{"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/adjusting-inverse-regression-for-predictors","title":"Adjusting inverse regression for predictors with clustered distribution","arxiv_id":"2308.15038","date":"2023-08-29","proceeding":null,"authors":["Wei Luo","Yan Guo"],"abstract":"A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\\beta^\\mathsf{T}X)$ and a degenerate $\\mathrm{var}(X|\\beta^\\mathsf{T}X)$ for the desired reduced predictor $\\beta^\\mathsf{T}X$. In this paper, we adjust the first and second-order inverse regression methods by modeling $E(X|\\beta^\\mathsf{T}X)$ and $\\mathrm{var}(X|\\beta^\\mathsf{T}X)$ under the mixture model assumption on $X$, which allows these terms to convey more complex patterns and is most suitable when $X$ has a clustered sample distribution. The proposed SDR methods build a natural path between inverse regression and the localized SDR methods, and in particular inherit the advantages of both; that is, they are $\\sqrt{n}$-consistent, efficiently implementable, directly adjustable under the high-dimensional settings, and fully recovering the desired reduced predictor. These findings are illustrated by simulation studies and a real data example at the end, which also suggest the effectiveness of the proposed methods for nonclustered data.","url_abs":"https://arxiv.org/abs/2308.15038v1","url_pdf":"https://arxiv.org/pdf/2308.15038v1.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":"adjusting-inverse-regression-for-predictors","repo_url":"https://github.com/yan-guo1120/irmn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}