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Mismatched estimation of non-symmetric rank-one matrices corrupted by structured noise

arXiv 2302.03306 ↗First posted 7 Feb 2023cs.IT cs.LG math.ITcited by 0

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Abstract (arXiv)

We study the performance of a Bayesian statistician who estimates a rank-one signal corrupted by non-symmetric rotationally invariant noise with a generic distribution of singular values. As the signal-to-noise ratio and the noise structure are unknown, a Gaussian setup is incorrectly assumed. We derive the exact analytic expression for the error of the mismatched Bayes estimator and also provide the analysis of an approximate message passing (AMP) algorithm. The first result exploits the asymptotic behavior of spherical integrals for rectangular matrices and of low-rank matrix perturbations; the second one relies on the design and analysis of an auxiliary AMP. The numerical experiments show that there is a performance gap between the AMP and Bayes estimators, which is due to the incorrect estimation of the signal norm.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 17 of its 45 references that are in the map. First posted on arXiv 7 Feb 2023.

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References · 17

  1. 2017Community Detection and Stochastic Block Modelscited by 317
  2. 2017Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Modelscited by 115
  3. 2017Estimation of Low-Rank Matrices via Approximate Message Passingcited by 41
  4. 2020Phase retrieval in high dimensions: Statistical and computational phase transitionscited by 39
  5. 2020Approximate Message Passing algorithms for rotationally invariant matricescited by 31
  6. 2016Mutual information for symmetric rank-one matrix estimation: A proof of the replica formulacited by 26
  7. 2020Approximate Message Passing with Spectral Initialization for Generalized Linear Modelscited by 22
  8. 2017The Computer Science and Physics of Community Detection: Landscapes, Phase Transitions, and Hardnesscited by 20
  9. 2016Message-passing algorithms for synchronization problems over compact groupscited by 18
  10. 2021Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initializationcited by 18
  11. 2020All-or-nothing statistical and computational phase transitions in sparse spiked matrix estimationcited by 16
  12. 2021PCA Initialization for Approximate Message Passing in Rotationally Invariant Modelscited by 14
5 more
  1. 2021A Random Matrix Perspective on Random Tensorscited by 12
  2. 2021When Random Tensors meet Random Matricescited by 10
  3. 2022The price of ignorance: how much does it cost to forget noise structure in low-rank matrix estimation?cited by 9
  4. 2020Information-theoretic limits of a multiview low-rank symmetric spiked matrix modelcited by 8
  5. 2022Bayes-optimal limits in structured PCA, and how to reach themcited by 3

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