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 infinitedimensional space of nonlinear functions to obtain Bayesian estimates of the "nonlinearity" 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.