Chapter

Computing and Combinatorics

Volume 4598 of the series Lecture Notes in Computer Science pp 296-306

When Does Greedy Learning of Relevant Attributes Succeed?

— A Fourier-Based Characterization —
  • Jan ArpeAffiliated withInstitut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538 Lübeck
  • , Rüdiger ReischukAffiliated withInstitut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538 Lübeck

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Abstract

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.