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Academic Commons Search Resultsen-usOn Decision Trees, Influences, and Learning Monotone Decision Trees
https://academiccommons.columbia.edu/catalog/ac:109797
O'Donnell, Ryan; Servedio, Rocco Anthony10.7916/D8J67QR8Fri, 16 Jun 2017 17:02:10 +0000In 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.Computer scienceras2005Computer ScienceReportsLearning mixtures of product distributions over discrete domains
https://academiccommons.columbia.edu/catalog/ac:110398
Feldman, Jon; O'Donnell, Ryan; Servedio, Rocco Anthony10.7916/D84X5KZ2Mon, 12 Jun 2017 20:42:29 +0000We consider the problem of learning mixtures of product distributions over discrete domains in the distribution learning framework introduced by Kearns et al. [18]. We give a poly(n/ε) time algorithm for learning a mixture of k arbitrary product distributions over the n-dimensional Boolean cube {0,1}n to accuracy ε, for any constant k. Previous polynomial time algorithms could only achieve this for k = 2 product distributions; our result answers an open question stated independently in [8] and [14]. We further give evidence that no polynomial time algorithm can succeed when k is superconstant, by reduction from a notorious open problem in PAC learning. Finally, we generalize our poly(n/ε) time algorithm to learn any mixture of k = O(1) product distributions over {0, 1, . . . , b}n, for any b = O(1).Computer scienceras2005Computer ScienceReports