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Approximate message passing from random initialization with applications to Z2 synchronization.

Gen Li1, Wei Fan1, Yuting Wei1

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Summary
This summary is machine-generated.

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.

Keywords:
approximate message passingglobal convergencenonasymptotic analysisrandom initializationspiked Wigner model

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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.