TY - GEN

T1 - Testing non-uniform k-wise independent distributions over product spaces

AU - Rubinfeld, Ronitt

AU - Xie, Ning

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955324035&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-14165-2_48

DO - 10.1007/978-3-642-14165-2_48

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:77955324035

SN - 3642141641

SN - 9783642141645

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 565

EP - 581

BT - Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings

T2 - 37th International Colloquium on Automata, Languages and Programming, ICALP 2010

Y2 - 6 July 2010 through 10 July 2010

ER -