{"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/distribution-free-predictive-inference-for","title":"Distribution-Free Predictive Inference For Regression","arxiv_id":"1604.04173","date":"2016-04-14","proceeding":null,"authors":["Jing Lei","Max G'Sell","Alessandro Rinaldo","Ryan J. Tibshirani","Larry Wasserman"],"abstract":"We develop a general framework for distribution-free predictive inference in\nregression, using conformal inference. The proposed methodology allows for the\nconstruction of a prediction band for the response variable using any estimator\nof the regression function. The resulting prediction band preserves the\nconsistency properties of the original estimator under standard assumptions,\nwhile guaranteeing finite-sample marginal coverage even when these assumptions\ndo not hold. We analyze and compare, both empirically and theoretically, the\ntwo major variants of our conformal framework: full conformal inference and\nsplit conformal inference, along with a related jackknife method. These methods\noffer different tradeoffs between statistical accuracy (length of resulting\nprediction intervals) and computational efficiency. As extensions, we develop a\nmethod for constructing valid in-sample prediction intervals called {\\it\nrank-one-out} conformal inference, which has essentially the same computational\nefficiency as split conformal inference. We also describe an extension of our\nprocedures for producing prediction bands with locally varying length, in order\nto adapt to heteroskedascity in the data. Finally, we propose a model-free\nnotion of variable importance, called {\\it leave-one-covariate-out} or LOCO\ninference. Accompanying this paper is an R package {\\tt conformalInference}\nthat implements all of the proposals we have introduced. In the spirit of\nreproducibility, all of our empirical results can also be easily (re)generated\nusing this package.","url_abs":"http://arxiv.org/abs/1604.04173v2","url_pdf":"http://arxiv.org/pdf/1604.04173v2.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":"distribution-free-predictive-inference-for","repo_url":"https://github.com/ryantibs/conformal","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-2.0"}},{"paper_slug":"distribution-free-predictive-inference-for","repo_url":"https://github.com/AIgen/QOOB","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"distribution-free-predictive-inference-for","repo_url":"https://github.com/DEck13/conformal.glm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"distribution-free-predictive-inference-for","repo_url":"https://github.com/DEck13/paraconformal","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"distribution-free-predictive-inference-for","repo_url":"https://github.com/Sudhir22/conformalInference","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"prediction","task_name":"Prediction"},{"task_slug":"prediction-intervals","task_name":"Prediction Intervals"},{"task_slug":"regression-1","task_name":"regression"},{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1604.04173","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}