A leave-one-out approach to approximate message passing
报告专家：鲍志刚 副教授（香港大学）
报告时间：2024年10月10日（星期四）10：00-11:00
报告地点：数学学院西202
报告摘要：Approximate message passing (AMP) has emerged both as a popular class of iterative algorithms and as a powerful analytic tool in a wide range of statistical estimation problems and statistical physics models. A well established line of AMP theory proves Gaussian approximations for the empirical distributions of the AMP iterate in the high dimensional limit, under the GOE random matrix model and its variants. In this talk, we will introduce a non-asymptotic, leave-one-out representation for the AMP iterate that holds under a broad class of Gaussian random matrix models with general variance profiles. In contrast to the typical AMP theory that describes the empirical distributions of the AMP iterate via a low dimensional state evolution, our leave-one-out representation yields an intrinsically high dimensional state evolution formula which provides non-asymptotic characterizations for the possibly heterogeneous, entrywise behavior of the AMP iterate under the prescribed random matrix models. Our leave-one-out method of proof differs significantly from the widely adopted conditioning approach for rotational invariant ensembles, and relies instead on an inductive method that utilizes almost solely integration-by-parts and concentration techniques. This talk is based on a joint work with Qiyang Han and Xiaocong Xu.
专家简介：鲍志刚，2013年获浙江大学博士学位，香港大学数学系副教授；获2022年度国家优秀青年科学基金(港澳)；主要研究方向包括概率，统计物理和高维统计；主要成果发表在《Forum of Mathematics, Sigma》，《Annals of Statistics》，《Annals of Probability》，《Probability Theory and Related Fields》，《Communications in Mathematical Physics》，《Advances in Mathematics》，《Journal of Functional Analysis》，《IEEE Transactions on Information Theory》，《International Mathematics Research Notices》等国内外重要学术期刊上。
邀请人：常寅山
