{"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/optimal-sparse-regression-trees","title":"Optimal Sparse Regression Trees","arxiv_id":"2211.14980","date":"2022-11-28","proceeding":null,"authors":["Rui Zhang","Rui Xin","Margo Seltzer","Cynthia Rudin"],"abstract":"Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic-programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm in 1-dimension over the set of labels. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.","url_abs":"https://arxiv.org/abs/2211.14980v3","url_pdf":"https://arxiv.org/pdf/2211.14980v3.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":"optimal-sparse-regression-trees","repo_url":"https://github.com/ruizhang1996/optimal-sparse-regression-tree-public","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"optimal-sparse-regression-trees","repo_url":"https://github.com/ruizhang1996/optimal-sparse-survival-trees-public","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"k-means-clustering","method_name":"k-Means Clustering"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2211.14980","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}