Towards Safe Weakly Supervised Learning.

In this paper, we study weakly supervised learning where a large amount of data supervision is not accessible. This includes i) incomplete supervision, where only a small subset of labels is given, such as semi-supervised learning and domain adaptation; ii) inexact supervision, where only coarse-grained labels are given, such as multi-instance learning and iii) inaccurate supervision, where the given labels are not always ground-truth, such as label noise learning. Unlike supervised learning which typically achieves performance improvement with more labeled examples, weakly supervised learning may sometimes even degenerate performance with more weakly supervised data. Such deficiency seriously hinders the deployment of weakly supervised learning to real tasks. It is thus highly desired to study safe weakly supervised learning, which never seriously hurts performance. To this end, we present a generic ensemble learning scheme to derive a safe prediction by integrating multiple weakly supervised learners. We optimize the worst-case performance gain and lead to a maximin optimization. This brings multiple advantages to safe weakly supervised learning. First, for many commonly used convex loss functions in classification and regression, it is guaranteed to derive a safe prediction under a mild condition. Second, prior knowledge related to the weight of the base weakly supervised learners can be flexibly embedded. Third, it can be globally and efficiently addressed by simple convex quadratic or linear program. Finally, it is in an intuitive geometric interpretation with the least square loss. Extensive experiments on various weakly supervised learning tasks, including semi-supervised learning, domain adaptation, multi-instance learning and label noise learning demonstrate our effectiveness.