  In contrast to conventional (single-label) classification, the setting of
multilabel classification (MLC) allows an instance to belong to several classes
simultaneously. Thus, instead of selecting a single class label, predictions
take the form of a subset of all labels. In this paper, we study an extension
of the setting of MLC, in which the learner is allowed to partially abstain
from a prediction, that is, to deliver predictions on some but not necessarily
all class labels. We propose a formalization of MLC with abstention in terms of
a generalized loss minimization problem and present first results for the case
of the Hamming loss, rank loss, and F-measure, both theoretical and
experimental.
