Multi-Complementary and Unlabeled Learning for Arbitrary Losses and Models
This work addresses a problem in weakly-supervised learning for researchers and practitioners by extending complementary-label learning to more informative data settings, though it is incremental in nature.
The paper tackles the limitations of existing complementary-label learning methods by proposing a framework that enables unbiased risk estimation from samples with multiple complementary labels and unlabeled data, achieving optimal parametric convergence rates in experiments.
A weakly-supervised learning framework named as complementary-label learning has been proposed recently, where each sample is equipped with a single complementary label that denotes one of the classes the sample does not belong to. However, the existing complementary-label learning methods cannot learn from the easily accessible unlabeled samples and samples with multiple complementary labels, which are more informative. In this paper, to remove these limitations, we propose the novel multi-complementary and unlabeled learning framework that allows unbiased estimation of classification risk from samples with any number of complementary labels and unlabeled samples, for arbitrary loss functions and models. We first give an unbiased estimator of the classification risk from samples with multiple complementary labels, and then further improve the estimator by incorporating unlabeled samples into the risk formulation. The estimation error bounds show that the proposed methods are in the optimal parametric convergence rate. Finally, the experiments on both linear and deep models show the effectiveness of our methods.