PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples

Abstract

We describe a polynomial-time algorithm for learning axis-aligned rectangles in Qd with respect to product distributions from multiple-instance examples in the PAC model. Here, each example consists of n elements of Qd together with a label indicating whether any of the n points is in the rectangle to be learned. We assume that there is an unknown product distribution D over Qd such that all instances are independently drawn according to D. The accuracy of a hypothesis is measured by the probability that it would incorrectly predict whether one of n more points drawn from D was in the rectangle to be learned. Our algorithm achieves accuracy ε with probability 1-δ in O(d5n12/ε20 log2 nd/εδ) time.