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Updated: Jul 21, 2025

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
Published on: September 21, 2017
Approximate message passing from random initialization with applications to Z2 synchronization
Gen Li1, Wei Fan1, Yuting Wei1
1Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104.
Abstract:
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes optimal estimator is intractable in general due to the requirement of computing high-dimensional integrations/summations, Approximate Message Passing (AMP) emerges as an efficient first-order method to approximate the Bayes optimal estimator. However, the theoretical underpinnings of AMP remain largely unavailable when it starts from random initialization, a scheme of critical practical utility. Focusing on a prototypical model called [Formula: see text] synchronization, we characterize the finite-sample dynamics of AMP from random initialization, uncovering its rapid global convergence. Our theory-which is nonasymptotic in nature-in this model unveils the non-necessity of a careful initialization for the success of AMP.
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