讲座题目：From Sub-Gaussian Non-asymptotic Inference to Robust Statistical Learning under Infinite Variance

讲座内容：In non-asymptotic statistical inferences, the variance-type parameters of sub-Gaussian distributions are of paramount importance. However, directly estimating these parameters using the empirical moment generating function is infeasible. To address this, we suggest using the sub-Gaussian intrinsic moment norm achieved by maximizing a sequence of normalized moments. In practice, we offer an intuitive method for checking sub-Gaussian data with a finite sample size using the sub-Gaussian plot. Intrinsic moment norm can be robustly estimated via a simple plug-in approach. Our theoretical findings are also applicable to the multi-armed bandit scenario.

In robust statistical learning, we thoroughly study a large family of robust statistical regressions by the proposed log-truncated M-estimator under the condition that the data have (1+ε)-th moment. With the Lipschitz conditions on the given loss functions and few moment assumptions, we obtain the excess risk bound and the consistency of various convex regressions [such as robust quantile regression and robust GLMs] as well as non-convex regressions including robust deep neural network regressions. 

报告人：张慧铭副教授，北京航空航天大学人工智能研究院

报告时间： 2023年9月17日 14：00-15：00。

报告地点：南教1-120教室；同时线上：#腾讯会议：347-5268-0550

报告人简介：

张慧铭，北航人工智能研究院的副教授(准聘)。北京大学获得统计学博士(2016-2020)；曾在澳门大学担任濠江学者博士后研究员(2020-2022)。研究方向：非渐近推断、高维概率统计、稳健估计、机器学习与深度学习理论、函数型数据等。发表SCI论文21篇(包括机器学习与人工智能领域顶刊JMLR;统计顶刊JASA,Biometrika;精算顶刊IME; 统计、数学、与物理主流刊Statistica Sinica, Journal of Complexity,和Physica Scripta等；谷歌学术引用超450次)，其中两篇为Web of Science高被引论文。主持国自科青基一项；担任美国《数学评论》评论员，SCI期刊Mathematics (Q1,中科院三区, IF=2.592)的"高维与非渐近统计专栏"客座主编。

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