{"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/integrative-multi-view-reduced-rank","title":"Integrative Multi-View Reduced-Rank Regression: Bridging Group-Sparse and Low-Rank Models","arxiv_id":"1807.10375","date":"2018-07-26","proceeding":null,"authors":["Gen Li","Xiaokang Liu","Kun Chen"],"abstract":"Multi-view data have been routinely collected in various fields of science\nand engineering. A general problem is to study the predictive association\nbetween multivariate responses and multi-view predictor sets, all of which can\nbe of high dimensionality. It is likely that only a few views are relevant to\nprediction, and the predictors within each relevant view contribute to the\nprediction collectively rather than sparsely. We cast this new problem under\nthe familiar multivariate regression framework and propose an integrative\nreduced-rank regression (iRRR), where each view has its own low-rank\ncoefficient matrix. As such, latent features are extracted from each view in a\nsupervised fashion. For model estimation, we develop a convex composite nuclear\nnorm penalization approach, which admits an efficient algorithm via alternating\ndirection method of multipliers. Extensions to non-Gaussian and incomplete data\nare discussed. Theoretically, we derive non-asymptotic oracle bounds of iRRR\nunder a restricted eigenvalue condition. Our results recover oracle bounds of\nseveral special cases of iRRR including Lasso, group Lasso and nuclear norm\npenalized regression. Therefore, iRRR seamlessly bridges group-sparse and\nlow-rank methods and can achieve substantially faster convergence rate under\nrealistic settings of multi-view learning. Simulation studies and an\napplication in the Longitudinal Studies of Aging further showcase the efficacy\nof the proposed methods.","url_abs":"http://arxiv.org/abs/1807.10375v1","url_pdf":"http://arxiv.org/pdf/1807.10375v1.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":"integrative-multi-view-reduced-rank","repo_url":"https://github.com/reagan0323/iRRR","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"multi-view-learning","task_name":"MULTI-VIEW LEARNING"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}