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On Decision Trees, Influences, and Learning Monotone Decision Trees

O'Donnell, Ryan; Servedio, Rocco Anthony

In this note we prove that a monotone boolean function computable by a decision tree of size s has average sensitivity at most √ log2 s. As a consequence we show that monotone functions are learnable to constant accuracy under the uniform distribution in time polynomial in their decision tree size.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-023-04
Published Here
April 22, 2011