, its adequacy for describing complex empirical data has been little studied in comparison to alternative approaches. Here data from the collective spiking activity of retinal neurons is reanalysed. The accuracy of the maximum entropy distribution constrained by mean firing rates and pairwise correlations is compared to a random ensemble of distributions constrained by the same observables. In general, maximum entropy approximates the true distribution better than the typical or mean distribution from that ensemble. This advantage improves with population size, with groups as small as 8 being almost always better described by maximum entropy. Failure of maximum entropy to outperform random models is found to be associated with strong correlations in the population.