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arXiv · 1911.07357

Random Restrictions of High-Dimensional Distributions and Uniformity Testing with Subcube Conditioning

Clément L. Canonne·Xi Chen·Gautam Kamath·Amit Levi·Erik Waingarten
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Abstract

We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)). The key technical component is a natural notion of random restriction for distributions on $\{-1,1\}^n$, and a quantitative analysis of how such a restriction affects the mean vector of the distribution. Along the way, we consider the problem of mean testing with independent samples and provide a nearly-optimal algorithm.

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Clément L. Canonne, Xi Chen, Gautam Kamath, Amit Levi, Erik Waingarten. 2019-11-17. Random Restrictions of High-Dimensional Distributions and Uniformity Testing with Subcube Conditioning. https://arxiv.org/abs/1911.07357

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