Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

Christian Donner,Klaus Obermayer,Hideaki Shimazaki,Matthias Bethge

doi:10.1371/journal.pcbi.1005309

Abstract

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

Highlights

Activity patterns of neuronal populations are constrained by biological mechanisms such as biophysical properties of each neuron and their anatomical connections [3]
Most analysis methods assume stationary data, in which activity rates of neurons and their correlations are constant over time
The characteristic correlations among neurons imposed by the biological mechanisms interplay with statistics of sensory inputs, and influence how the sensory information is represented in the population activity [4,5,6]

Summary

Introduction

Activity patterns of neuronal populations are constrained by biological mechanisms such as biophysical properties of each neuron (e.g., synaptic integration and spike generation [1, 2]) and their anatomical connections [3]. The maximum entropy (ME) principle and derived ME models—known as the pairwise ME model or the Ising model—have been used to explain neural population activities using fewer activity features such as event rates or correlations between pairs of neurons [7, 8] This approach has been employed to explain the activity of neuronal networks and other types of biological networks [9,10,11]. Researchers have employed approximation methods [12,13,14,15,16,17,18] While they successfully extended the number of neurons that could be analyzed, it was pointed out that the pairwise ME model might fail to explain large neural populations because the effect of higher-order interactions may become prominent [19,20,21]. It remains to be examined how much the pairwise ME model can explain the data if the inappropriate stationary assumption is removed

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