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

Electronic Colloquium on Computational Complexity (ECCC), pp. 1652019.

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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\...More

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