{"file_date_updated":"2025-02-03T08:27:59Z","publisher":"American Physical Society","publication_identifier":{"issn":["2643-1564"]},"title":"Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noise","day":"22","citation":{"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>.","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>","short":"J. Barbier, F. Camilli, Y. Xu, M. Mondelli, Physical Review Research 7 (2025).","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>","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>.","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.","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."},"publication":"Physical Review Research","ddc":["530"],"publication_status":"published","date_published":"2025-01-22T00:00:00Z","article_number":"013081","OA_type":"gold","date_created":"2025-02-02T23:01:54Z","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","article_processing_charge":"Yes","doi":"10.1103/PhysRevResearch.7.013081","file":[{"checksum":"52c5f72d80ffc928542469114fcdb62b","date_updated":"2025-02-03T08:27:59Z","content_type":"application/pdf","file_size":702543,"success":1,"file_name":"2025_PhysReviewResearch_Barbier.pdf","file_id":"18988","date_created":"2025-02-03T08:27:59Z","relation":"main_file","access_level":"open_access","creator":"dernst"}],"external_id":{"arxiv":["2405.20993"]},"intvolume":"         7","scopus_import":"1","DOAJ_listed":"1","language":[{"iso":"eng"}],"arxiv":1,"volume":7,"date_updated":"2025-04-15T07:50:13Z","status":"public","OA_place":"publisher","article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"_id":"18986","department":[{"_id":"MaMo"}],"project":[{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"oa":1,"abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","related_material":{"link":[{"relation":"software","url":"https://github.com/xu-yz19/spiked-matrix-models-with-structured-noise"}]},"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.","has_accepted_license":"1","oa_version":"Published Version","type":"journal_article","author":[{"first_name":"Jean","last_name":"Barbier","full_name":"Barbier, Jean"},{"first_name":"Francesco","last_name":"Camilli","full_name":"Camilli, Francesco"},{"full_name":"Xu, Yizhou","last_name":"Xu","first_name":"Yizhou"},{"orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425","last_name":"Mondelli","first_name":"Marco"}]}