  Machine learning is increasingly deployed in safety-critical domains where
robustness against adversarial attacks is crucial and erroneous predictions
could lead to potentially catastrophic consequences. This highlights the need
for learning systems to be equipped with the means to determine a model's
confidence in its prediction and the epistemic uncertainty associated with it,
'to know when a model does not know'. In this paper, we propose a novel
Random-Set Convolutional Neural Network (RS-CNN) for classification which
predicts belief functions rather than probability vectors over the set of
classes, using the mathematics of random sets, i.e., distributions over the
power set of the sample space. Based on the epistemic deep learning approach,
random-set models are capable of representing the 'epistemic' uncertainty
induced in machine learning by limited training sets. We estimate epistemic
uncertainty by approximating the size of credal sets associated with the
predicted belief functions, and experimentally demonstrate how our approach
outperforms competing uncertainty-aware approaches in a classical evaluation
setting. The performance of RS-CNN is best demonstrated on OOD samples where it
manages to capture the true prediction while standard CNNs fail.
