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Abstract
Samplers are the backbone of the implementations of any randomized algorithm. Unfortunately, obtaining an efficient algorithm to test the correctness of samplers is very hard to find. Recently, in a series of works, testers like Barbarik, Teq, Flash for testing of some particular kinds of samplers, like CNF-samplers and Horn-samplers, were obtained. However, their techniques have a significant limitation because one can not expect to use their methods to test for other samplers, such as perfect matching samplers or samplers for sampling linear extensions in posets. In this paper, we present a new testing algorithm that works for such samplers and can estimate the distance of a new sampler from a known sampler (say, the uniform sampler). Testing the identity of distributions is the heart of testing the correctness of samplers. This paper's main technical contribution is developing a new distance estimation algorithm for distributions over high-dimensional cubes using the recently proposed subcube conditioning sampling model. Given subcube conditioning access to an unknown distribution P, and a known distribution Q defined over an n-dimensional Boolean hypercube, our algorithm CubeProbeEst estimates the variation distance between P and Q within additive error using subcube conditional samples from P. Following the testing-via-learning paradigm, we also get a tester that distinguishes between the cases when P and Q are close or far in variation distance with high probability using subcube conditional samples. This estimation algorithm CubeProbeEst in the subcube conditioning sampling model helps us to design the first tester for self-reducible samplers. The correctness of the tester is formally proved. Moreover, we implement CubeProbeEst to test the quality of three samplers for sampling linear extensions in posets.
Original language | English |
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Title of host publication | Proceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence |
Publisher | AAAI Press |
Pages | 7952-7960 |
Number of pages | 9 |
ISBN (Print) | 9781577358879, 1577358872 |
DOIs | |
Publication status | Published - 24 Mar 2024 |
Event | The 38th Annual AAAI Conference on Artificial Intelligence - Vancouver Convention Centre – West Building, Vancouver, Canada Duration: 20 Feb 2024 → 27 Feb 2024 https://aaai.org/aaai-conference/ |
Publication series
Name | Proceedings of the AAAI Conference on Artificial Intelligence |
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Publisher | AAAI |
Number | 8 |
Volume | 38 |
ISSN (Print) | 2159-5399 |
ISSN (Electronic) | 2374-3468 |
Conference
Conference | The 38th Annual AAAI Conference on Artificial Intelligence |
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Abbreviated title | AAAI-24 |
Country/Territory | Canada |
City | Vancouver |
Period | 20/02/24 → 27/02/24 |
Internet address |
Bibliographical note
Acknowledgments:Rishiraj Bhattacharyya acknowledges the support of UKRI by EPSRC grant number EP/Y001680/1. Uddalok Sarkar is supported by the Google PhD Fellowship. Sayantan Sen’s research is supported by the National Research Foundation Singapore under its NRF Fellowship Programme (NRFNRFFAI1- 2019-0002). This research is part of the programme DesCartes and is supported by the National Research Foundation, Prime Minister’s Office, Singapore, under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. The computational works of this article were performed on the resources of the National Supercomputing Centre, Singapore www.nscc.sg.
Keywords
- CSO: Solvers and Tools
- RU: Other Foundations of Reasoning under Uncertainty
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Subcube Conditional Samples and Testing Properties of Probability Distributions
Bhattacharyya, R. (Principal Investigator)
Engineering & Physical Science Research Council
1/12/23 → 30/11/25
Project: Research Councils