  Partial-label learning is a kind of weakly-supervised learning with inexact
labels, where for each training example, we are given a set of candidate labels
instead of only one true label. Recently, various approaches on partial-label
learning have been proposed under different generation models of candidate
label sets. However, these methods require relatively strong distributional
assumptions on the generation models. When the assumptions do not hold, the
performance of the methods is not guaranteed theoretically. In this paper, we
propose the notion of properness on partial labels. We show that this proper
partial-label learning framework requires a weaker distributional assumption
and includes many previous partial-label learning settings as special cases. We
then derive a unified unbiased estimator of the classification risk. We prove
that our estimator is risk-consistent, and we also establish an estimation
error bound. Finally, we validate the effectiveness of our algorithm through
experiments.
