Agnostically Learning Juntas from Random Walks
Abstract
We prove that the class of functions g:-1,+1n -> -1,+1 that only depend on an unknown subset of k<<n variables (so-called k-juntas) is agnostically learnable from a random walk in time polynomial in n, 2k2, epsilon-k, and log(1/delta). In other words, there is an algorithm with the claimed running time that, given epsilon, delta > 0 and access to a random walk on -1,+1n labeled by an arbitrary function f:-1,+1n -> -1,+1, finds with probability at least 1-delta a k-junta that is (opt(f)+epsilon)-close to f, where opt(f) denotes the distance of a closest k-junta to f.
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