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APPROX
2009
Springer

Baum's Algorithm Learns Intersections of Halfspaces with Respect to Log-Concave Distributions

10 years 8 months ago
Baum's Algorithm Learns Intersections of Halfspaces with Respect to Log-Concave Distributions
In 1990, E. Baum gave an elegant polynomial-time algorithm for learning the intersection of two origin-centered halfspaces with respect to any symmetric distribution (i.e., any D such that D(E) = D(−E)) [3]. Here we prove that his algorithm also succeeds with respect to any mean zero distribution D with a log-concave density (a broad class of distributions that need not be symmetric). As far as we are aware, prior to this work, it was not known how to efficiently learn any class of intersections of halfspaces with respect to log-concave distributions. The key to our proof is a “Brunn-Minkowski” inequality for log-concave densities that may be of independent interest.
Adam R. Klivans, Philip M. Long, Alex K. Tang
Added 25 May 2010
Updated 25 May 2010
Type Conference
Year 2009
Where APPROX
Authors Adam R. Klivans, Philip M. Long, Alex K. Tang
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