A Simple Mechanism for Beyond-Pairwise Correlations in Integrate-and-Fire Neurons.

David A Leen,Eric Shea-Brown

doi:10.1186/s13408-015-0030-9

Abstract

The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. We have developed an understanding of the circuit mechanisms that lead to correlations among cell pairs, but little is known about what determines the population firing statistics among larger groups of cells. Here, we examine this question for a simple, but ubiquitous, circuit feature: common fluctuating input arriving to spiking neurons of integrate-and-fire type. We show that this leads to strong beyond-pairwise correlations—that is, correlations that cannot be captured by maximum entropy models that extrapolate from pairwise statistics—as for earlier work with discrete threshold crossing (dichotomous Gaussian) models. Moreover, we find that the same is true for another widely used, doubly stochastic model of neural spiking, the linear–nonlinear cascade. We demonstrate the strong connection between the collective dynamics produced by integrate-and-fire and dichotomous Gaussian models, and show that the latter is a surprisingly accurate model of the former. Our conclusion is that beyond-pairwise correlations can be both broadly expected and possible to describe by simplified (and tractable) statistical models.

Highlights

In the present paper, beyond-pairwise correlations are defined by comparing with a pairwise maximum entropy (PME) model of spike trains: that is, a statistical model built with minimal assumptions about collective spiking beyond the rates of spiking in single cells and correlations in the spikes from cell pairs
We have shown that Exponential-Integrate-and-Fire (EIF) neurons receiving common input give rise to strong beyond-pairwise correlations—that is, distributions of population spike counts that cannot be described by a pairwise maximum entropy (PME) approach
The population output that results can be predicted from a linear–nonlinear (LNL) cascade model, which forms a tractable reduction of the exponential integrate-and-fire (EIF) neuron

Summary

Introduction

Interest in the collective dynamics of neural populations is rapidly increasing, as new recording technologies yield views into neural activity on larger and larger scales, and new statistical analyses yield potential consequences for the neural code [4, 5, 9, 20, 28, 34]. Different stimuli or different (or larger) populations can produce beyond-pairwise correlations [9, 16, 18, 31, 33] In these studies, and in the present paper, beyond-pairwise correlations are defined by comparing with a pairwise maximum entropy (PME) model of spike trains: that is, a statistical model built with minimal assumptions about collective spiking beyond the rates of spiking in single cells and correlations in the spikes from cell pairs. In the present paper, beyond-pairwise correlations are defined by comparing with a pairwise maximum entropy (PME) model of spike trains: that is, a statistical model built with minimal assumptions about collective spiking beyond the rates of spiking in single cells and correlations in the spikes from cell pairs Despite these rich empirical findings, we are only beginning to understand what dynamical features of neural circuits determine whether or not they will produce substantial beyond-pairwise statistical correlations. In particular we show that, in contrast to the PME, the dichotomous Gaussian model gives a highly accurate description of the complete correlation structure of an integrate-and-fire population with common inputs

An Exponential Integrate-and-Fire Population with Common Inputs

Emergence of Strong Beyond-Pairwise Correlations in EIF Populations

Conclusion