Efficient and direct estimation of a neural subunit model for sensory coding

Many visual and auditory neurons have response properties that are well explained by pooling the rectified responses of a set of self-similar linear filters. These filters cannot be found using spike-triggered averaging (STA), which estimates only a single filter. Other methods, like spike-triggered covariance (STC), define a multi-dimensional response subspace, but require substantial amounts of data and do not produce unique estimates of the linear filters. Rather, they provide a linear basis for the subspace in which the filters reside. Here, we define a subunit' model as an LN-LN cascade, in which the first linear stage is restricted to a set of shifted (``convolutional’’) copies of a common filter, and the first nonlinear stage consists of rectifying nonlinearities that are identical for all filter outputs; we refer to these initial LN elements as thesubunits' of the receptive field. The second linear stage then computes a weighted sum of the responses of the rectified subunits. We present a method for directly fitting this model to spike data. The method performs well for both simulated and real data (from primate V1), and the resulting model outperforms STA and STC in terms of both cross-validated accuracy and efficiency.