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Equivalence Testing: The Power of Bounded Adaptivity.
Diptarka Chakraborty, Sourav Chakraborty, Gunjan Kumar and Kuldeep S. Meel.
In Proceedings of International Conference on Artificial Intelligence and Statistics (AISTATS), April 2024.
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful query model and has been investigated by theoreticians and practitioners alike, leading to the design of optimal algorithms albeit in a sequential setting (also referred to as adaptive tester). Given the profound impact of parallel computing over the past decades, there has been a strong desire to design algorithms that enable high parallelization. Despite significant algorithmic advancements over the last decade, parallelizable techniques (also termed non-adaptive testers) have $\TildeO(łog^12n)$ query complexity, a prohibitively large complexity to be of practical usage. Therefore, the primary challenge is whether it is possible to design algorithms that enable high parallelization while achieving efficient query complexity. Our work provides an affirmative answer to the aforementioned challenge: we present a highly parallelizable tester with a query complexity of $\TildeO(łog n)$, achieved through a single round of adaptivity, marking a significant stride towards harmonizing parallelizability and efficiency in equivalence testing.
@inproceedings{CCKM24,
author={Chakraborty, Diptarka and Chakraborty, Sourav and Kumar, Gunjan and Meel, Kuldeep S.},
title={ Equivalence Testing: The Power of Bounded Adaptivity},
abstract={ Equivalence testing, a fundamental problem
in the field of distribution testing,
seeks to infer if two unknown distributions
on $[n]$ are the same or far apart in the
total variation distance. Conditional
sampling has emerged as a powerful query
model and has been investigated by
theoreticians and practitioners alike,
leading to the design of optimal algorithms
albeit in a sequential setting (also
referred to as adaptive tester).
Given the profound impact of parallel
computing over the past decades, there has been a
strong desire to design algorithms that
enable high parallelization. Despite
significant algorithmic advancements over
the last decade, parallelizable techniques
(also termed non-adaptive testers) have
$\Tilde{O}(\log^{12}n)$ query complexity, a
prohibitively large complexity to be of
practical usage.
Therefore, the primary challenge is whether
it is possible to design algorithms that
enable high parallelization while achieving
efficient query complexity.
Our work provides an affirmative answer to
the aforementioned challenge: we present a
highly parallelizable tester with a query
complexity of $\Tilde{O}(\log n)$, achieved
through a single round of adaptivity,
marking a significant stride towards
harmonizing parallelizability and
efficiency in equivalence testing.},
year={2024},
month=apr,
booktitle=AISTATS,
bib2html_pubtype={Refereed Conference},
bib2html_rescat={Distribution Testing},
bib2html_dl_pdf={https://arxiv.org/abs/2403.04230.pdf},
}
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