Learning monotone dnf from a teacher that almost does not answer membership queries

Authors:
Nader H. Bshouty;Nadav Eiron
Affiliations:
Department of Computer Science, Technion - Israel Institute of Technology, Haifa 32000, Israel;IBM Almaden Research Center, 52BC/B2, 650 Harry Road, San Jose, CA
Venue:
The Journal of Machine Learning Research
Year:
2003

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Abstract

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 1. An early version of this paper appeared as Bshouty and Eiron (2001).