One of the greatest challenges in systems neuroscience is to understand how large networks of neurons collectively process and encode information. In this work we present a statistical model for multiple simultaneously-recorded single units that includes terms corresponding to a) the dependence of the firing-rate on an experimentally controlled stimulus, b) the spiking history of the observed cells, and c) the effect of common-input terms. These common-input terms model the effect of unobserved cells which are presynaptic to two or more cells in the observed population, and therefore constitute a hidden common-driving term for our observed cells.

The consideration of these common-input terms is the primary contribution of this work. To perform inference in this model, we implement a fast, although approximate, algorithm based on the extended Kalman filter to perform the expectation step in the Expectation-Maximization (EM) algorithm.