Thinning to improve two-sample discrepancy

Gleb Smirnov; Roman Vershynin

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arXiv · 2506.20932

Thinning to improve two-sample discrepancy

Gleb Smirnov·Roman Vershynin

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Abstract

The discrepancy between two independent samples $X_1,\dots,X_n$ and $Y_1,\dots,Y_n$ drawn from the same distribution on $\mathbb{R}^d$ typically has order $O(\sqrt{n})$ even in one dimension. We give a simple online algorithm that reduces the discrepancy to $O(\log^{2d} n)$ by discarding a small fraction of the points.

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Gleb Smirnov, Roman Vershynin. 2025-06-26. Thinning to improve two-sample discrepancy. https://arxiv.org/abs/2506.20932

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