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Updated: Jul 21, 2025
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Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
Published on: September 21, 2017
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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.
Summary
This study shows Approximate Message Passing (AMP) can efficiently reconstruct rank-one matrices from noisy data. Our theory proves AMP converges globally even with random initialization, removing the need for careful setup.
Area of Science:
- Signal Processing
- Machine Learning Theory
- Statistical Inference
Background:
- Reconstructing rank-one matrices from noisy data is challenging.
- Bayes optimal estimators are often computationally intractable.
- Approximate Message Passing (AMP) is an efficient approximation method.
Purpose of the Study:
- To analyze the theoretical underpinnings of AMP for rank-one matrix reconstruction.
- To investigate AMP's performance starting from random initialization.
- To demonstrate AMP's global convergence properties.
Main Methods:
- Non-asymptotic analysis of AMP dynamics.
- Focus on the [Formula: see text] synchronization model.
- Characterization of finite-sample behavior.
Main Results:
- AMP demonstrates rapid global convergence from random initialization.
- Theoretical guarantees are provided for AMP's performance.
- The necessity of careful initialization for AMP is disproven.
Conclusions:
- AMP is a robust and efficient method for rank-one matrix reconstruction.
- Random initialization is sufficient for successful AMP application.
- The study provides theoretical validation for practical AMP usage.
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