Computing linear approximations to nonlinear neuronal response

We present an approach to obtain nonlinear information about neuronal response by computing multiple linear approximations. By calculating local linear approximations centered around particular stimuli, one can obtain insight into stimulus features that drive the response of highly nonlinear neurons, such as neurons highly selective to a small set of stimuli. We implement this approach based on stimulus-spike correlation (i.e., reverse correlation or spike-triggered average) methods. We illustrate the benefits of these linear approximations with a simplified two-dimensional model and a model of an auditory neuron that is highly selective to particular features of a song.