{"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/boosted-sparse-and-low-rank-tensor-regression","title":"Boosted Sparse and Low-Rank Tensor Regression","arxiv_id":"1811.01158","date":"2018-11-03","proceeding":"NeurIPS 2018 12","authors":["Lifang He","Kun Chen","Wanwan Xu","Jiayu Zhou","Fei Wang"],"abstract":"We propose a sparse and low-rank tensor regression model to relate a\nunivariate outcome to a feature tensor, in which each unit-rank tensor from the\nCP decomposition of the coefficient tensor is assumed to be sparse. This\nstructure is both parsimonious and highly interpretable, as it implies that the\noutcome is related to the features through a few distinct pathways, each of\nwhich may only involve subsets of feature dimensions. We take a\ndivide-and-conquer strategy to simplify the task into a set of sparse unit-rank\ntensor regression problems. To make the computation efficient and scalable, for\nthe unit-rank tensor regression, we propose a stagewise estimation procedure to\nefficiently trace out its entire solution path. We show that as the step size\ngoes to zero, the stagewise solution paths converge exactly to those of the\ncorresponding regularized regression. The superior performance of our approach\nis demonstrated on various real-world and synthetic examples.","url_abs":"http://arxiv.org/abs/1811.01158v1","url_pdf":"http://arxiv.org/pdf/1811.01158v1.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":"boosted-sparse-and-low-rank-tensor-regression","repo_url":"https://github.com/LifangHe/SURF","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"boosted-sparse-and-low-rank-tensor-regression","repo_url":"https://github.com/LifangHe/NeurIPS18_SURF","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1811.01158","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}