On the hardness of learning intersections of two halfspaces

Subhash Khot, Rishi Saket

Research output: Contribution to journalArticle

Abstract

We show that unless NP = RP, it is hard to (even) weakly PAC-learn intersection of two halfspaces in Rn using a hypothesis which is a function of up to ℓ halfspaces (linear threshold functions) for any integer ℓ. Specifically, we show that for every integer ℓ and an arbitrarily small constant ε>0, unless NP = RP, no polynomial time algorithm can distinguish whether there is an intersection of two halfspaces that correctly classifies a given set of labeled points in Rn, or whether any function of ℓ halfspaces can correctly classify at most 12+ε fraction of the points.

Original languageEnglish (US)
Pages (from-to)129-141
Number of pages13
JournalJournal of Computer and System Sciences
Volume77
Issue number1
DOIs
StatePublished - Jan 2011

Fingerprint

Half-space
Hardness
Intersection
Classify
Threshold Function
Integer
Polynomials
Linear Function
Polynomial-time Algorithm
Learning

Keywords

  • Approximation
  • Halfspaces
  • Hardness
  • Learning

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

On the hardness of learning intersections of two halfspaces. / Khot, Subhash; Saket, Rishi.

In: Journal of Computer and System Sciences, Vol. 77, No. 1, 01.2011, p. 129-141.

Research output: Contribution to journalArticle

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