  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.
