On learning random DNF formulas under the uniform distribution

We study the average-case learnability of DNF formulas in the model of learning from uniformly distributed random examples. We define a natural model of random monotone DNF formulas and give an efficient algorithm which with high probability can learn, for any fixed constant gamma > 0, a random t-term monotone DNF for any t = O(n(2-gamma)). We also define a model of random nonmonotone DNF and give an efficient algorithm which with high probability can learn a random t-term DNF for any t = O(n(3/2-gamma)). These are the first known algorithms that can successfully learn a broad class of polynomial-size DNF in a reasonable average-case model of learning from random examples.