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

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

11 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

@article{63c1fcd92a8b4233a6ddf174d03c619b,

title = "Learning convex polytopes with margin",

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.",

author = "Gottlieb, \{Lee Ad\} and Eran Kaufman and Gabriel Nivasch and Aryeh Kontorovich",

note = "Publisher Copyright: {\textcopyright} 2018 Curran Associates Inc.All rights reserved.; 32nd Conference on Neural Information Processing Systems, NeurIPS 2018 ; Conference date: 02-12-2018 Through 08-12-2018",

year = "2018",

month = jan,

day = "1",

language = "English",

volume = "2018-December",

pages = "5706--5716",

journal = "Advances in Neural Information Processing Systems",

issn = "1049-5258",

publisher = "Neural information processing systems foundation",

}

TY - JOUR

T1 - Learning convex polytopes with margin

AU - Gottlieb, Lee Ad

AU - Kaufman, Eran

AU - Nivasch, Gabriel

AU - Kontorovich, Aryeh

PY - 2018/1/1

Y1 - 2018/1/1

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.

UR - https://www.scopus.com/pages/publications/85064821051

M3 - Conference article

AN - SCOPUS:85064821051

SN - 1049-5258

VL - 2018-December

SP - 5706

EP - 5716

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

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

Other files and links

Fingerprint

Cite this