eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-09-16
48:1
48:21
10.4230/LIPIcs.APPROX/RANDOM.2024.48
article
Improved Bounds for High-Dimensional Equivalence and Product Testing Using Subcube Queries
Adar, Tomer
1
https://orcid.org/0009-0004-2371-1339
Fischer, Eldar
1
Levi, Amit
2
https://orcid.org/0000-0002-8530-5182
Technion - Israel Institute of Technology, Haifa, Israel
University of Haifa, Israel
We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for n-dimensional distributions that is quasi-linear in n, improving the previously known Õ(n²/ε²) query complexity bound to Õ(n/ε²). We extend this result to general finite alphabets with logarithmic cost in the alphabet size.
By exploiting the specific structure of the queries that we use (which are more restrictive than general subcube queries), we obtain a cubic improvement over the best known test for distributions over {1,…,N} under the interval querying model of Canonne, Ron and Servedio (2015), attaining a query complexity of Õ((log N)/ε²), which for fixed ε almost matches the known lower bound of Ω((log N)/log log N). We also derive a product test for n-dimensional distributions with Õ(n/ε²) queries, and provide an Ω(√n/ε²) lower bound for this property.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol317-approx-random2024/LIPIcs.APPROX-RANDOM.2024.48/LIPIcs.APPROX-RANDOM.2024.48.pdf
Distribution testing
conditional sampling
sub-cube sampling