Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label learning have been proposed under different generation models of candidate label sets. However, these methods require relatively strong distributional assumptions on the generation models. When the assumptions do not hold, the performance of the methods is not guaranteed theoretically. In this paper, we propose the notion of properness on partial labels. We show that this proper partial-label learning framework includes many previous partial-label learning settings as special cases. We then derive a unified unbiased estimator of the classification risk. We prove that our estimator is risk-consistent by obtaining its estimation error bound. Finally, we validate the effectiveness of our algorithm through experiments.

翻译：部分标签学习是一种以不精确标签进行不精确标签的薄弱监督学习, 在每个培训实例中, 我们得到一套候选标签, 而不是一个真正的标签。 最近, 在不同的代代代代代代代代代代代代代代代代代代代代代代代代代代代代代代代代代名词模式中, 提出了关于部分标签学习的各种方法。 但是, 这些方法需要相对强大的分配假设。 如果假设不成立, 方法的性能在理论上得不到保障 。 在本文中, 我们提出部分标签正确性的概念 。 我们显示, 这个适当的部分标签学习框架包含许多先前的部分标签学习设置, 并将其作为特殊案例 。 然后我们得出一个统一的、 不带偏见的分类风险估计标准 。 我们证明, 我们的估算者是风险一致的, 其估算错误被约束 。 最后, 我们通过实验来验证我们的算法的有效性 。