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We study binary classification in the setting where the learner is presentedwith multiple corrupted training samples, with possibly different sample sizesand degrees of corruption, and introduce an approach based on minimizing aweighted combination of corruption-corrected empirical risks. We establish ageneralization error bound, and further show that the bound is optimized whenthe weights are certain interpretable and intuitive functions of the samplesizes and degrees of corruptions. We then apply this setting to the problem oflearning with label proportions (LLP), and propose an algorithm that enjoys themost general statistical performance guarantees known for LLP. Experimentsdemonstrate the utility of our theory.

Learning from Multiple Corrupted Sources, with Application to Learning from Label Proportions