Approximate Message Passing for
Rotationally-Invariant Models:
A Unified Framework and Applications
to Spiked Models
报告专家：马俊杰（中国科学院数学与系统科学研究院）
报告时间：5月12日（星期一）14：00-15：00
报告地点：国家天元数学西南中心516
报告摘要：In the first part of this talk, we present a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP (OAMP), we systematically derive the correct Onsager terms of AMP algorithms. This approach allows us to re-derive an AMP algorithm introduced by Fan and Opper et al., while shedding new light on the role of free cumulants of the spectral law. The free cumulants arise naturally from a recursive centering operation, potentially of independent interest beyond the scope of AMP.
In the second part of this talk, we consider the applications of our framework to signal estimation in spiked models with rotationally-invariant noise. We develop a new class of AMP algorithms and show that the resulting algorithm achieves the smallest possible asymptotic estimation error among a broad class of iterative algorithms under a fixed iteration budget.
This talk is based on joint work with Songbin Liu (AMSS, CAS) and Rishabh Dudeja (UW-Madison).
专家简介：马俊杰，中国科学院数学与系统科学研究院副研究员。2010年本科毕业于西安电子科技大学，2015年获香港城市大学博士学位，之后分别于香港城市大学、哥伦比亚大学和哈佛大学从事博士后研究。研究兴趣包括通信信号处理、信息论、高维统计、随机矩阵等交叉领域，近年来主要关注近似消息传递（AMP）算法理论及应用。曾入选中科院百人计划，主持自然基金青年项目并参与中科院先导科技专项、科技部重点专项等科研项目。
邀请人：王治国
