Multilabel predictions with sets of probabilities: The Hamming and ranking loss cases

• We consider the problem of multilabel prediction with probability sets.
• We show that efficient approximations can be obtained for the Hamming loss.
• We show that efficient approximations can be obtained for the ranking loss.
• We perform first experiments confirming the expected behaviour of the approximations.

In this paper, we study how multilabel predictions can be obtained when our uncertainty is described by a convex set of probabilities. Such predictions, typically consisting of a set of potentially optimal decisions, are hard to make in large decision spaces such as the one considered in multilabel problems. However, we show that when considering the Hamming or the ranking loss, outer-approximating predictions can be efficiently computed from label-wise information, as in the precise case. We also perform some first experiments showing the behaviour of the partial predictions obtained through these approximations. Such experiments also confirm that predictions become partial on those labels where the precise prediction is likely to make an error.