The combination of two major challenges in algorithmic learning is investigated: dealing with huge amounts of irrelevant information and learning from noisy data. It is shown that large classes of Boolean concepts that only depend on a small fraction of their variables—so-called juntas—can be learned efficiently from uniformly distributed examples that are corrupted by random attribute and classification noise. We present solutions to cope with the manifold problems that inhibit a straightforward generalization of the noise-free case. Additionally, we extend our methods to non-uniformly distributed examples and derive new results for monotone juntas in this setting. We assume that the attribute noise is generated by a product distribution. Otherwise fault-tolerant learning is in general impossible which follows from the construction of a noise distribution P and a concept class C such that it is impossible to learn C under P-noise.
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