{"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/why-stable-learning-works-a-theory-of","title":"A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalization","arxiv_id":"2111.02355","date":"2021-11-03","proceeding":null,"authors":["Renzhe Xu","Xingxuan Zhang","Zheyan Shen","Tong Zhang","Peng Cui"],"abstract":"Covariate-shift generalization, a typical case in out-of-distribution (OOD) generalization, requires a good performance on the unknown test distribution, which varies from the accessible training distribution in the form of covariate shift. Recently, independence-driven importance weighting algorithms in stable learning literature have shown empirical effectiveness to deal with covariate-shift generalization on several learning models, including regression algorithms and deep neural networks, while their theoretical analyses are missing. In this paper, we theoretically prove the effectiveness of such algorithms by explaining them as feature selection processes. We first specify a set of variables, named minimal stable variable set, that is the minimal and optimal set of variables to deal with covariate-shift generalization for common loss functions, such as the mean squared loss and binary cross-entropy loss. Afterward, we prove that under ideal conditions, independence-driven importance weighting algorithms could identify the variables in this set. Analysis of asymptotic properties is also provided. These theories are further validated in several synthetic experiments.","url_abs":"https://arxiv.org/abs/2111.02355v4","url_pdf":"https://arxiv.org/pdf/2111.02355v4.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":"why-stable-learning-works-a-theory-of","repo_url":"https://github.com/windxrz/independence-driven-iw","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"feature-selection","task_name":"feature selection"}],"methods":[{"method_slug":"feature-selection","method_name":"Feature Selection"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2111.02355","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2111.02355"}},"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/windxrz/independence-driven-iw","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":0,"samples":[{"code_sha256_prefix":"315cc2e0e080a34c","entry":"get_method","repo":"windxrz/independence-driven-iw","repo_kind":"official","path":"idiw/methods/methods.py","file_url":"https://github.com/windxrz/independence-driven-iw/blob/HEAD/idiw/methods/methods.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"315cc2e0e080a34c"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}