{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/mmse-of-probabilistic-low-rank-matrix","title":"MMSE of probabilistic low-rank matrix estimation: Universality with respect to the output channel","arxiv_id":"1507.03857","date":"2015-07-14","proceeding":null,"authors":["Thibault Lesieur","Florent Krzakala","Lenka Zdeborová"],"abstract":"This paper considers probabilistic estimation of a low-rank matrix from\nnon-linear element-wise measurements of its elements. We derive the\ncorresponding approximate message passing (AMP) algorithm and its state\nevolution. Relying on non-rigorous but standard assumptions motivated by\nstatistical physics, we characterize the minimum mean squared error (MMSE)\nachievable information theoretically and with the AMP algorithm. Unlike in\nrelated problems of linear estimation, in the present setting the MMSE depends\non the output channel only trough a single parameter - its Fisher information.\nWe illustrate this striking finding by analysis of submatrix localization, and\nof detection of communities hidden in a dense stochastic block model. For this\nexample we locate the computational and statistical boundaries that are not\nequal for rank larger than four.","url_abs":"http://arxiv.org/abs/1507.03857v2","url_pdf":"http://arxiv.org/pdf/1507.03857v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"mmse-of-probabilistic-low-rank-matrix","repo_url":"https://github.com/krzakala/LowRAMP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"stochastic-block-model","task_name":"Stochastic Block Model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1507.03857","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}