Editing Open Problems:86
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{{Header | {{Header | ||
+ | |title=Equivalence testing lower bound via communication complexity | ||
|source=focs17 | |source=focs17 | ||
|who=Clément Canonne | |who=Clément Canonne | ||
}} | }} | ||
− | Blais, Canonne, and Gur {{cite|BlaisCG-17}} recently described a reduction technique to obtain distribution testing lower bounds from communication complexity (specifically, even from the simultaneous message-passing (SMP) setting in communication complexity). Using this technique, which is the analogue of the | + | Blais, Canonne, and Gur {{cite|BlaisCG-17}} recently described a reduction technique to obtain distribution testing lower bounds from communication complexity (specifically, even from the simultaneous message-passing (SMP) setting in communication complexity). Using this technique, which is the analogue of the "usual property testing" framework of Blais, Brody, and Matulef {{cite|BlaisBM-12}}, they prove and (re)-derive lower bounds for many of the standard distribution testing questions, including ''identity testing'' (and ''instance-specific'' identity testing — see [[Instance-specific Hellinger testing|this other open problem]]). |
− | + | Can one use this framework to re-establish an $\tilde{\Omega}}(n^{2/3})$ sample complexity lower bound for ''equivalence'' testing (a.k.a. closeness testing; where now both distributions are unknown, instead of one known and one unknown, available through sample access)? If so, can it yield some sort of ''instance-specific'' equivalence testing lower bound? | |
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− | Can one use |