摘要： 
Approximate message passing (AMP) refers to a class of iterative algorithms solving structured high-dimensional statistical problems, such as low-rank matrix estimation, generalized linear models and neural networks. Originated from loopy belief propagation in statistical physics and engineering literatures, the AMP-based algorithms are popular and practical in applications. In a statistical perspective, AMP is also attractive : 1. In AMP it is easy to utilize prior information on the structure, such as sparsity. 2. It provides precise asymptotic guarantees in high-dimensional regime and sometimes attain optimal asymptotic rate.

In this talk, we will briefly introduce the AMP framework based on the latest tutorial [Feng et al. 2022] using the simplest rank-1 matrix estimation problem as an example. The lessons and techniques can be easily extended to other problems. Some recent progress will also be discussed.