Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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*Joshua Robinson, Stefanie Jegelka, Suvrit Sra*

We study generalization properties of weakly supervised learning. That is, learning where only a few ``strong'' labels (the actual target of our prediction) are present but many more ``weak'' labels are available. In particular, we show that having access to weak labels can significantly accelerate the learning rate for the strong task to the fast rate of $\mathcal{O}(\nicefrac1n)$, where $n$ denotes the number of strongly labeled data points. This acceleration can happen even if by itself the strongly labeled data admits only the slower $\mathcal{O}(\nicefrac{1}{\sqrt{n}})$ rate. The actual acceleration depends continuously on the number of weak labels available, and on the relation between the two tasks. Our theoretical results are reflected empirically across a range of tasks and illustrate how weak labels speed up learning on the strong task.

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