Partial Label Learning (PLL) is a typical weakly supervised learning task, which assumes each training instance is annotated with a set of candidate labels containing the ground-truth label. Recent PLL methods adopt identification-based disambiguation to alleviate the influence of false positive labels and achieve promising performance. However, they require all classes in the test set to have appeared in the training set, ignoring the fact that new classes will keep emerging in real applications. To address this issue, in this paper, we focus on the problem of Partial Label Learning with Augmented Class (PLLAC), where one or more augmented classes are not visible in the training stage but appear in the inference stage. Specifically, we propose an unbiased risk estimator with theoretical guarantees for PLLAC, which estimates the distribution of augmented classes by differentiating the distribution of known classes from unlabeled data and can be equipped with arbitrary PLL loss functions. Besides, we provide a theoretical analysis of the estimation error bound of the estimator, which guarantees the convergence of the empirical risk minimizer to the true risk minimizer as the number of training data tends to infinity. Furthermore, we add a risk-penalty regularization term in the optimization objective to alleviate the influence of the over-fitting issue caused by negative empirical risk. Extensive experiments on benchmark, UCI and real-world datasets demonstrate the effectiveness of the proposed approach.

本研究解决了现有部分标签学习方法在测试集中新类出现时的不足，提出了一种带有理论保证的无偏风险估计器。这种方法能够通过区分已知类和未标记数据的分布来估计增强类的分布，并通过添加风险惩罚正则项来缓解过拟合问题。实验结果表明，该方法在多个基准和真实数据集上表现出色。

带增强类的部分标签学习的无偏风险估计器