Annotating datasets is one of the main costs in nowadays supervised learning. The goal of weak supervision is to enable models to learn using only forms of labelling which are cheaper to collect, as partial labelling. This is a type of incomplete annotation where, for each datapoint, supervision is cast as a set of labels containing the real one. The problem of supervised learning with partial labelling has been studied for specific instances such as classification, multi-label, ranking or segmentation, but a general framework is still missing. This paper provides a unified framework based on structured prediction and on the concept of infimum loss to deal with partial labelling over a wide family of learning problems and loss functions. The framework leads naturally to explicit algorithms that can be easily implemented and for which proved statistical consistency and learning rates. Experiments confirm the superiority of the proposed approach over commonly used baselines.

本文提出了一种基于结构化预测和概念的下确界损失的统一框架，以处理一系列学习问题和损失函数中的部分标注，其中监督以包含实际标签的标签集的形式呈现，并且明确的算法可以轻松实现，并且证明了统计一致性和学习速率。实验证实所提出的方法优于常用的基准方法。

通过Infimum Loss实现部分标注的结构化预测