{"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/statistical-physics-of-inference-thresholds","title":"Statistical physics of inference: Thresholds and algorithms","arxiv_id":"1511.02476","date":"2015-11-08","proceeding":null,"authors":["Lenka Zdeborová","Florent Krzakala"],"abstract":"Many questions of fundamental interest in todays science can be formulated as\ninference problems: Some partial, or noisy, observations are performed over a\nset of variables and the goal is to recover, or infer, the values of the\nvariables based on the indirect information contained in the measurements. For\nsuch problems, the central scientific questions are: Under what conditions is\nthe information contained in the measurements sufficient for a satisfactory\ninference to be possible? What are the most efficient algorithms for this task?\nA growing body of work has shown that often we can understand and locate these\nfundamental barriers by thinking of them as phase transitions in the sense of\nstatistical physics. Moreover, it turned out that we can use the gained\nphysical insight to develop new promising algorithms. Connection between\ninference and statistical physics is currently witnessing an impressive\nrenaissance and we review here the current state-of-the-art, with a pedagogical\nfocus on the Ising model which formulated as an inference problem we call the\nplanted spin glass. In terms of applications we review two classes of problems:\n(i) inference of clusters on graphs and networks, with community detection as a\nspecial case and (ii) estimating a signal from its noisy linear measurements,\nwith compressed sensing as a case of sparse estimation. Our goal is to provide\na pedagogical review for researchers in physics and other fields interested in\nthis fascinating topic.","url_abs":"http://arxiv.org/abs/1511.02476v5","url_pdf":"http://arxiv.org/pdf/1511.02476v5.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":"statistical-physics-of-inference-thresholds","repo_url":"https://github.com/rodsveiga/AMP_tutorial","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"community-detection","task_name":"Community Detection"},{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1511.02476","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}