2021/09/29 by Vo Nguyen Le Duy, Ichiro Takeuchi, Duy, Vo Nguyen Le +1 · 1 citation
Computer Science · Engineering · Mathematics · #Algorithm #Anomaly Detection Techniques and Applications #Applied mathematics #Artificial intelligence #Computer science #Confidence interval #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Geometric Analysis and Curvature Flows #Inference #Interval (graph theory) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine learning #Mathematics #Sample (material) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #Statistical inference #Statistics #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2109.14206
openalex publication_date 2021/09/29 · arxiv created 2022/01/20 · arxiv updated 2022/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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