题目：Convergence and Concentration of Empirical Measures under Wasserstein Distance

主讲人：卡耐基梅隆大学统计系 雷径副教授

主持人：西南财经大学统计学院 常晋源教授

时间：2019年5月30日（星期四）10:30-11:30

地点：西南财经大学光华校区光华楼1007会议室

报告摘要：

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization can cover Euclidean spaces with large dimensionality, with the optimal dependence on the dimensionality. Our method also covers the important case of Gaussian processes in separable Hilbert spaces, with rate-optimal upper bounds for functional data distributions whose coordinates decay geometrically or polynomially. Moreover, our bounds of the expected value can be combined with mean-concentration results to yield improved exponential tail probability bounds for the Wasserstein error of empirical measures under Bernstein-type or log Sobolev-type conditions.

主讲人简介：

Jing Lei is an Associate Professor in the Department of Statistics at Carnegie Mellon University. He completed his undergraduate studies at Beijing University in 2005 and received PhD in statistics at University of California, Berkeley, in 2010. His main research interest includes model-free predictive inference, network data analysis, high dimensional multivariate analysis, functional data analysis, sequential Monte Carlo methods and state space models. He has co-authored over 40 publications in leading journals including Nature, PNAS, JRSSB, Annals of Statistics, JASA, Biometrika and Journal of Machine Learning Research. Dr. Lei currently serves as the Associate Editor of Annals of Statistics、Statistica Sinica and Journal of the Korean Statistical Society.