Abstract

At the beginning of this talk, two popular priors defined on function spaces are discussed: Gaussian priors, which come with a set of orthogonal basis functions, and Bayesian Neural Networks (BNNs), which are popular in the machine learning community. I argue that both priors come with disadvantages, and propose a new class of BNN priors that alleviate them. The resulting posteriors are amenable to sampling using Hilbert space Markov chain Monte Carlo methods (unlike standard BNNs), and scale more favourably in the dimension of the function’s domain (unlike most Gaussian measures). Some theoretical results as well as numerical illustrations are presented, and my talk will end by posing future research directions. This talk is loosely based on the following preprint: https://arxiv.org/abs/2012.10943.