Exact Statistical Inference for the Wasserstein Distance by Selective Inference
This addresses the need for reliable uncertainty quantification in Wasserstein distance applications across machine learning, offering a non-asymptotic solution for both one-dimensional and multi-dimensional problems.
The paper tackles the problem of statistical inference for the Wasserstein distance, which lacks finite-sample validity in existing methods, by proposing an exact inference method based on conditional Selective Inference that provides valid confidence intervals with finite-sample coverage guarantees, as demonstrated on synthetic and real-world datasets.
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.