Active learning of neural response functions with Gaussian processes

A sizeable literature has focused on the problem of estimating a low-dimensional feature space for a neuron's stimulus sensitivity. However, comparatively little work has addressed the problem of estimating the nonlinear function from feature space to spike rate. Here, we use a Gaussian process (GP) prior over the infinite-dimensional space of nonlinear functions to obtain Bayesian estimates of the "non-linearity" in the linear-nonlinear-Poisson (LNP) encoding model. This approach offers increased flexibility, robustness, and computational tractability compared to traditional methods (e.g., parametric forms, histograms, cubic splines). We then develop a framework for optimal experimental design under the GP-Poisson model using uncertainty sampling. This involves adaptively selecting stimuli according to an information-theoretic criterion, with the goal of characterizing the nonlinearity with as little experimental data as possible. Our framework relies on a method for rapidly updating hyperparameters under a Gaussian approximation to the posterior. We apply these methods to neural data from a color-tuned simple cell in macaque V1, characterizing its nonlinear response function in the 3D space of cone contrasts. We find that it combines cone inputs in a highly nonlinear manner. With simulated experiments, we show that optimal design substantially reduces the amount of data required to estimate these nonlinear combination rules.