{"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/wasserstein-regularization-for-sparse-multi","title":"Wasserstein regularization for sparse multi-task regression","arxiv_id":"1805.07833","date":"2018-05-20","proceeding":null,"authors":["Hicham Janati","Marco Cuturi","Alexandre Gramfort"],"abstract":"We focus in this paper on high-dimensional regression problems where each\nregressor can be associated to a location in a physical space, or more\ngenerally a generic geometric space. Such problems often employ sparse priors,\nwhich promote models using a small subset of regressors. To increase\nstatistical power, the so-called multi-task techniques were proposed, which\nconsist in the simultaneous estimation of several related models. Combined with\nsparsity assumptions, it lead to models enforcing the active regressors to be\nshared across models, thanks to, for instance L1 / Lq norms. We argue in this\npaper that these techniques fail to leverage the spatial information associated\nto regressors. Indeed, while sparse priors enforce that only a small subset of\nvariables is used, the assumption that these regressors overlap across all\ntasks is overly simplistic given the spatial variability observed in real data.\nIn this paper, we propose a convex regularizer for multi-task regression that\nencodes a more flexible geometry. Our regularizer is based on unbalanced\noptimal transport (OT) theory, and can take into account a prior geometric\nknowledge on the regressor variables, without necessarily requiring overlapping\nsupports. We derive an efficient algorithm based on a regularized formulation\nof OT, which iterates through applications of Sinkhorn's algorithm along with\ncoordinate descent iterations. The performance of our model is demonstrated on\nregular grids with both synthetic and real datasets as well as complex\ntriangulated geometries of the cortex with an application in neuroimaging.","url_abs":"http://arxiv.org/abs/1805.07833v3","url_pdf":"http://arxiv.org/pdf/1805.07833v3.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":"wasserstein-regularization-for-sparse-multi","repo_url":"https://github.com/hichamjanati/mtw","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1805.07833","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}