Exact Statistical Inference for the Wasserstein Distance by Selective Inference

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