{"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/a-nonparametric-maximum-likelihood-approach-1","title":"A Nonparametric Maximum Likelihood Approach to Mixture of Regression","arxiv_id":"2108.09816","date":"2021-08-22","proceeding":null,"authors":["Hansheng Jiang","Adityanand Guntuboyina"],"abstract":"We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the mixing distribution form and rely on the EM algorithm, we develop a fully nonparametric maximum likelihood estimator (NPMLE). We show that this estimator exists under broad conditions and can be computed via a discrete approximation procedure inspired by the exemplar method. We further establish theoretical guarantees demonstrating that the NPMLE achieves near-parametric rates in estimating the conditional density of $Y|X$, both for fixed and random designs, when $\\sigma$ is known and $G^*$ has compact support. In the random design setting, we also prove consistency of the estimated mixing distribution in the L\\'evy-Prokhorov distance. Numerical experiments indicate that our approach performs well and additionally enables posterior-based individualized coefficient inference through an empirical Bayes framework.","url_abs":"https://arxiv.org/abs/2108.09816v1","url_pdf":"https://arxiv.org/pdf/2108.09816v1.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":"a-nonparametric-maximum-likelihood-approach-1","repo_url":"https://github.com/hanshengjiang/npmle_git","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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}