Multi-complementary and unlabeled learning for arbitrary losses and models

A weakly-supervised learning framework named as complementary-label has been proposed recently, where each sample is equipped with a single complementary label that denotes one of the classes does not belong to. However, existing methods cannot learn from easily accessible unlabeled samples and multiple labels, which are more informative. In this paper, to remove these limitations, we propose novel multi-complementary allows unbiased estimation classification risk any number labels samples, for arbitrary loss functions models. We first give an estimator then further improve by incorporating into formulation. The error bounds show in optimal parametric convergence rate. also correction scheme alleviating over-fitting caused negative empirical risk. Finally, experiments on both linear deep models effectiveness our methods.