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 such that ) [3]. Here we prove that his algorithm also succeeds with respect to any mean zero distribution 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. © 2009 Springer.
CITATION STYLE
Klivans, A. R., Long, P. M., & Tang, A. K. (2009). Baum’s algorithm learns intersections of halfspaces with respect to log-concave distributions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5687 LNCS, pp. 588–600). https://doi.org/10.1007/978-3-642-03685-9_44
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