A unifying tutorial on Approximate Message Passing

TL;DR

This paper provides a comprehensive tutorial on Approximate Message Passing (AMP), explaining its statistical foundations, demonstrating its versatility, and unifying existing results to clarify its role in high-dimensional inference.

Contribution

It offers a unified, accessible overview of AMP algorithms from a statistical perspective, consolidating and strengthening prior theoretical results.

Findings

AMP algorithms are powerful for high-dimensional problems

The tutorial clarifies the connection between AMP and belief propagation

Unified framework enhances understanding of AMP's capabilities

Abstract

Over the last decade or so, Approximate Message Passing (AMP) algorithms have become extremely popular in various structured high-dimensional statistical problems. The fact that the origins of these techniques can be traced back to notions of belief propagation in the statistical physics literature lends a certain mystique to the area for many statisticians. Our goal in this work is to present the main ideas of AMP from a statistical perspective, to illustrate the power and flexibility of the AMP framework. Along the way, we strengthen and unify many of the results in the existing literature.