Learning with Unreliable Boundary Queries

We introduce a new model for learning with membership queries in which queries near the boundary of a target concept may receive incorrect or “don’t care” responses. In partial compensation, we assume the distribution of examples has zero probability mass on the boundary region. The motivation behind this model is that the reason for the incorrect (or “don’t care”) response is that these examples are extremely rare in practice. Thus, it does not matter how the learner classifies them. We present several positive results in this new model. We show how to learn the intersection of two halfspaces when membership queries near the boundary may be answered incorrectly. Our algorithm is an extension of an algorithm of Baum [6, 5] which learns intersections of two homogeneous halfspaces in the PAC-with-membership-queries model. We also describe algorithms for learning several subclasses of monotone DNF formulas.

• Type: Conference
• Year: 1995
• Where: COLT
• Authors: Avrim Blum, Prasad Chalasani, Sally A. Goldman, Donna K. Slonim
• Keywords: Boundary Region, COLT 1995, Machine Learning, Membership Queries, Target Concept