{"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/high-dimensional-asymptotics-of-prediction","title":"High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification","arxiv_id":"1507.03003","date":"2015-07-10","proceeding":null,"authors":["Edgar Dobriban","Stefan Wager"],"abstract":"We provide a unified analysis of the predictive risk of ridge regression and\nregularized discriminant analysis in a dense random effects model. We work in a\nhigh-dimensional asymptotic regime where $p, n \\to \\infty$ and $p/n \\to \\gamma\n\\in (0, \\, \\infty)$, and allow for arbitrary covariance among the features. For\nboth methods, we provide an explicit and efficiently computable expression for\nthe limiting predictive risk, which depends only on the spectrum of the\nfeature-covariance matrix, the signal strength, and the aspect ratio $\\gamma$.\nEspecially in the case of regularized discriminant analysis, we find that\npredictive accuracy has a nuanced dependence on the eigenvalue distribution of\nthe covariance matrix, suggesting that analyses based on the operator norm of\nthe covariance matrix may not be sharp. Our results also uncover several\nqualitative insights about both methods: for example, with ridge regression,\nthere is an exact inverse relation between the limiting predictive risk and the\nlimiting estimation risk given a fixed signal strength. Our analysis builds on\nrecent advances in random matrix theory.","url_abs":"http://arxiv.org/abs/1507.03003v2","url_pdf":"http://arxiv.org/pdf/1507.03003v2.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":"high-dimensional-asymptotics-of-prediction","repo_url":"https://github.com/dobriban/high-dim-risk-experiments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"classification-1","task_name":"Classification"},{"task_slug":"classification","task_name":"General Classification"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1507.03003","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}