Learning random monotone DNF Original Research Article

We give an algorithm that with high probability properly learns random monotone DNF with image terms of length image under the uniform distribution on the Boolean cube image. For any function image the algorithm runs in time image and with high probability outputs an image-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.