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

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