{"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/a-minimax-approach-to-supervised-learning","title":"A Minimax Approach to Supervised Learning","arxiv_id":"1606.02206","date":"2016-06-07","proceeding":"NeurIPS 2016 12","authors":["Farzan Farnia","David Tse"],"abstract":"Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of\nprobability distributions $\\Gamma$ on $(X,Y)$, what is the optimal decision\nrule minimizing the worst-case expected loss over $\\Gamma$? In this paper, we\naddress this question by introducing a generalization of the principle of\nmaximum entropy. Applying this principle to sets of distributions with marginal\non $X$ constrained to be the empirical marginal from the data, we develop a\ngeneral minimax approach for supervised learning problems. While for some loss\nfunctions such as squared-error and log loss, the minimax approach rederives\nwell-knwon regression models, for the 0-1 loss it results in a new linear\nclassifier which we call the maximum entropy machine. The maximum entropy\nmachine minimizes the worst-case 0-1 loss over the structured set of\ndistribution, and by our numerical experiments can outperform other well-known\nlinear classifiers such as SVM. We also prove a bound on the generalization\nworst-case error in the minimax approach.","url_abs":"http://arxiv.org/abs/1606.02206v5","url_pdf":"http://arxiv.org/pdf/1606.02206v5.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":"a-minimax-approach-to-supervised-learning","repo_url":"https://github.com/KaloshinPE/MEM_detector","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"svm","method_name":"SVM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1606.02206","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}