Abstract
We give an algorithm that with high probability properly learns random monotone DNF with t ( n ) terms of length ≈ log t ( 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 / ϵ ) and with high probability outputs an ϵ -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.
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