  Partial-label learning is a popular weakly supervised learning setting that
allows each training example to be annotated with a set of candidate labels.
Previous studies on partial-label learning only focused on the classification
setting where candidate labels are all discrete, which cannot handle continuous
labels with real values. In this paper, we provide the first attempt to
investigate partial-label regression, where each training example is annotated
with a set of real-valued candidate labels. To solve this problem, we first
propose a simple baseline method that takes the average loss incurred by
candidate labels as the predictive loss. The drawback of this method lies in
that the loss incurred by the true label may be overwhelmed by other false
labels. To overcome this drawback, we propose an identification method that
takes the least loss incurred by candidate labels as the predictive loss. We
further improve it by proposing a progressive identification method to
differentiate candidate labels using progressively updated weights for incurred
losses. We prove that the latter two methods are model-consistent and provide
convergence analyses. Our proposed methods are theoretically grounded and can
be compatible with any models, optimizers, and losses. Experiments validate the
effectiveness of our proposed methods.
