Abstract: Approximate message passing (AMP) has emerged as a powerful framework for the design and analysis of iterative algorithms for high dimensional inference problems involving regression and low-rank matrix factorization. The basic form of an AMP algorithm consists of a recursion defined on a random matrix. Under suitable conditions, the distribution of this recursion can be well approximated by a Gaussian process whose mean and covariance are defined via a recursive process called state evolution.
This talk will briefly summarize some of the key ideas in AMP (no background is assumed). I will then describe a new approach for analyzing these algorithms that constructs an explicit coupling between the AMP iterates and a Gaussian process. Under mild regularity conditions, this coupling argument provides simple and interpretable guarantees on the non-asymptotic behavior of AMP algorithms.
Related work can be found in the arXiv papers: https://arxiv.org/abs/2405.08225 and https://arxiv.org/abs/2306.15580
Bio: Galen Reeves is an Associate Professor at Duke University with a joint appointment in the Department of Electrical Computer Engineering and the Department of Statistical Science. He completed his PhD in Electrical Engineering and Computer Sciences at the University of California, Berkeley in 2011, and he was a postdoctoral associate in the Departments of Statistics at Stanford University from 2011 to 2013. His research interests include information theory and high-dimensional statistics. He received the NSF CAREER award in 2017.