When Does Greedy Learning of Relevant Attributes Succeed?

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We introduce a new notion called Fourier-accessibility that allows us to precisely characterize the class of Boolean functions for which a standard greedy learning algorithm successfully learns all relevant attributes. If the target function is Fourier-accessible, then the success probability of the greedy algorithm can be made arbitrarily close to one. On the other hand, if the target function is not Fourier-accessible, then the error probability tends to one. Finally, we extend these results to the situation where the input data are corrupted by random attribute and classification noise and prove that greedy learning is quite robust against such errors.