Learning boxes in high dimension

Amos Beimel, Eyal Kushilevitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

We present exact learning algorithms that learn several classes of (discrete) boxes in {0,..., ℓ−1}n. In particular we learn: (1) The class of unions of O(log n) boxes in time poly(n, log ℓ) (solving an open problem of [15, 11]). (2) The class of unions of disjoint boxes in time poly(n, t,log ℓ), 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 particular our algorithm learns the class of decision trees (over n variables that take values in {0,..., ℓ−1}) with comparison nodes in time poly (n, t, log ℓ), where t is the number of leaves (this was an open problem in [8] which was shown in [3] to be learnable in time poly(n, t, ℓ)). (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, log ℓ) (generalizing the learnability ofO(1)-DNF and of boxes in O(1) dimensions). The algorithm for this class uses only equivalence queries and it can also be used to learn the class of unions ofO(1) boxes (from equivalence queries only).

Original languageEnglish
Title of host publicationComputational Learning Theory - 3rd European Conference, EuroCOLT 1997, Proceedings
EditorsShai Ben-David
PublisherSpringer Verlag
Pages3-15
Number of pages13
ISBN (Print)3540626859, 9783540626855
DOIs
StatePublished - 1 Jan 1997
Externally publishedYes
Event3rd European Conference on Computational Learning Theory, EuroCOLT 1997 - Jerusalem, Israel
Duration: 17 Mar 199719 Mar 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1208
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd European Conference on Computational Learning Theory, EuroCOLT 1997
Country/TerritoryIsrael
CityJerusalem
Period17/03/9719/03/97

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