On Learning Monotone DNF under Product Distributions

We show that the class of monotone 2O( √ 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(log2 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. ∗ This research was performed while the author was at Harvard University supported by NSF Grant CCR-98-77049 and by an NSF Mathematical Sciences Postdoctoral Research Fellowship. 1 

• Type: Conference
• Year: 2001
• Where: COLT
• Authors: Rocco A. Servedio
• Keywords: COLT 2001, Machine Learning, N)-term Dnf, Polynomial Time, Uniform Distribution