Exact statistical inference for the Wasserstein distance by selective inference

Vo Nguyen Le Duy () and Ichiro Takeuchi ()
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Vo Nguyen Le Duy: Nagoya Institute of Technology
Ichiro Takeuchi: RIKEN

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 1, No 6, 127-157

Abstract: 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.

Keywords: Selective inference; Wasserstein distance; Confidence interval; Optimal transport; Uncertainty quantification (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10463-022-00837-3

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