Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time

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

Researchers

Research units

  • Aalto University

Abstract

We derandomize G. Valiant's [J.ACM 62(2015) Art.13] subquadratic-time algorithm for finding outlier correlations in binary data. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiant's randomized algorithm, but the precise constants we save over quadratic scaling are more modest. Our main technical tool for derandomization is an explicit family of correlation amplifiers built via a family of zigzag-product expanders in Reingold, Vadhan, and Wigderson [Ann. of Math 155(2002), 157-187]. We say that a function f:{-1,1}^d ->{-1,1}^D is a correlation amplifier with threshold 0 <= tau <= 1, error gamma >= 1, and strength p an even positive integer if for all pairs of vectors x,y in {-1,1}^d it holds that (i) |<x,y>|<tau d implies |<f(x),f(y)>| <= (tau*gamma)^p*D; and (ii) |<x,y>| >= tau*d implies (<x,y>/gamma^d})^p*D <= <f(x),f(y)> <= (gamma*<x,y>/d)^p*D.

Details

Original languageEnglish
Title of host publication24th Annual European Symposium on Algorithms
Subtitle of host publicationESA 2016, August 22–24, 2016, Aarhus, Denmark
EditorsPiotr Sankowski, Christos Zaroliagis
Publication statusPublished - 22 Aug 2016
MoE publication typeA4 Article in a conference publication
EventEuropean Symposium on Algorithms - Aarhus University, Aarhus, Denmark
Duration: 22 Aug 201624 Aug 2016
Conference number: 24
http://conferences.au.dk/algo16/algo-frontpage/

Publication series

NameLeibniz International Proceedings in Informatics
PublisherSchloss Dagstuhl – Leibniz-Zentrum für Informatik GmbH, Dagstuhl Publishing
Volume57
ISSN (Electronic)1868-8969

Conference

ConferenceEuropean Symposium on Algorithms
Abbreviated titleESA
CountryDenmark
CityAarhus
Period22/08/201624/08/2016
Internet address

    Research areas

  • correlation, derandomization, outlier, similarity search, expander graph

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