A Moment-Based Maximum Entropy Model for Fitting Higher-Order Interactions in Neural Data.

N Cayco-Gajic,Eric Shea-Brown,Joel Zylberberg

doi:10.3390/e20070489

Abstract

Correlations in neural activity have been demonstrated to have profound consequences for sensory encoding. To understand how neural populations represent stimulus information, it is therefore necessary to model how pairwise and higher-order spiking correlations between neurons contribute to the collective structure of population-wide spiking patterns. Maximum entropy models are an increasingly popular method for capturing collective neural activity by including successively higher-order interaction terms. However, incorporating higher-order interactions in these models is difficult in practice due to two factors. First, the number of parameters exponentially increases as higher orders are added. Second, because triplet (and higher) spiking events occur infrequently, estimates of higher-order statistics may be contaminated by sampling noise. To address this, we extend previous work on the Reliable Interaction class of models to develop a normalized variant that adaptively identifies the specific pairwise and higher-order moments that can be estimated from a given dataset for a specified confidence level. The resulting “Reliable Moment” model is able to capture cortical-like distributions of population spiking patterns. Finally, we show that, compared with the Reliable Interaction model, the Reliable Moment model infers fewer strong spurious higher-order interactions and is better able to predict the frequencies of previously unobserved spiking patterns.

Highlights

An essential step in understanding neural coding is the characterization of the correlated structure of neural activity
We introduce an adaptive maximum entropy model that identifies and fits spiking interactions of all orders, based on the criterion that they can be accurately estimated from the data for a specified confidence level
Certain spiking features of neural population activity are likely to be more relevant for modeling than others: for example, each neuron’s firing rate and the correlations between pairs of neurons

Summary

Introduction

An essential step in understanding neural coding is the characterization of the correlated structure of neural activity. Recent experimental studies have shown evidence of higher-order correlations in cortical [7,8,9,10,11] and retinal [12,13] population activity. Depending on their stimulus-dependent structure, these higher-order correlations could have a strong impact on population coding [14,15]. Capturing higher-order correlations in neural spiking may be important for identifying functional networks in neural circuits [16], or for characterizing their collective statistical activity [17]. To incorporate higher-order spiking statistics into an information theoretic framework, we require flexible modeling tools that can capture the coordinated spiking of arbitrary orders within neural populations

Methods

Results

Conclusion