{"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/non-convex-global-minimization-and-false","title":"Non-convex Global Minimization and False Discovery Rate Control for the TREX","arxiv_id":"1604.06815","date":"2016-04-22","proceeding":null,"authors":["Jacob Bien","Irina Gaynanova","Johannes Lederer","Christian Müller"],"abstract":"The TREX is a recently introduced method for performing sparse\nhigh-dimensional regression. Despite its statistical promise as an alternative\nto the lasso, square-root lasso, and scaled lasso, the TREX is computationally\nchallenging in that it requires solving a non-convex optimization problem. This\npaper shows a remarkable result: despite the non-convexity of the TREX problem,\nthere exists a polynomial-time algorithm that is guaranteed to find the global\nminimum. This result adds the TREX to a very short list of non-convex\noptimization problems that can be globally optimized (principal components\nanalysis being a famous example). After deriving and developing this new\napproach, we demonstrate that (i) the ability of the preexisting TREX heuristic\nto reach the global minimum is strongly dependent on the difficulty of the\nunderlying statistical problem, (ii) the new polynomial-time algorithm for TREX\npermits a novel variable ranking and selection scheme, (iii) this scheme can be\nincorporated into a rule that controls the false discovery rate (FDR) of\nincluded features in the model. To achieve this last aim, we provide an\nextension of the results of Barber & Candes (2015) to establish that the\nknockoff filter framework can be applied to the TREX. This investigation thus\nprovides both a rare case study of a heuristic for non-convex optimization and\na novel way of exploiting non-convexity for statistical inference.","url_abs":"http://arxiv.org/abs/1604.06815v2","url_pdf":"http://arxiv.org/pdf/1604.06815v2.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":"non-convex-global-minimization-and-false","repo_url":"https://github.com/muellsen/TREX","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}