“Exact Statistical Inference for the Wasserstein Distance by Selective Inference”
September 7, 2022 | Time 11:00am CET
The Wasserstein distance (WD), which is a metric used to compare the probability distributions, has attracted significant attention and is being used more and more in statistics and machine learning. When the WD calculated from noisy data is used for various decision-making problems, it is necessary to quantify its statistical reliability, e.g., in the form of confidence interval (CI). 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 WD inspired by the concept of conditional Selective Inference (SI). We will show that, by conditioning on the optimal coupling, the exact sampling distribution of the WD can be derived, which enables us to construct CI that has finite-sample coverage guarantee.
Vo Nguyen Le Duy is currently a PhD student at Nagoya Institute of Technology and Junior Research Associate at RIKEN Center for Advanced Intelligence Project, Japan. He received the B.S. degree from the Danang University of Science and Technology, Vietnam, in 2017. After that, he received the M.S. degree from Nagoya Institute of Technology, Japan,in 2020. His research interests include machine learning, data mining, and statistical data analysis.