报告人：张慧铭（澳门大学）
报告时间：2021年11月13日星期六10:00-11:00
报告地点：腾讯会议ID：206 921 047
摘要：
In statistical machine learning, variance-like parameters for popular-used sub-classic distributions aim to identify some high probability event with constants-specified and data-dependent probability bounds for small sample size. Directly estimating the variance-like parameters based on empirical MGF is a non-convex problem with multiple possible solutions. To handle this challenging problem, we proposed a new definition of sub-R norms for studying concentration of sub-R distributions by maximizing a series of normalized higher-moments, borrowing insights from GANs and GMM. As essential cases, the proposed sub-Gaussian and -exponential norms could not only recover exponential upper bounds in their original MGF definitions, but also could construct tight Hoeffding- and Bernstein-type concentration inequalities for sum of independent random variables. For independent non-identically distributed data, it is easy to estimate the sub-R norms robustly and consistently by median-of-mean estimators. We also obtain tighter concentration inequalities for the function (includes general norms, suprema of unbounded empirical processes) of random vectors based on the sub-R norms, we also apply the results to study the Wasserstein distance concentration for empirical measures of unbounded data. The applications vary from the non-asymptotical excess risk bounds for learning under Lipschitz losses, the multi-armed bandit analysis by bootstrapped upper confidence bound in reinforcement learning, and the estimation of bounds on the Rademacher complexity and excess risk for learning under deep neural networks.
报告人简介：
张慧铭，澳门大学濠江学者博士后、珠海澳门大学科技研究院助理研究员。于华中师范大学获得学士（2009-2013）和硕士（2013-2016）学位；于北京大学获得统计学博士学位（2016-2020）。研究方向为高维统计、机器学习理论、函数型数据、经验过程与高维概率论等。曾在Journal of the American Statistical Association，Insurance: Mathematics and Economics，Statistica Sinica，Journal of Complexity等国际学术权威期刊上发表论文，其中一篇论文为WOS高被引论文。曾获奖励有：国家奖学金（硕、博）、北大校长奖学金、BICMR北大数学研究生奖学金、湖北省优秀学士论文等。
邀请人：张园园