Spiked Matrix Models with Rotationally Invariant Noise: AMP Algorithms and Optimality

Speaker:       Junjie Ma

Time:            13:00, Dec. 25th.

Location:      Rm. 204, Teaching Center

Host:             Prof. Ziping Zhao

Abstract:

In this talk, I will present our recent work on the optimality of Approximate Message Passing (AMP) algorithms for spiked matrix models with rotationally invariant noise. We introduce a new AMP algorithm that employs a matrix denoiser—acting on the eigenvalues of the observed matrix—and an iterate denoiser—applied to the AMP iterates. The resulting dynamics admit a simple state-evolution characterization, which allows us to identify the optimal pair of denoisers achieving the minimum possible asymptotic estimation error among a broad class of iterative algorithms.

I will also discuss ongoing work that extends this framework to rectangular spiked matrix models, where we develop an AMP algorithm with optimal spectral initialization, further broadening the scope and applicability of the theory.

Bio:

Junjie Ma is an Associate Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He received his Ph.D. from the City University of Hong Kong in 2015 and held postdoctoral positions at Columbia University and Harvard University. His research interests include signal processing, information theory, and high-dimensional statistics. He has published multiple research papers in leading journals and conferences such as the Annals of Statistics, IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing, NeurIPS, and ICML.