While the predictions produced by conformal prediction are set-valued, the data used for training and calibration is supposed to be precise. In the setting of superset learning or learning from partial labels, a variant of weakly supervised learning, it is exactly the other way around: training data is possibly imprecise (set-valued), but the model induced from this data yields precise predictions. In this paper, we combine the two settings by making conformal prediction amenable to set-valued training data. We propose a generalization of the conformal prediction procedure that can be applied to set-valued training and calibration data. We prove the validity of the proposed method and present experimental studies in which it compares favorably to natural baselines.

翻译：虽然共形预测产生的预测结果是集合形式的，但用于训练和校准的数据被假定是精确的。在超集学习或部分标签学习（弱监督学习的一种变体）中，情况恰好相反：训练数据可能是不精确的（呈集合形式），但由此数据推导出的模型却能产生精确的预测。本文通过使共形预测能够处理集合形式的训练数据，将这两种设定结合起来。我们提出了一种共形预测过程的推广形式，可应用于集合形式的训练和校准数据。我们证明了所提方法的有效性，并进行了实验研究，结果显示该方法优于自然基线。