  In this paper, we consider the problem of making distributionally robust,
skeptical inferences for the multi-label problem, or more generally for Boolean
vectors. By distributionally robust, we mean that we consider a set of possible
probability distributions, and by skeptical we understand that we consider as
valid only those inferences that are true for every distribution within this
set. Such inferences will provide partial predictions whenever the considered
set is sufficiently big. We study in particular the Hamming loss case, a common
loss function in multi-label problems, showing how skeptical inferences can be
made in this setting. Our experimental results are organised in three sections;
(1) the first one indicates the gain computational obtained from our
theoretical results by using synthetical data sets, (2) the second one
indicates that our approaches produce relevant cautiousness on those
hard-to-predict instances where its precise counterpart fails, and (3) the last
one demonstrates experimentally how our approach copes with imperfect
information (generated by a downsampling procedure) better than the partial
abstention [31] and the rejection rules.
