---
APC_amount: 3272,21 EUR
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '18986'
abstract:
- lang: eng
  text: 'We consider a prototypical problem of Bayesian inference for a structured
    spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic
    and algorithmic limits are well understood when the noise is a Gaussian Wigner
    matrix, the more realistic case of structured noise still remains challenging.
    To capture the structure while maintaining mathematical tractability, a line of
    work has focused on rotationally invariant noise. However, existing studies either
    provide suboptimal algorithms or are limited to a special class of noise ensembles.
    In this paper, using tools from statistical physics (replica method) and random
    matrix theory (generalized spherical integrals) we establish the characterization
    of the information-theoretic limits for a noise matrix drawn from a general trace
    ensemble. Remarkably, our analysis unveils the asymptotic equivalence between
    the rotationally invariant model and a surrogate Gaussian one. Finally, we show
    how to saturate the predicted statistical limits using an efficient algorithm
    inspired by the theory of adaptive Thouless-Anderson-Palmer (TAP) equations.'
acknowledgement: J.B., F.C., and Y.X. were funded by the European Union (ERC, CHORAL,
  Project No. 101039794). Views and opinions expressed are however those of the authors
  only and do not necessarily reflect those of the European Union or the European
  Research Council. Neither the European Union nor the granting authority can be held
  responsible for them. M.M. was supported by the 2019 Lopez-Loreta Prize. J.B. acknowledges
  discussions with TianQi Hou at the initial stage of the project, as well as with
  Antoine Bodin.
article_number: '013081'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Jean
  full_name: Barbier, Jean
  last_name: Barbier
- first_name: Francesco
  full_name: Camilli, Francesco
  last_name: Camilli
- first_name: Yizhou
  full_name: Xu, Yizhou
  last_name: Xu
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: Barbier J, Camilli F, Xu Y, Mondelli M. Information limits and Thouless-Anderson-Palmer
    equations for spiked matrix models with structured noise. <i>Physical Review Research</i>.
    2025;7. doi:<a href="https://doi.org/10.1103/PhysRevResearch.7.013081">10.1103/PhysRevResearch.7.013081</a>
  apa: Barbier, J., Camilli, F., Xu, Y., &#38; Mondelli, M. (2025). Information limits
    and Thouless-Anderson-Palmer equations for spiked matrix models with structured
    noise. <i>Physical Review Research</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevResearch.7.013081">https://doi.org/10.1103/PhysRevResearch.7.013081</a>
  chicago: Barbier, Jean, Francesco Camilli, Yizhou Xu, and Marco Mondelli. “Information
    Limits and Thouless-Anderson-Palmer Equations for Spiked Matrix Models with Structured
    Noise.” <i>Physical Review Research</i>. American Physical Society, 2025. <a href="https://doi.org/10.1103/PhysRevResearch.7.013081">https://doi.org/10.1103/PhysRevResearch.7.013081</a>.
  ieee: J. Barbier, F. Camilli, Y. Xu, and M. Mondelli, “Information limits and Thouless-Anderson-Palmer
    equations for spiked matrix models with structured noise,” <i>Physical Review
    Research</i>, vol. 7. American Physical Society, 2025.
  ista: Barbier J, Camilli F, Xu Y, Mondelli M. 2025. Information limits and Thouless-Anderson-Palmer
    equations for spiked matrix models with structured noise. Physical Review Research.
    7, 013081.
  mla: Barbier, Jean, et al. “Information Limits and Thouless-Anderson-Palmer Equations
    for Spiked Matrix Models with Structured Noise.” <i>Physical Review Research</i>,
    vol. 7, 013081, American Physical Society, 2025, doi:<a href="https://doi.org/10.1103/PhysRevResearch.7.013081">10.1103/PhysRevResearch.7.013081</a>.
  short: J. Barbier, F. Camilli, Y. Xu, M. Mondelli, Physical Review Research 7 (2025).
date_created: 2025-02-02T23:01:54Z
date_published: 2025-01-22T00:00:00Z
date_updated: 2026-05-06T12:57:36Z
day: '22'
ddc:
- '530'
department:
- _id: MaMo
doi: 10.1103/PhysRevResearch.7.013081
external_id:
  arxiv:
  - '2405.20993'
file:
- access_level: open_access
  checksum: 52c5f72d80ffc928542469114fcdb62b
  content_type: application/pdf
  creator: dernst
  date_created: 2025-02-03T08:27:59Z
  date_updated: 2025-02-03T08:27:59Z
  file_id: '18988'
  file_name: 2025_PhysReviewResearch_Barbier.pdf
  file_size: 702543
  relation: main_file
  success: 1
file_date_updated: 2025-02-03T08:27:59Z
has_accepted_license: '1'
intvolume: '         7'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: Physical Review Research
publication_identifier:
  issn:
  - 2643-1564
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
related_material:
  link:
  - relation: software
    url: https://github.com/xu-yz19/spiked-matrix-models-with-structured-noise
scopus_import: '1'
status: public
title: Information limits and Thouless-Anderson-Palmer equations for spiked matrix
  models with structured noise
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2025'
...