On the Convergence of Orthogonal/Vector AMP: Long-Memory Message-Passing Strategy

TL;DR

This paper establishes the convergence of Bayes-optimal orthogonal and vector AMP algorithms by leveraging a long-memory message-passing framework and analyzing their state evolution dynamics.

Contribution

It introduces a systematic convergence proof for orthogonal/vector AMP using Bayes-optimal long-memory message-passing and state evolution analysis.

Findings

Proves convergence of Bayes-optimal orthogonal/vector AMP.

Shows state evolution recursions converge.

Reduces state evolution to AMP fixed points.

Abstract

This paper proves the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point in the large system limit. The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that is guaranteed to converge systematically. The dynamics of Bayes-optimal LM-MP is analyzed via an existing state evolution framework. The obtained state evolution recursions are proved to converge. The convergence of Bayes-optimal orthogonal/vector AMP is proved by confirming an exact reduction of the state evolution recursions to those for Bayes-optimal orthogonal/vector AMP.