题目：Statistical Analysis of Conditional Group Distributionally Robust Optimization with Cross-Entropy Loss

报告人：郭子剑 教授（浙江大学）

地点：致远楼108室

时间: 2025年9月29日 10:30-11:30

Abstract：

In multi-source learning with discrete labels, distributional heterogeneity across domains poses a central challenge to developing predictive models that transfer reliably to unseen domains. We study multi-source unsupervised domain adaptation, where labeled data are available from multiple source domains and only unlabeled data from a target domain. To address potential distribution shifts, we propose a novel {\bf C}onditional {\bf G}roup {\bf D}istributionally {\bf R}obust {\bf O}ptimization (CG-DRO) framework that learns a classifier by minimizing the worst-case cross-entropy loss over the convex combinations of the conditional outcome distributions from the sources. We develop an efficient Mirror Prox algorithm for solving the minimax problem and employ a double machine learning procedure to estimate the risk function, ensuring that errors in nuisance estimation contribute only at higher-order rates.

We establish fast statistical convergence rates for the empirical CG-DRO estimator by constructing two surrogate minimax optimization problems that serve as theoretical bridges. A distinguishing challenge for CG-DRO is the emergence of nonstandard asymptotics: the empirical CG-DRO estimator may fail to converge to a standard limiting distribution due to boundary effects and system instability. To address this, we introduce a perturbation-based inference procedure that enables uniformly valid inference, including confidence interval construction and hypothesis testing.

报告人简介: 郭子剑，浙江大学求是讲席教授、博士生导师。2012年香港中文大学学士，2017年宾夕法尼亚大学统计学博士，师从著名统计学家、COPSS奖获得者蔡天文教授。2017—2025年于美国罗格斯大学统计系任教，历任助理教授、终身副教授，并于2025年回国加入浙江大学数据科学研究中心。主要研究方向为因果推断、高维统计、多源学习与分布鲁棒优化、非常规统计推断及优化—统计交叉方法，强调在异质性与分布漂移条件下的稳健学习与推断，应用于健康与遗传学等领域。研究成果发表于 Annals of Statistics 、Journal of the Royal Statistical Society – Series B、Cell Genomics、Journal of the American Statistical Association、Journal of Machine Learning Research、Biometrika、Journal of Econometrics 等顶级期刊。入选国家高层次人才计划，获 ICSA Outstanding Young Researcher Award 与 Bernoulli Society Young Researcher Award 荣誉提名（Honorable Mention）。担任 Journal of the American Statistical Association（Theory and Methods）与 TEST 等权威学术期刊编委。

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