Correlated spiking activity in nearby neurons is a common feature of neural circuits. We show that a generalized linear model can be used to account for the correlation structure in the spike responses of a group of nearby neurons in primate retina. The model consists of: (1) a linear receptive field that operates on the stimulus; (2) a linear filter that captures the effects of the neuron's own spike history; (3) a set of linear filters that capture the effects of spiking in neighboring cells; and (4) an output nonlinearity that converts the total input to an instantaneous probability of spiking. The model is closely related to the more biophysically realistic integrate-and-fire model, and can exhibit a wide array of biologically relevant dynamical behaviors, such as refractoriness, spike rate adaptation, and bursting. It has previously been used to characterize the isolated responses of individual neurons.
We have applied the model to simultaneously-recorded responses of groups of macaque ON and OFF parasol retinal ganglion cells, stimulated with a 120-Hz spatiotemporal binary white noise stimulus. We find that the model accurately describes the stimulus-driven response (PSTH), and reproduces both the autocorrelations and pairwise cross-correlations of multi-cell responses. Moreover, by examining the contribution of stimulus and spike train dependent inputs, the model allows us to reliably predict the relative significance of signal and noise-dependent correlations, which we verify by examining responses to a repeated stimulus. Finally, we show that the model can be used to map functional connectivity, providing a complete description of the identity, direction and form of functionally significant connections between cells.