{"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/polynomial-regression-as-an-alternative-to","title":"Polynomial Regression As an Alternative to Neural Nets","arxiv_id":"1806.06850","date":"2018-06-13","proceeding":null,"authors":["Xi Cheng","Bohdan Khomtchouk","Norman Matloff","Pete Mohanty"],"abstract":"Despite the success of neural networks (NNs), there is still a concern among\nmany over their \"black box\" nature. Why do they work? Here we present a simple\nanalytic argument that NNs are in fact essentially polynomial regression\nmodels. This view will have various implications for NNs, e.g. providing an\nexplanation for why convergence problems arise in NNs, and it gives rough\nguidance on avoiding overfitting. In addition, we use this phenomenon to\npredict and confirm a multicollinearity property of NNs not previously reported\nin the literature. Most importantly, given this loose correspondence, one may\nchoose to routinely use polynomial models instead of NNs, thus avoiding some\nmajor problems of the latter, such as having to set many tuning parameters and\ndealing with convergence issues. We present a number of empirical results; in\neach case, the accuracy of the polynomial approach matches or exceeds that of\nNN approaches. A many-featured, open-source software package, polyreg, is\navailable.","url_abs":"http://arxiv.org/abs/1806.06850v3","url_pdf":"http://arxiv.org/pdf/1806.06850v3.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":"polynomial-regression-as-an-alternative-to","repo_url":"https://github.com/matloff/polyreg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"polynomial-regression-as-an-alternative-to","repo_url":"https://github.com/mac-theobio/Lab_meeting","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}