{"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/more-data-can-hurt-for-linear-regression","title":"More Data Can Hurt for Linear Regression: Sample-wise Double Descent","arxiv_id":"1912.07242","date":"2019-12-16","proceeding":null,"authors":["Preetum Nakkiran"],"abstract":"In this expository note we describe a surprising phenomenon in overparameterized linear regression, where the dimension exceeds the number of samples: there is a regime where the test risk of the estimator found by gradient descent increases with additional samples. In other words, more data actually hurts the estimator. This behavior is implicit in a recent line of theoretical works analyzing \"double-descent\" phenomenon in linear models. In this note, we isolate and understand this behavior in an extremely simple setting: linear regression with isotropic Gaussian covariates. In particular, this occurs due to an unconventional type of bias-variance tradeoff in the overparameterized regime: the bias decreases with more samples, but variance increases.","url_abs":"https://arxiv.org/abs/1912.07242v1","url_pdf":"https://arxiv.org/pdf/1912.07242v1.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":"more-data-can-hurt-for-linear-regression","repo_url":"https://github.com/IyarLin/paper_results_reproduction","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"},{"method_slug":"test","method_name":"Test"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1912.07242","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}