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Over the last decade, Approximate Message Passing (AMP) algorithms
have become extremely popular in various structured
high-dimensional statistical problems. Many of the original ideas
of AMP were developed in the physics and engineering literature and
have recently been extended for use in computer science and machine
learning. In this tutorial the authors give a comprehensive and
rigorous introduction to what AMP can offer, as well as to unifying
and formalizing the core concepts within the large body of recent
work in the area. They lead the reader through the basic concepts
of AMP before introducing the concept of low-rank matrix
estimation. The authors conclude by covering generalized models. To
complete the picture for researchers, proofs, technical remarks and
mathematical background are also provided. This tutorial is an in
depth introduction to Approximate Message Passing for students and
researchers new to the topic.
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