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Exact statistical inference for the Wasserstein distance by selective inference

Author

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  • Vo Nguyen Le Duy

    (Nagoya Institute of Technology
    RIKEN)

  • Ichiro Takeuchi

    (RIKEN
    Nagoya University)

Abstract

In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of them are based on asymptotic approximation and do not have finite-sample validity. In this study, we propose an exact (non-asymptotic) inference method for the Wasserstein distance inspired by the concept of conditional selective inference (SI). To our knowledge, this is the first method that can provide a valid confidence interval (CI) for the Wasserstein distance with finite-sample coverage guarantee, which can be applied not only to one-dimensional problems but also to multi-dimensional problems. We evaluate the performance of the proposed method on both synthetic and real-world datasets.

Suggested Citation

  • Vo Nguyen Le Duy & Ichiro Takeuchi, 2023. "Exact statistical inference for the Wasserstein distance by selective inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 127-157, February.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:1:d:10.1007_s10463-022-00837-3
    DOI: 10.1007/s10463-022-00837-3
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    References listed on IDEAS

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    2. del Barrio, Eustasio & Gordaliza, Paula & Lescornel, Hélène & Loubes, Jean-Michel, 2019. "Central limit theorem and bootstrap procedure for Wasserstein’s variations with an application to structural relationships between distributions," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 341-362.
    3. Ryan J. Tibshirani & Jonathan Taylor & Richard Lockhart & Robert Tibshirani, 2016. "Exact Post-Selection Inference for Sequential Regression Procedures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 600-620, April.
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