  Reliable predictive uncertainty estimation plays an important role in
enabling the deployment of neural networks to safety-critical settings. A
popular approach for estimating the predictive uncertainty of neural networks
is to define a prior distribution over the network parameters, infer an
approximate posterior distribution, and use it to make stochastic predictions.
However, explicit inference over neural network parameters makes it difficult
to incorporate meaningful prior information about the data-generating process
into the model. In this paper, we pursue an alternative approach. Recognizing
that the primary object of interest in most settings is the distribution over
functions induced by the posterior distribution over neural network parameters,
we frame Bayesian inference in neural networks explicitly as inferring a
posterior distribution over functions and propose a scalable function-space
variational inference method that allows incorporating prior information and
results in reliable predictive uncertainty estimates. We show that the proposed
method leads to state-of-the-art uncertainty estimation and predictive
performance on a range of prediction tasks and demonstrate that it performs
well on a challenging safety-critical medical diagnosis task in which reliable
uncertainty estimation is essential.
