LIPIcs.APPROX-RANDOM.2024.48.pdf
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Improved Bounds for High-Dimensional Equivalence and Product Testing Using Subcube Queries
Authors
Tomer Adar 
,
Amit Levi
-
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-16
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Tomer Adar, Eldar Fischer, and Amit Levi. Improved Bounds for High-Dimensional Equivalence and Product Testing Using Subcube Queries. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 48:1-48:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.48
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.48
Abstract
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.
Subject Classification
ACM Subject Classification
- Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
- Distribution testing
- conditional sampling
- sub-cube sampling
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