What’s beyond second order? Kernel regression techniques for nonlinear functional characterization of visual neurons

Michael Wu, University of California, Berkeley

Nonparametric regressions are powerful and versatile techniques that can be used to identify and quantify the nonlinear response properties of sensory neurons. In practice, however, most nonlinear regression techniques, such as Volterra series expansion, become impractical beyond second order. This is due largely to the exponential growth of data needed for an accurate regression estimate. Recent developments in kernel methods provide an avenue to circumvent this data limitation problem. In brief, kernel methods first nonlinearly map the input data into a high dimensional feature space, and then apply a robust and efficient linear regression algorithm within this feature space. In this way, the kernel method effectively converts a difficult nonlinear curve fitting problem into a convex optimization problem, which we know how to solve. In terms of Volterra expansion, it can be shown that kernel regression using a D-degree polynomial kernel is equivalent to a Dth order Volterra series estimate. Kernel regression is able to exploit the data efficiently, making higher order Volterra estimation feasible even with limited data.

We propose a class of kernel regression algorithm for spatiotemporal receptive field (STRF) estimation in sensory neurons. We implemented nu-support vector regression, kernel partial least squares, and kernel ridge regression for STRF estimation. When applied to macaque V1 neurons with natural inputs, we find that these kernel regression techniques are competitive when compared to neural network and other nonlinear reverse correlation techniques. Moreover, these techniques are general and are by no means restricted to V1. They can be use to determine response properties in other visual areas and other sensory modalities. In particular, kernel regression techniques are potentially very useful in higher visual areas where robust and accurate STRF estimation techniques are not available.

Abstract Author(s): Michael C.-K. Wu and Jack L. Gallant<br />Biophysics, Psychology and Neuroscience, University of California, Berkeley, CA, USA