Tight Lower Bound on Equivalence Testing in Conditional Sampling Model
Document Type
Conference Article
Publication Title
Proceedings of the Annual ACM SIAM Symposium on Discrete Algorithms
Abstract
We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on [n] are equal or ε-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS, SICOMP15) wherein a tester can get a sample from the distribution conditioned on any subset. Equivalence testing is a central problem in distribution testing, and there has been a plethora of work on this topic in various sampling models. Despite significant efforts over the years, there remains a gap in the current best-known upper bound of Õ(log log n) [FJOPS, COLT 2015] and lower bound of Ω(√log log n)[ACK, RANDOM 2015, Theory of Computing 2018]. Closing this gap has been repeatedly posed as an open problem (listed as problems 66 and 87 at sublinear.info). In this paper, we completely resolve the query complexity of this problem by showing a lower bound of Ω̃(log log n). For that purpose, we develop a novel and generic proof technique that enables us to break the √log log n barrier, not only for the equivalence testing problem but also for other distribution testing problems, such as uniblock property.
First Page
4371
Last Page
4394
DOI
10.1137/1.9781611977912.153
Publication Date
1-1-2024
Recommended Citation
Chakraborty, Diptarka; Chakraborty, Sourav; and Kumar, Gunjan, "Tight Lower Bound on Equivalence Testing in Conditional Sampling Model" (2024). Conference Articles. 903.
https://digitalcommons.isical.ac.in/conf-articles/903
Comments
Open Access; Green Open Access