  Despite their successes, deep neural networks may make unreliable predictions
when faced with test data drawn from a distribution different to that of the
training data, constituting a major problem for AI safety. While this has
recently motivated the development of methods to detect such
out-of-distribution (OoD) inputs, a robust solution is still lacking. We
propose a new probabilistic, unsupervised approach to this problem based on a
Bayesian variational autoencoder model, which estimates a full posterior
distribution over the decoder parameters using stochastic gradient Markov chain
Monte Carlo, instead of fitting a point estimate. We describe how
information-theoretic measures based on this posterior can then be used to
detect OoD inputs both in input space and in the model's latent space. We
empirically demonstrate the effectiveness of our proposed approach.
