{"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/approximate-leave-one-out-for-fast-parameter","title":"Approximate Leave-One-Out for Fast Parameter Tuning in High Dimensions","arxiv_id":"1807.02694","date":"2018-07-07","proceeding":"ICML 2018 7","authors":["Shuaiwen Wang","Wenda Zhou","Haihao Lu","Arian Maleki","Vahab Mirrokni"],"abstract":"Consider the following class of learning schemes: $$\\hat{\\boldsymbol{\\beta}}\n:= \\arg\\min_{\\boldsymbol{\\beta}}\\;\\sum_{j=1}^n\n\\ell(\\boldsymbol{x}_j^\\top\\boldsymbol{\\beta}; y_j) + \\lambda\nR(\\boldsymbol{\\beta}),\\qquad\\qquad (1) $$ where $\\boldsymbol{x}_i \\in\n\\mathbb{R}^p$ and $y_i \\in \\mathbb{R}$ denote the $i^{\\text{th}}$ feature and\nresponse variable respectively. Let $\\ell$ and $R$ be the loss function and\nregularizer, $\\boldsymbol{\\beta}$ denote the unknown weights, and $\\lambda$ be\na regularization parameter. Finding the optimal choice of $\\lambda$ is a\nchallenging problem in high-dimensional regimes where both $n$ and $p$ are\nlarge. We propose two frameworks to obtain a computationally efficient\napproximation ALO of the leave-one-out cross validation (LOOCV) risk for\nnonsmooth losses and regularizers. Our two frameworks are based on the primal\nand dual formulations of (1). We prove the equivalence of the two approaches\nunder smoothness conditions. This equivalence enables us to justify the\naccuracy of both methods under such conditions. We use our approaches to obtain\na risk estimate for several standard problems, including generalized LASSO,\nnuclear norm regularization, and support vector machines. We empirically\ndemonstrate the effectiveness of our results for non-differentiable cases.","url_abs":"http://arxiv.org/abs/1807.02694v1","url_pdf":"http://arxiv.org/pdf/1807.02694v1.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":"approximate-leave-one-out-for-fast-parameter","repo_url":"https://github.com/wendazhou/alocv-package","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"approximate-leave-one-out-for-fast-parameter","repo_url":"https://github.com/Francis-Hsu/alocv","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.02694","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}