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arXiv · 1709.02087

Sharp Bounds for Generalized Uniformity Testing

Ilias Diakonikolas·Daniel M. Kane·Alistair Stewart
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Abstract

We study the problem of generalized uniformity testing \cite{BC17} of a discrete probability distribution: Given samples from a probability distribution $p$ over an {\em unknown} discrete domain $\mathbfΩ$, we want to distinguish, with probability at least $2/3$, between the case that $p$ is uniform on some {\em subset} of $\mathbfΩ$ versus $ε$-far, in total variation distance, from any such uniform distribution. We establish tight bounds on the sample complexity of generalized uniformity testing. In more detail, we present a computationally efficient tester whose sample complexity is optimal, up to constant factors, and a matching information-theoretic lower bound. Specifically, we show that the sample complexity of generalized uniformity testing is $Θ\left(1/(ε^{4/3}\|p\|_3) + 1/(ε^{2} \|p\|_2) \right)$.

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BibTeXRIS

Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart. 2017-09-07. Sharp Bounds for Generalized Uniformity Testing. https://arxiv.org/abs/1709.02087

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