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.

在本文中，我们研究了 Wasserstein 距离的统计推断，该距离备受关注并已应用于各种机器学习任务。文献中提出了几项研究，但几乎所有研究都基于渐近近似，不具有有限样本有效性。在这项研究中，我们提出了一个精确的（非渐近的）受条件选择性推理 (SI) 概念启发的 Wasserstein 距离推理方法。据我们所知，这是第一个可以为 Wasserstein 距离提供有效置信区间 (CI) 并具有有限样本覆盖保证的方法，该方法不仅可以应用于一维问题，还可以应用于多维问题。我们评估了该方法在合成数据集和真实数据集上的性能。