Testing non-uniform k-wise independent distributions over product spaces

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

Abstract

A distribution D over ∑1×⋯×∑ n is called (non-uniform) k-wise independent if for any set of k indices {i 1, ..., i k } and for any , . We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al. [1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Pages565-581
Number of pages17
EditionPART 1
DOIs
StatePublished - 2010
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: 6 Jul 201010 Jul 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6198 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference37th International Colloquium on Automata, Languages and Programming, ICALP 2010
Country/TerritoryFrance
CityBordeaux
Period6/07/1010/07/10

Fingerprint

Dive into the research topics of 'Testing non-uniform k-wise independent distributions over product spaces'. Together they form a unique fingerprint.

Cite this