Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms. Berrett, T. B. & Butucea, C. CoRR, 2020. To appear in NeurIPS'20.[BB20] Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\mathbf{q}$ (while the other two works focus on the worst-case $\mathbf{q}$, i.e., the uniform distribution).
bibtex @article{BB20,
title={Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms},
author={Thomas B. Berrett and Cristina Butucea},
journal = {CoRR},
year={2020},
volume = {abs/2005.12601},
note = {To appear in {NeurIPS'20}.},
bibbase_note = {<div class="well well-small bibbase"><span class="bluecite">[BB20]</span> Obtains, among others, a tight lower bound for identity testing (goodness-of-fit) under local privacy. This lower bound applies to sequentially interactive protocols, and is slightly more general than those of [AJM20,ACLST20] for the same problem, in that it provides an explicit dependence on the reference distribution $\mathbf{q}$ (while the other two works focus on the worst-case $\mathbf{q}$, i.e., the uniform distribution).</div>}
}
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