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• W2950216025 abstract "We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $ell_2$-norm. These problems have been extensively studied in distribution testing and sample-optimal estimators are known for them~cite{Paninski:08, CDVV14, VV14, DKN:15}. In this work, we show that the original collision-based testers proposed for these problems ~cite{GRdist:00, BFR+:00} are sample-optimal, up to constant factors. Previous analyses showed sample complexity upper bounds for these testers that are optimal as a function of the domain size $n$, but suboptimal by polynomial factors in the error parameter $epsilon$. Our main contribution is a new tight analysis establishing that these collision-based testers are information-theoretically optimal, up to constant factors, both in the dependence on $n$ and in the dependence on $epsilon$." @default.
• W2950216025 created "2019-06-27" @default.
• W2950216025 creator A5054966819 @default.
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• W2950216025 date "2016-11-11" @default.
• W2950216025 modified "2023-09-27" @default.
• W2950216025 title "Collision-based Testers are Optimal for Uniformity and Closeness" @default.
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