Sharpee TO, Miller KD, Stryker MP. On the importance of static nonlinearity in estimating spatiotemporal neural filters with natural stimuli. J Neurophysiol 99: 2496 -2509. First published March 19, 2008 doi:10.1152/jn.01397.2007. Understanding neural responses with natural stimuli has increasingly become an essential part of characterizing neural coding. Neural responses are commonly characterized by a linear-nonlinear (LN) model, in which the output of a linear filter applied to the stimulus is transformed by a static nonlinearity to determine neural response. To estimate the linear filter in the LN model, studies of responses to natural stimuli commonly use methods that are unbiased only for a linear model (in which there is no static nonlinearity): spike-triggered averages with correction for stimulus power spectrum, with or without regularization. Although these methods work well for artificial stimuli, such as Gaussian white noise, we show here that they estimate neural filters of LN models from responses to natural stimuli much more poorly. We studied simple cells in cat primary visual cortex. We demonstrate that the filters computed by directly taking the nonlinearity into account have better predictive power and depend less on the stimulus than those computed under the linear model. With noise stimuli, filters computed using the linear and LN models were similar, as predicted theoretically. With natural stimuli, filters of the two models can differ profoundly. Noise and natural stimulus filters differed significantly in spatial properties, but these differences were exaggerated when filters were computed using the linear rather than the LN model. Although regularization of filters computed under the linear model improved their predictive power, it also led to systematic distortions of their spatial frequency profiles, especially at low spatial and temporal frequencies.
I N T R O D U C T I O NOver the course of nearly 50 years neurons in the primary visual cortex have been studied with a variety of stimuli, ranging from the classic studies using edges, bars, and moving gratings, to more recent studies with random inputs and stimuli derived from the natural environment, as reviewed by Felsen and Dan (2005) and . It is becoming increasingly important to develop unified models for neural responses to stimuli with a wide range of statistical properties, ideally extending to the fully natural case.To accomplish this, it is important to be able to derive a neural response model from responses to natural stimuli. One cannot simply derive a response model from responses to a simpler ensemble, such as noise, and then extrapolate to the natural case. Typically there are significant differences between response models derived for a given cell from responses to different stimulus ensembles. In particular, neural response models derived from one stimulus ensemble often provide better predictions for neural responses to novel stimuli of the same type than to novel stimuli with different statistical properties (David ...