{"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/adaptive-concentration-of-regression-trees","title":"Adaptive Concentration of Regression Trees, with Application to Random Forests","arxiv_id":"1503.06388","date":"2015-03-22","proceeding":null,"authors":["Stefan Wager","Guenther Walther"],"abstract":"We study the convergence of the predictive surface of regression trees and\nforests. To support our analysis we introduce a notion of adaptive\nconcentration for regression trees. This approach breaks tree training into a\nmodel selection phase in which we pick the tree splits, followed by a model\nfitting phase where we find the best regression model consistent with these\nsplits. We then show that the fitted regression tree concentrates around the\noptimal predictor with the same splits: as d and n get large, the discrepancy\nis with high probability bounded on the order of sqrt(log(d) log(n)/k)\nuniformly over the whole regression surface, where d is the dimension of the\nfeature space, n is the number of training examples, and k is the minimum leaf\nsize for each tree. We also provide rate-matching lower bounds for this\nadaptive concentration statement. From a practical perspective, our result\nenables us to prove consistency results for adaptively grown forests in high\ndimensions, and to carry out valid post-selection inference in the sense of\nBerk et al. [2013] for subgroups defined by tree leaves.","url_abs":"http://arxiv.org/abs/1503.06388v3","url_pdf":"http://arxiv.org/pdf/1503.06388v3.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":"adaptive-concentration-of-regression-trees","repo_url":"https://github.com/celiaescribe/guess_and_check","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"adaptive-concentration-of-regression-trees","repo_url":"https://github.com/gaspardbe/guess_and_check","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"model-selection","task_name":"Model Selection"},{"task_slug":"regression-1","task_name":"regression"},{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1503.06388","atlas_url":"https://app.syntology.ai/?focus=1503.06388","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}