  Multi-label learning (MLL) learns from the examples each associated with
multiple labels simultaneously, where the high cost of annotating all relevant
labels for each training example is challenging for real-world applications. To
cope with the challenge, we investigate single-positive multi-label learning
(SPMLL) where each example is annotated with only one relevant label, and show
that one can successfully learn a theoretically grounded multi-label classifier
for the problem. In this paper, a novel SPMLL method named SMILE, i.e.,
Single-positive MultI-label learning with Label Enhancement, is proposed.
Specifically, an unbiased risk estimator is derived, which could be guaranteed
to approximately converge to the optimal risk minimizer of fully supervised
learning and shows that one positive label of each instance is sufficient to
train the predictive model. Then, the corresponding empirical risk estimator is
established via recovering the latent soft label as a label enhancement
process, where the posterior density of the latent soft labels is approximate
to the variational Beta density parameterized by an inference model.
Experiments on benchmark datasets validate the effectiveness of the proposed
method.
