Thinning to improve two-sample discrepancy

Q: What type of study is this?

This is a Quantitative Study study.

Gleb Smirnov; Roman Vershynin

doi:10.48550/arxiv.2506.20932

June 26, 2025Open Access

Thinning to improve two-sample discrepancy

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Key Points

Discrepancy is reduced from O(√n) to O(log²n) by removing points, enhancing performance.
The algorithm provided simplifies the process of managing discrepancies in sampling, proving effective in higher dimensions.
An online algorithm operates in real-time, effectively adjusting sample sizes as new data comes in, optimizing results.
The study's findings indicate that applying this technique can have significant implications for data sampling practices.

Implication

The online algorithm reduces discrepancy to O(log²n) in independent samples, suggesting improved efficiency.

Abstract

The discrepancy between two independent samples \(X_1,,X_n\) and \(Y_1,,Y_n\) drawn from the same distribution on Rᵈ typically has order \(O(√n)\) even in one dimension. We give a simple online algorithm that reduces the discrepancy to \(O(log²ᵈ n)\) by discarding a small fraction of the points.

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Cite This Study

Smirnov et al. (2025) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e636 https://doi.org/10.48550/arxiv.2506.20932

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Thinning to improve two-sample discrepancy

Key Points

Implication

Abstract

Discussion

Cite This Study

Thinning to improve two-sample discrepancy

Key Points

Implication

Abstract

Discussion

Cite This Study

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