R. Servedio.

Preliminary version in

We show that the class of monotone $2^{O(\sqrt{\log n})}$-term DNF formulae can be PAC learned in polynomial time under the uniform distribution from random examples only. This is an exponential improvement over the best previous polynomial-time algorithms in this model, which could learn monotone $o(\log^2 n)$-term DNF. We also show that various classes of small constant-depth circuits which compute monotone functions are PAC learnable in polynomial time under the uniform distribution. All of our results extend to learning under any constant-bounded product distribution.

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