License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2017.10
URN: urn:nbn:de:0030-drops-75390
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7539/
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De, Anindya ; Mossel, Elchanan ; Neeman, Joe

Noise Stability Is Computable and Approximately Low-Dimensional

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LIPIcs-CCC-2017-10.pdf (0.5 MB)

Abstract

Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions of R^n for n >= 1 to k parts with given Gaussian measures mu_1, ..., mu_k. We call a partition epsilon-optimal, if its noise stability is optimal up to an additive epsilon. In this paper, we give an explicit, computable function n(epsilon) such that an epsilon-optimal partition exists in R^{n(epsilon)}. This result has implications for the computability of certain problems in non-interactive simulation, which are addressed in a subsequent work.

BibTeX - Entry

@InProceedings{de_et_al:LIPIcs:2017:7539,
  author =	{Anindya De and Elchanan Mossel and Joe Neeman},
  title =	{{Noise Stability Is Computable and Approximately Low-Dimensional}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{10:1--10:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{Ryan O'Donnell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7539},
  URN =		{urn:nbn:de:0030-drops-75390},
  doi =		{10.4230/LIPIcs.CCC.2017.10},
  annote =	{Keywords: Gaussian noise stability; Plurality is stablest; Ornstein Uhlenbeck operator}
}

Keywords: Gaussian noise stability; Plurality is stablest; Ornstein Uhlenbeck operator
Collection: 32nd Computational Complexity Conference (CCC 2017)
Issue Date: 2017
Date of publication: 01.08.2017

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