Imposing functional priors on Bayesian neural networks

Specifying sensible priors for Bayesian neural networks (BNNs) is key to obtain state-of-the-art predictive performance while obtaining sound predictive uncertainties. However, this is generally difficult because of the complex way prior distributions induce distributions over the functions that BNNs can represent. Switching the focus from the prior over the weights to such functional priors allows for the reasoning on what meaningful prior information should be incorporated. We propose to enforce such meaningful functional priors through Gaussian processes (GPs), which we view as a form of implicit prior over the weights, and we employ scalable Markov chain Monte Carlo (MCMC) to obtain samples from an approximation to the posterior distribution over BNN weights. Unlike previous approaches, our proposal does not require the modification of the original BNN model, it does not require any expensive preliminary optimization, and it can use any inference techniques and any functional prior that can be expressed in closed form. We illustrate the effectiveness of our approach with an extensive experimental campaign.