Nonlinear Modeling of the Early and Mid-Level Visual System

The work presented in this thesis is toward the goal of extracting structure and meaning from neuroscientific data. Data in visual neuroscience is becoming increasingly high dimensional and the stimulus-response relationships can be highly nonlinear. Data in visual neuroscience is also somewhat noisy due to the imprecise separation of signals from multiple neurons on an electrode, nonstationary effects in the brain, and inherent noise in the brain; neurons rarely respond identically to identical stimuli. Finding nonlinear relationships between a high dimensional stimulus and neural responses in the presence of substantial noise is a challenging nonlinear regression problem. This thesis presents effective techniques for solving this problem and creating highly predictive models of neural function. I first introduce linearized regression, a technique for modeling nonlinear responses using linear regression on a nonlinear transformation of the stimulus. Next I demonstrate a method for efficiently finding Volterra series representations of nonlinear neural responses. Finally, I demonstrate that deep neural networks can provide accurate and interpretable models of the neural computations in visual cortex.