Reliable Multi-class Classification based on Pairwise Epistemic and Aleatoric Uncertainty

We propose a method for reliable prediction in multi-class classification, where reliability refers to the possibility of partial abstention in cases of uncertainty. More specifically, we allow for predictions in the form of preorder relations on the set of classes, thereby generalizing the idea of set-valued predictions. Our approach relies on combining learning by pairwise comparison with a recent proposal for modeling uncertainty in classification, in which a distinction is made between reducible (a.k.a. epistemic) uncertainty caused by a lack of information and irreducible (a.k.a. aleatoric) uncertainty due to intrinsic randomness. The problem of combining uncertain pairwise predictions into a most plausible preorder is then formalized as an integer programming problem. Experimentally, we show that our method is able to appropriately balance reliability and precision of predictions.