Learning Juntas in the Presence of Noise

We investigate the combination of two major challenges in computational learning: dealing with huge amounts of irrelevant information and learning from noisy data. It is shown that large classes of Boolean concepts that depend only 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 and for parity juntas in this setting. It is assumed that the attribute noise is generated by a product distribution. Without any restrictions of the attribute noise distribution, learning in the presence of noise is in general impossible. This follows from our construction of a noise distribution P and a concept class C such that it is impossible to learn C under P -noise.