机器学习与数据科学博士生系列论坛（第九十九期）—— Matrix Probability Inequalities for Martingales and Markov Chains with Applications in Statistical Learning
报告人：彭洋（色控
）
时间：2026-04-02 16:00-17:00
地点：腾讯会议：928-6293-8217
摘要：
In this talk, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal and BDG inequalities for matrix martingales, as well as matrix Bernstein inequality for ergodic Markov chains. Compared with previous work, our results assume geometric ergodicity, a condition commonly used in statistical applications. Furthermore, our results have leading terms that match the Markov chain central limit theorem, rather than relying on suboptimal variance proxies. We also give dimension-free versions of the inequalities, enabling the generalization to infinite-dimensional Hilbert spaces. Our results have extensive applications in statistics and machine learning; in particular, we obtain improved bounds in covariance estimation and principal component analysis on Markovian data.
论坛简介：该线上论坛是由张志华教授机器学习实验室组织，每两周主办一次（除了公共假期）。论坛每次邀请一位博士生就某个前沿课题做较为系统深入的介绍，主题包括但不限于机器学习、高维统计学、运筹优化和理论计算机科学。
