High-dimensional Statistics and Approximate Message Passing Algorithms

High-dimensional Statistics and Approximate Message Passing Algorithms

Speaker：

Cindy Rush (Columbia University)

Time：

Fri. & Thur., 2:30-5:30 pm,

May 15 & May 21, 2026

Venue：

B541, Shuangqing Complex Building A

Description:

In these lectures, we will introduce the notion of high-dimensional statistics where one wishes to perform statistical prediction or inference in settings where the sample size of the data is smaller than or comparable to the number of parameters in the problem. In such settings, classical asymptotics and standard statistical methods can fail in unexpected ways. We will include a special focus on approximate message passing (AMP), which is a class of efficient, iterative algorithms that have been successfully employed in many statistical learning tasks like high-dimensional linear regression and low-rank matrix estimation. AMP algorithms have two features that make them particularly attractive: they can easily be tailored to take advantage of prior information on the structure of the signal, such as sparsity, and under suitable assumptions on a design matrix, AMP theory provides precise asymptotic guarantees for statistical procedures in the high-dimensional regime. Our aim is to introduce the main ideas of AMP from a statistical perspective to illustrate the power and flexibility of the AMP framework and look at its application to matrix estimation.