Theory of population coupling and applications to describe high order correlations in large populations of interacting neurons

Abstract: To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, I develop a mean field theory for the population coupling recently proposed in the studies of visual cortex of mouse and monkey, relating the individual neuron activity to the population activity, and extend the original form to the second order, relating neuron-pair's activity to the population activity, to explain the high order correlations observed in the neural data. I test the computational framework on the salamander retinal data and the cortical spiking data of behaving rats. For the retinal data, the original form of population coupling and its advanced form can explain a significant fraction of two-cell correlations and three-cell correlations, respectively. For the cortical data, the performance becomes much better, and the second order population coupling reveals non-local effects in local cortical circuits.