Learning convex polytopes with margin

Lee Ad Gottlieb; Eran Kaufman; Gabriel Nivasch; Aryeh Kontorovich

Learning convex polytopes with margin

Lee Ad Gottlieb, Eran Kaufman, Gabriel Nivasch, Aryeh Kontorovich

Department of Computer Science

Research output: Contribution to journal › Conference article › peer-review

10 Scopus citations

Abstract

We present an improved algorithm for properly learning convex polytopes in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polytope as an intersection of about t log t halfspaces with margins in time polynomial in t (where t is the number of halfspaces forming an optimal polytope). We also identify distinct generalizations of the notion of margin from hyperplanes to polytopes and investigate how they relate geometrically; this result may be of interest beyond the learning setting.

Original language	English
Pages (from-to)	5706-5716
Number of pages	11
Journal	Advances in Neural Information Processing Systems
Volume	2018-December
State	Published - 1 Jan 2018
Event	32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: 2 Dec 2018 → 8 Dec 2018

ASJC Scopus subject areas

Computer Networks and Communications
Information Systems
Signal Processing

Cite this

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N2 - We present an improved algorithm for properly learning convex polytopes in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polytope as an intersection of about t log t halfspaces with margins in time polynomial in t (where t is the number of halfspaces forming an optimal polytope). We also identify distinct generalizations of the notion of margin from hyperplanes to polytopes and investigate how they relate geometrically; this result may be of interest beyond the learning setting.

AB - We present an improved algorithm for properly learning convex polytopes in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polytope as an intersection of about t log t halfspaces with margins in time polynomial in t (where t is the number of halfspaces forming an optimal polytope). We also identify distinct generalizations of the notion of margin from hyperplanes to polytopes and investigate how they relate geometrically; this result may be of interest beyond the learning setting.

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SN - 1049-5258

VL - 2018-December

SP - 5706

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T2 - 32nd Conference on Neural Information Processing Systems, NeurIPS 2018

Y2 - 2 December 2018 through 8 December 2018

ER -

Learning convex polytopes with margin

Abstract

ASJC Scopus subject areas

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