PAC Learning Axis-aligned Rectangles with Respect to Product Distributions from Multiple-Instance Examples Article DOI :
10.1023/A:1007450326753

Cite this article as: Long, P.M. & Tan, L. Machine Learning (1998) 30: 7. doi:10.1023/A:1007450326753
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Abstract We describe a polynomial-time algorithm for learning axis-aligned rectangles in Q^{d} with respect to product distributions from multiple-instance examples in the PAC model. Here, each example consists of n elements of Q^{d} 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 Q^{d} 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 ∈ with probability 1- δ in O (d^{5} n^{12} /∈^{20} log^{2} nd/∈δ time.

PAC learning multiple-instance examples axis-aligned hyperrectangles

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© Kluwer Academic Publishers 1998

Authors and Affiliations 1. ISCS Department National University of Singapore Singapore Republic of Singapore. E-mail 2. Redmond