Machine Learning

, Volume 30, Issue 1, pp 7–21 | Cite as

PAC Learning Axis-aligned Rectangles with Respect to Product Distributions from Multiple-Instance Examples

  • Philip M. Long
  • Lei Tan


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 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 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 (d5 n12/∈20 log2 nd/∈δ time.

PAC learning multiple-instance examples axis-aligned hyperrectangles 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Philip M. Long
    • 1
  • Lei Tan
    • 2
  1. 1.ISCS DepartmentNational University of SingaporeSingaporeRepublic of Singapore. E-mail
  2. 2.Redmond

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