  Multi-label classification is the task of assigning a subset of labels to a
given query instance. For evaluating such predictions, the set of predicted
labels needs to be compared to the ground-truth label set associated with that
instance, and various loss functions have been proposed for this purpose. In
addition to assessing predictive accuracy, a key concern in this regard is to
foster and to analyze a learner's ability to capture label dependencies. In
this paper, we introduce a new class of loss functions for multi-label
classification, which overcome disadvantages of commonly used losses such as
Hamming and subset 0/1. To this end, we leverage the mathematical framework of
non-additive measures and integrals. Roughly speaking, a non-additive measure
allows for modeling the importance of correct predictions of label subsets
(instead of single labels), and thereby their impact on the overall evaluation,
in a flexible way - by giving full importance to single labels and the entire
label set, respectively, Hamming and subset 0/1 are rather extreme in this
regard. We present concrete instantiations of this class, which comprise
Hamming and subset 0/1 as special cases, and which appear to be especially
appealing from a modeling perspective. The assessment of multi-label
classifiers in terms of these losses is illustrated in an empirical study.
