{"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/generalized-concomitant-multi-task-lasso-for","title":"Generalized Concomitant Multi-Task Lasso for sparse multimodal regression","arxiv_id":"1705.09778","date":"2017-05-27","proceeding":null,"authors":["Mathurin Massias","Olivier Fercoq","Alexandre Gramfort","Joseph Salmon"],"abstract":"In high dimension, it is customary to consider Lasso-type estimators to\nenforce sparsity. For standard Lasso theory to hold, the regularization\nparameter should be proportional to the noise level, yet the latter is\ngenerally unknown in practice. A possible remedy is to consider estimators,\nsuch as the Concomitant/Scaled Lasso, which jointly optimize over the\nregression coefficients as well as over the noise level, making the choice of\nthe regularization independent of the noise level. However, when data from\ndifferent sources are pooled to increase sample size, or when dealing with\nmultimodal datasets, noise levels typically differ and new dedicated estimators\nare needed. In this work we provide new statistical and computational solutions\nto deal with such heteroscedastic regression models, with an emphasis on\nfunctional brain imaging with combined magneto- and electroencephalographic\n(M/EEG) signals. Adopting the formulation of Concomitant Lasso-type estimators,\nwe propose a jointly convex formulation to estimate both the regression\ncoefficients and the (square root of the) noise covariance. When our framework\nis instantiated to de-correlated noise, it leads to an efficient algorithm\nwhose computational cost is not higher than for the Lasso and Concomitant\nLasso, while addressing more complex noise structures. Numerical experiments\ndemonstrate that our estimator yields improved prediction and support\nidentification while correctly estimating the noise (square root) covariance.\nResults on multimodal neuroimaging problems with M/EEG data are also reported.","url_abs":"http://arxiv.org/abs/1705.09778v2","url_pdf":"http://arxiv.org/pdf/1705.09778v2.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":"generalized-concomitant-multi-task-lasso-for","repo_url":"https://github.com/samiatto/colide","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"eeg-1","task_name":"EEG"},{"task_slug":"eeg","task_name":"Electroencephalogram (EEG)"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1705.09778","atlas_url":"https://app.syntology.ai/?focus=1705.09778","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}