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Learning Boxes in High Dimension

By Amos Beimel and Eyal Kushilevitz

Abstract

We present exact learning algorithms that learn several classes of (discrete) boxes in f0; : : : ; ` \Gamma 1g n . In particular we learn: (1) The class of unions of O(log n) boxes in time poly(n; log `) (solving an open problem of [16, 12]; in [3] this class is shown to be learnable in time poly(n; `)). (2) The class of unions of disjoint boxes in time poly(n; t; log `), where t is the number of boxes. (Previously this was known only in the case where all boxes are disjoint in one of the dimensions; in [3] this class is shown to be learnable in time poly(n; t; `)). In particular our algorithm learns the class of decision trees over n variables, that take values in f0; : : : ; ` \Gamma 1g, with comparison nodes in time poly(n; t; log `), where t is the number of leaves (this was an open problem in [9] which was shown in [4] to be learnable in time poly(n; t; `)). (3) The class of unions of O(1)-degenerate boxes (that is, boxes that depend only on O(1) variables) in time poly(n; t;..

Topics: Key words, Boxes, Discrete Geometric Objects, Decision Trees, Exact Learning, Multiplicity Automata, Hankel Matrices
Publisher: Springer
Year: 1997
OAI identifier: oai:CiteSeerX.psu:10.1.1.41.3212
Provided by: CiteSeerX
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