  Partial label learning deals with the problem where each training instance is
assigned a set of candidate labels, only one of which is correct. This paper
provides the first attempt to leverage the idea of self-training for dealing
with partially labeled examples. Specifically, we propose a unified formulation
with proper constraints to train the desired model and perform pseudo-labeling
jointly. For pseudo-labeling, unlike traditional self-training that manually
differentiates the ground-truth label with enough high confidence, we introduce
the maximum infinity norm regularization on the modeling outputs to
automatically achieve this consideratum, which results in a convex-concave
optimization problem. We show that optimizing this convex-concave problem is
equivalent to solving a set of quadratic programming (QP) problems. By
proposing an upper-bound surrogate objective function, we turn to solving only
one QP problem for improving the optimization efficiency. Extensive experiments
on synthesized and real-world datasets demonstrate that the proposed approach
significantly outperforms the state-of-the-art partial label learning
approaches.
