Difference between revisions of "Open Problems:86"
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Recall that the ''equivalence'' testing problem (also known as closeness testing) is the generalization of identity testing where, instead of having a known reference distribution $q$ and access to samples from an unknown $p$, now both distributions are unknown and only available via samples. | Recall that the ''equivalence'' testing problem (also known as closeness testing) is the generalization of identity testing where, instead of having a known reference distribution $q$ and access to samples from an unknown $p$, now both distributions are unknown and only available via samples. | ||
| − | Can one use the {{cite|BlaisCG-17}} framework to re-establish an $\tilde{\Omega}(n^{2/3})$ sample complexity lower bound for | + | Can one use the {{cite|BlaisCG-17}} framework to re-establish an $\tilde{\Omega}(n^{2/3})$ sample complexity lower bound for equivalence testing? If so, can it yield some sort of ''instance-specific'' equivalence testing lower bound, for some meaningful notion of "instance-specific"? |
Revision as of 22:09, 25 October 2017
| Suggested by | Clément Canonne |
|---|---|
| Source | FOCS 2017 |
| Short link | https://sublinear.info/86 |
Blais, Canonne, and Gur [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 [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 this other open problem).
Recall that the equivalence testing problem (also known as closeness testing) is the generalization of identity testing where, instead of having a known reference distribution $q$ and access to samples from an unknown $p$, now both distributions are unknown and only available via samples.
Can one use the [BlaisCG-17] framework to re-establish an $\tilde{\Omega}(n^{2/3})$ sample complexity lower bound for equivalence testing? If so, can it yield some sort of instance-specific equivalence testing lower bound, for some meaningful notion of "instance-specific"?
