Improved Bounds for High-Dimensional Equivalence and Product Testing Using Subcube Queries
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.
Distribution testing
conditional sampling
sub-cube sampling
Theory of computation~Streaming, sublinear and near linear time algorithms
48:1-48:21
RANDOM
Tomer
Adar
Tomer Adar
Technion - Israel Institute of Technology, Haifa, Israel
https://orcid.org/0009-0004-2371-1339
Eldar
Fischer
Eldar Fischer
Technion - Israel Institute of Technology, Haifa, Israel
Research supported by an Israel Science Foundation grant number 879/22.
Amit
Levi
Amit Levi
University of Haifa, Israel
https://orcid.org/0000-0002-8530-5182
10.4230/LIPIcs.APPROX/RANDOM.2024.48
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Tomer Adar, Eldar Fischer, and Amit Levi
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