  We present a novel approach to uncertainty quantification in classification
tasks based on label-wise decomposition of uncertainty measures. This
label-wise perspective allows uncertainty to be quantified at the individual
class level, thereby improving cost-sensitive decision-making and helping
understand the sources of uncertainty. Furthermore, it allows to define total,
aleatoric, and epistemic uncertainty on the basis of non-categorical measures
such as variance, going beyond common entropy-based measures. In particular,
variance-based measures address some of the limitations associated with
established methods that have recently been discussed in the literature. We
show that our proposed measures adhere to a number of desirable properties.
Through empirical evaluation on a variety of benchmark data sets -- including
applications in the medical domain where accurate uncertainty quantification is
crucial -- we establish the effectiveness of label-wise uncertainty
quantification.
