{"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/exact-post-selection-inference-for-sequential","title":"Exact Post-Selection Inference for Sequential Regression Procedures","arxiv_id":"1401.3889","date":"2014-01-16","proceeding":null,"authors":["Ryan J. Tibshirani","Jonathan Taylor","Richard Lockhart","Robert Tibshirani"],"abstract":"We propose new inference tools for forward stepwise regression, least angle regression, and the lasso. Assuming a Gaussian model for the observation vector y, we first describe a general scheme to perform valid inference after any selection event that can be characterized as y falling into a polyhedral set. This framework allows us to derive conditional (post-selection) hypothesis tests at any step of forward stepwise or least angle regression, or any step along the lasso regularization path, because, as it turns out, selection events for these procedures can be expressed as polyhedral constraints on y. The p-values associated with these tests are exactly uniform under the null distribution, in finite samples, yielding exact type I error control. The tests can also be inverted to produce confidence intervals for appropriate underlying regression parameters. The R package \"selectiveInference\", freely available on the CRAN repository, implements the new inference tools described in this paper.","url_abs":"http://arxiv.org/abs/1401.3889v5","url_pdf":"http://arxiv.org/pdf/1401.3889v5.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"exact-post-selection-inference-for-sequential","repo_url":"https://github.com/selective-inference/Python-software","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1401.3889","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1401.3889"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/selective-inference/Python-software","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"official":{"samples":1,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":1,"samples":[{"code_sha256_prefix":"144177013da8732f","entry":"MSE_three","repo":"selective-inference/Python-software","repo_kind":"official","path":"sandbox/randomized_tests/test_estimation.py","file_url":"https://github.com/selective-inference/Python-software/blob/HEAD/sandbox/randomized_tests/test_estimation.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NOASSERTION","inline_ok":false,"mcp_get_code":{"code_sha256":"144177013da8732f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}