A Random Subspace Technique That Is Resistant to a Limited Number of Features Corrupted by an Adversary

In this paper, we consider batch supervised learning where an adversary is allowed to corrupt instances with arbitrarily large noise. The adversary is allowed to corrupt any $l$ features in each instance and the adversary can change their values in any way. This noise is introduced on test instances and the algorithm receives no label feedback for these instances. We provide several subspace voting techniques that can be used to transform existing algorithms and prove data-dependent performance bounds in this setting. The key insight to our results is that we set our parameters so that a significant fraction of the voting hypotheses do not contain corrupt features and, for many real world problems, these uncorrupt hypotheses are sufficient to achieve high accuracy. We empirically validate our approach on several datasets including three new datasets that deal with side channel electromagnetic information.