{"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/generalization-error-of-generalized-linear","title":"Generalization Error of Generalized Linear Models in High Dimensions","arxiv_id":"2005.00180","date":"2020-05-01","proceeding":"ICML 2020 1","authors":["Melikasadat Emami","Mojtaba Sahraee-Ardakan","Parthe Pandit","Sundeep Rangan","Alyson K. Fletcher"],"abstract":"At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our understanding of their generalization capabilities is incomplete. This task is made harder by the non-convexity of the underlying learning problems. We provide a general framework to characterize the asymptotic generalization error for single-layer neural networks (i.e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems. This framework enables analyzing the effect of (i) over-parameterization and non-linearity during modeling; and (ii) choices of loss function, initialization, and regularizer during learning. Our model also captures mismatch between training and test distributions. As examples, we analyze a few special cases, namely linear regression and logistic regression. We are also able to rigorously and analytically explain the \\emph{double descent} phenomenon in generalized linear models.","url_abs":"https://arxiv.org/abs/2005.00180v1","url_pdf":"https://arxiv.org/pdf/2005.00180v1.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":"generalization-error-of-generalized-linear","repo_url":"https://github.com/appleternity/generating-figure-captions-as-a-text-summarization-task","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"generalization-error-of-generalized-linear","repo_url":"https://github.com/crowd-ai-lab/generating-figure-captions-as-a-text-summarization-task","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"generalization-error-of-generalized-linear","repo_url":"https://github.com/melikaemami/Generalization-Error-of-GLMs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"},{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2005.00180","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}