Learning Monotone DNF from a Teacher That Almost Does Not Answer Membership Queries

We present results concerning the learning of Monotone DNF (MDNF) from Incomplete Membership Queries and Equivalence Queries. Our main result is a new algorithm that allows efficient learning of MDNF using Equivalence Queries and Incomplete Membership Queries with probability of p = 1 − 1/poly(n, t) of failing. Our algorithm is expected to make O tn 1 − p 2 queries, when learning a MDNF formula with t terms over n variables. Note that this is polynomial for any failure probability p = 1−1/poly(n, t). The algorithm’s running time is also polynomial in t, n, and 1/(1 − p). In a sense this is the best possible, as learning with p = 1−1/ω(poly(n, t)) would imply learning MDNF, and thus also DNF, from equivalence queries alone.1

• Type: Conference
• Year: 2001
• Where: COLT
• Authors: Nader H. Bshouty, Nadav Eiron
• Keywords: COLT 2001, Equivalence Queries, Incomplete Membership Queries, Machine Learning, Monotone Dnf