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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 $epsilon$.
This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons. Given a collection of $n$ items and a few pairwise comparisons across them, one wishes to identify the set of $K$ items that receive the highest ranks. To tackle t
We study the problem of testing identity against a given distribution with a focus on the high confidence regime. More precisely, given samples from an unknown distribution $p$ over $n$ elements, an explicitly given distribution $q$, and parameters $
A centrally differentially private algorithm maps raw data to differentially private outputs. In contrast, a locally differentially private algorithm may only access data through public interaction with data holders, and this interaction must be a di
Unmanned aerial vehicles (UAVs) are expected to be an integral part of wireless networks, and determining collision-free trajectories for multiple UAVs while satisfying requirements of connectivity with ground base stations (GBSs) is a challenging ta
In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best known eff