A unifying tutorial on Approximate Message Passing
This work offers a unifying tutorial for statisticians and researchers interested in structured high-dimensional statistical problems, but it is incremental as it consolidates and clarifies existing knowledge rather than introducing new methods.
The authors provide a tutorial on Approximate Message Passing (AMP) algorithms, presenting their main ideas from a statistical perspective to illustrate their power and flexibility, while strengthening and unifying existing results in the literature.
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.