We present a model-based method to infer functional properties of subunits indirectly from RGC responses. The method confers advantages over previous approaches: fewer assumptions, more efficient estimation, and more accurate response predictions. We test the model and estimation procedure using stimuli designed to highlight nonlinearities.

ON and OFF parasol cells in macaque retina were recorded using a 512-electrode recording system. Responses were modeled as a linear-nonlinear-linear (LNL) cascade: outputs of spatio-temporal filters (subunits) are exponentiated and summed to generate a time-varying rate for Poisson spike generation. A maximum-likelihood estimate of subunit filters corresponds to soft-clustering the ensemble of stimuli preceding spikes and identifying their centroids. The number of reliably estimated subunits was determined by cross-validation.

In simulation, the algorithm correctly identified subunits, or with limited data, aggregates of subunits. With recorded data at coarse spatial resolution, estimated subunits were larger than bipolar cell receptive fields, spatially localized, and non-overlapping, as would be expected from aggregates of bipolar cells. To test whether estimated subunits captured a significant component of spatial nonlinearity, we designed ``null'' stimuli, orthogonal to the linear RF measured by reverse correlation. By construction, a linear RGC would not respond to these stimuli. Recorded RGCs exhibited strong responses to null stimuli, especially OFF cells, consistent with previous reports of stronger nonlinearities in OFF cells. Subunits fitted with the above approach substantially improved predictions of responses to null stimuli.