One Positive Label is Sufficient: Single-Positive Multi-Label Learning with Label Enhancement

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 on SPMLL training examples. In this paper, a novel SPMLL method named SMILE, i.e., Singlepositive 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 in fully supervised learning and shows that one positive label of each instance is sufficient to train a 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 twelve corrupted MLL datasets show the effectiveness of SMILE over several existing SPMLL approaches. Source code is available at https://github.com/palm-ml/smile .