欢迎大家参与5月21号的午餐会。报告时间是12:00-13:00，午餐于11:45开始提供。
应用数学青年讨论班(午餐会)--Localization Methods for High Dimensional Distribution Generation
报告人: 刘水根(新加坡国立大学)
时间: 2025-05-21 11:45-13:00
地点: 智华楼四元厅
摘要:In this talk, I will introduce a general strategy for sampling from high-dimensional distributions by exploiting conditional independence structure that arises from local interactions in many spatial and temporal systems. The structure induces a form of low-dimensionality that can be exploited algorithmically. I will introduce how to localize existing sampling methods, turning a high-dimensional problem into many low-dimensional subproblems. This localization not only reduces statistical complexity, but also enables efficient local and parallel computation. As examples, I will discuss MALA-within-Gibbs sampler and localized diffusion models. The localization method is grounded in a novel marginal Stein’s method, which provides quantitative estimates of the correlation decay in localized systems. This yields refined controls of the localization error, for instance, a dimension-free transport inequality for marginals. These results offer a unified perspective on how locality can be leveraged to make high-dimensional sampling both tractable and theoretically controlled.
报告人信息：刘水根，新加坡国立大学数学学院博士生，主要研究方向为不确定量化和高维采样，导师为童心教授和包维柱教授。
