On Using the Fourier Transform to Learn Disjoint DNF

This note addresses the problem of learning DNF expressions using membership queries. We extend the results of Kushilevitz and Mansour [5], on learning through Fourier representations, to show learnability of various subsets of DNF. In particular we show the polynomial learnability of Disjoint DNF expressions under the uniform distribution, and exact learnability of Disjoint logn DNF. These extend the learnability results of the corresponding classes of decision trees given in [5]. We further show the learnability of log n term DNF under the uniform distribution. The learnability of this class (even for the distribution free case) is already known [2], but the algorithm and analysis given here are di erent. The learning framework and algorithm are the same as in [5]. The main contribution of this note is a di erent analysis of the Fourier spectrum of these function classes. This enables us to show the learnability of wider classes and with somewhat simpli ed proofs.