Learning random monotone DNF

Authors:
Jeffrey C. Jackson;Homin K. Lee;Rocco A. Servedio;Andrew Wan
Affiliations:
Duquesne University, Pittsburgh, PA 15282, United States;Columbia University, New York, NY 10027, United States and University of Texas at Austin, Austin, TX 78712, United States;Columbia University, New York, NY 10027, United States;Columbia University, New York, NY 10027, United States
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 19
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Abstract

We give an algorithm that with high probability properly learns random monotone DNF with t(n) terms of length ~logt(n) under the uniform distribution on the Boolean cube {0,1}^n. For any function t(n)@?poly(n) the algorithm runs in time poly(n,1/@e) and with high probability outputs an @e-accurate monotone DNF hypothesis. This is the first algorithm that can learn monotone DNF of arbitrary polynomial size in a reasonable average-case model of learning from random examples only. Our approach relies on the discovery and application of new Fourier properties of monotone functions which may be of independent interest.