  Uncertainty quantification and robustness to distribution shifts are
important goals in machine learning and artificial intelligence. Although
Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be
assessed, different sources of uncertainty are indistinguishable. We present
Credal Bayesian Deep Learning (CBDL). Heuristically, CBDL allows to train an
(uncountably) infinite ensemble of BNNs, using only finitely many elements.
This is possible thanks to prior and likelihood finitely generated credal sets
(FGCSs), a concept from the imprecise probability literature. Intuitively,
convex combinations of a finite collection of prior-likelihood pairs are able
to represent infinitely many such pairs. After training, CBDL outputs a set of
posteriors on the parameters of the neural network. At inference time, such
posterior set is used to derive a set of predictive distributions that is in
turn utilized to distinguish between aleatoric and epistemic uncertainties, and
to quantify them. The predictive set also produces either (i) a collection of
outputs enjoying desirable probabilistic guarantees, or (ii) the single output
that is deemed the best, that is, the one having the highest predictive lower
probability -- another imprecise-probabilistic concept. CBDL is more robust
than single BNNs to prior and likelihood misspecification, and to distribution
shift. We show that CBDL is better at quantifying and disentangling different
types of uncertainties than single BNNs, ensemble of BNNs, and Bayesian Model
Averaging. In addition, we apply CBDL to two case studies to demonstrate its
downstream tasks capabilities: one, for motion prediction in autonomous driving
scenarios, and two, to model blood glucose and insulin dynamics for artificial
pancreas control. We show that CBDL performs better when compared to an
ensemble of BNNs baseline.
