  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.
