{"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/bayesian-matrix-completion-via-adaptive","title":"Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization","arxiv_id":"1512.01110","date":"2015-12-03","proceeding":null,"authors":["Yang Song","Jun Zhu"],"abstract":"Bayesian matrix completion has been studied based on a low-rank matrix\nfactorization formulation with promising results. However, little work has been\ndone on Bayesian matrix completion based on the more direct spectral\nregularization formulation. We fill this gap by presenting a novel Bayesian\nmatrix completion method based on spectral regularization. In order to\ncircumvent the difficulties of dealing with the orthonormality constraints of\nsingular vectors, we derive a new equivalent form with relaxed constraints,\nwhich then leads us to design an adaptive version of spectral regularization\nfeasible for Bayesian inference. Our Bayesian method requires no parameter\ntuning and can infer the number of latent factors automatically. Experiments on\nsynthetic and real datasets demonstrate encouraging results on rank recovery\nand collaborative filtering, with notably good results for very sparse\nmatrices.","url_abs":"http://arxiv.org/abs/1512.01110v2","url_pdf":"http://arxiv.org/pdf/1512.01110v2.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":"bayesian-matrix-completion-via-adaptive","repo_url":"https://github.com/yang-song/GASR","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"collaborative-filtering","task_name":"Collaborative Filtering"},{"task_slug":"matrix-completion","task_name":"Matrix Completion"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}