Sharp Bounds for Generalized Uniformity Testing
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Sharp Bounds for Generalized Uniformity Testing
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 $mathbf{Omega}$, we want to distinguish, with probability at least $2/3$, between the case that $p$ is uniform on some {em subset} of $mathbf{Omega}$ versus $epsilon$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 informationtheoretic lower bound. Specifically, we show that the sample complexity of generalized uniformity testing is $Thetaleft(1/(epsilon^{4/3}p_3) + 1/(epsilon^{2} p_2) right)$.
Sharp Bounds for Generalized Uniformity Testing
by Ilias Diakonikolas, Daniel M. Kane, Alistair Stewart
https://arxiv.org/pdf/1709.02087v1.pdf
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