Uniformity Testing over Hypergrids with Subcube Conditioning
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We give an algorithm for testing uniformity of distributions supported on hypergrids [m]^n, which makes Õ(poly(m)√(n)/ϵ^2) queries to a subcube conditional sampling oracle. When the side length m of the hypergrid is a constant, our algorithm is nearly optimal and strengthens the algorithm of [CCK+21] which has the same query complexity but works for hypercubes {± 1}^n only. A key technical contribution behind the analysis of our algorithm is a proof of a robust version of Pisier's inequality for functions over ℤ_m^n using Fourier analysis.
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