{"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/phase-transitions-in-sparse-pca","title":"Phase Transitions in Sparse PCA","arxiv_id":"1503.00338","date":"2015-03-01","proceeding":null,"authors":["Thibault Lesieur","Florent Krzakala","Lenka Zdeborova"],"abstract":"We study optimal estimation for sparse principal component analysis when the\nnumber of non-zero elements is small but on the same order as the dimension of\nthe data. We employ approximate message passing (AMP) algorithm and its state\nevolution to analyze what is the information theoretically minimal mean-squared\nerror and the one achieved by AMP in the limit of large sizes. For a special\ncase of rank one and large enough density of non-zeros Deshpande and Montanari\n[1] proved that AMP is asymptotically optimal. We show that both for low\ndensity and for large rank the problem undergoes a series of phase transitions\nsuggesting existence of a region of parameters where estimation is information\ntheoretically possible, but AMP (and presumably every other polynomial\nalgorithm) fails. The analysis of the large rank limit is particularly\ninstructive.","url_abs":"http://arxiv.org/abs/1503.00338v1","url_pdf":"http://arxiv.org/pdf/1503.00338v1.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":"phase-transitions-in-sparse-pca","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":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1503.00338","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}