{"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/scalable-algorithms-for-learning-high","title":"Scalable Algorithms for Learning High-Dimensional Linear Mixed Models","arxiv_id":"1803.04431","date":"2018-03-12","proceeding":null,"authors":["Zilong Tan","Kimberly Roche","Xiang Zhou","Sayan Mukherjee"],"abstract":"Linear mixed models (LMMs) are used extensively to model dependecies of\nobservations in linear regression and are used extensively in many application\nareas. Parameter estimation for LMMs can be computationally prohibitive on big\ndata. State-of-the-art learning algorithms require computational complexity\nwhich depends at least linearly on the dimension $p$ of the covariates, and\noften use heuristics that do not offer theoretical guarantees. We present\nscalable algorithms for learning high-dimensional LMMs with sublinear\ncomputational complexity dependence on $p$. Key to our approach are novel dual\nestimators which use only kernel functions of the data, and fast computational\ntechniques based on the subsampled randomized Hadamard transform. We provide\ntheoretical guarantees for our learning algorithms, demonstrating the\nrobustness of parameter estimation. Finally, we complement the theory with\nexperiments on large synthetic and real data.","url_abs":"http://arxiv.org/abs/1803.04431v1","url_pdf":"http://arxiv.org/pdf/1803.04431v1.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":"scalable-algorithms-for-learning-high","repo_url":"https://github.com/ZilongTan/arLMM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"high","task_name":"Vocal Bursts Intensity Prediction"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[{"method_slug":"linear-regression","method_name":"Linear Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}