{"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/2505-11006","title":"Supervised Models Can Generalize Also When Trained on Random Label","arxiv_id":"2505.11006","date":"2025-05-16","proceeding":null,"authors":["Oskar Allerbo","Thomas B. Schön"],"abstract":"The success of unsupervised learning raises the question of whether also supervised models can be trained without using the information in the output $y$. In this paper, we demonstrate that this is indeed possible. The key step is to formulate the model as a smoother, i.e. on the form $\\hat{f}=Sy$, and to construct the smoother matrix $S$ independently of $y$, e.g. by training on random labels. We present a simple model selection criterion based on the distribution of the out-of-sample predictions and show that, in contrast to cross-validation, this criterion can be used also without access to $y$. We demonstrate on real and synthetic data that $y$-free trained versions of linear and kernel ridge regression, smoothing splines, and neural networks perform similarly to their standard, $y$-based, versions and, most importantly, significantly better than random guessing.","url_abs":"https://arxiv.org/abs/2505.11006v1","url_pdf":"https://arxiv.org/pdf/2505.11006v1.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":"2505-11006","repo_url":"https://github.com/allerbo/training_without_y","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}