Learning Sub-classes of Monotone DNF on the Uniform Distribution

In this paper, we give learning algorithms for two new sub-class of DNF formulas: poly-disjoint One-read-once Monotone DNF; and Read-once Factorable Monotone DNF, which is a generalization of Read-once Monotone DNF formulas. Our result uses Fourier analysis to construct the terms of the target formula based on the Fourier coeficients corresponding to these terms. To facilitate this result, we give a novel theorem on the approximation of Read-once Factorable Monotone DNF formulas, in which we show that if a set of terms of the target formula have polynomially small mutually disjoint satisfying sets, then the set of terms can be approximated with small error by the greatest common factor of the set of terms. This approximation theorem may be of independent interest.