The Difficulty of Random Attribute Noise
Sally A. Goldman · Open Scholarship Institutional Repository (Washington University in St. Louis) · 1991
This paper studies the robustness of pac learning algorithms when the instance space is {0,1}n, and the examples are corrupted by purely random noise affecting only the instances (and not the labels). In the past, conflicting results on this subject have been obtained-- the "best agreement" rule can only tolerate small amounts of noise, yet in some cases large amounts of noise can be tolerated. We show the truth lies somewhere between the two alternatives. For uniform attribute noise, in which each attribute is flipped independently at random with the same probability, we present an algorithm that pac learns monomial for an (unknown) noise rate less than 1/2. Contrasting this positive result, we show that nonuniform random attribute noise, where each attribute i is flipped randomly and independently with its own probability pi, is nearly as harmful as malicious noise-- no algorithm can tolerate more than a small amount of such noise.