Timezone: »
A limitation of Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regression coefficients. Additionally, in many applications, the data is obtained by averaging multiple measurements: this reduces the noise variance, but it dramatically reduces sample sizes and prevents refined noise modeling. In this work, we propose a concomitant estimator that can cope with complex noise structure by using non-averaged measurements, its data-fitting term arising as a smoothing of the nuclear norm. The resulting optimization problem is convex and amenable, thanks to smoothing theory, to state-of-the-art optimization techniques that leverage the sparsity of the solutions. Practical benefits are demonstrated on toy datasets, realistic simulated data and real neuroimaging data.
Author Information
Quentin Bertrand (INRIA)
Mathurin Massias (Inria)
Alexandre Gramfort (INRIA)
Joseph Salmon (Université de Montpellier)
More from the Same Authors
-
2021 : Electromagnetic neural source imaging under sparsity constraints with SURE-based hyperparameter tuning »
Pierre-Antoine Bannier · Quentin Bertrand · Joseph Salmon · Alexandre Gramfort -
2021 Poster: HNPE: Leveraging Global Parameters for Neural Posterior Estimation »
Pedro Rodrigues · Thomas Moreau · Gilles Louppe · Alexandre Gramfort -
2021 : The NeurIPS 2021 BEETL Competition: Benchmarks for EEG Transfer Learning + Q&A »
Xiaoxi Wei · Vinay Jayaram · Sylvain Chevallier · Giulia Luise · Camille Jeunet · Moritz Grosse-Wentrup · Alexandre Gramfort · Aldo A Faisal -
2021 Poster: Shared Independent Component Analysis for Multi-Subject Neuroimaging »
Hugo Richard · Pierre Ablin · Bertrand Thirion · Alexandre Gramfort · Aapo Hyvarinen -
2020 Poster: Modeling Shared responses in Neuroimaging Studies through MultiView ICA »
Hugo Richard · Luigi Gresele · Aapo Hyvarinen · Bertrand Thirion · Alexandre Gramfort · Pierre Ablin -
2020 Spotlight: Modeling Shared responses in Neuroimaging Studies through MultiView ICA »
Hugo Richard · Luigi Gresele · Aapo Hyvarinen · Bertrand Thirion · Alexandre Gramfort · Pierre Ablin -
2020 Poster: Statistical control for spatio-temporal MEG/EEG source imaging with desparsified mutli-task Lasso »
Jerome-Alexis Chevalier · Joseph Salmon · Alexandre Gramfort · Bertrand Thirion -
2019 Poster: Learning step sizes for unfolded sparse coding »
Pierre Ablin · Thomas Moreau · Mathurin Massias · Alexandre Gramfort -
2019 Poster: Manifold-regression to predict from MEG/EEG brain signals without source modeling »
David Sabbagh · Pierre Ablin · Gael Varoquaux · Alexandre Gramfort · Denis A. Engemann -
2018 Poster: Multivariate Convolutional Sparse Coding for Electromagnetic Brain Signals »
Tom Dupré la Tour · Thomas Moreau · Mainak Jas · Alexandre Gramfort -
2017 Poster: Learning the Morphology of Brain Signals Using Alpha-Stable Convolutional Sparse Coding »
Mainak Jas · Tom Dupré la Tour · Umut Simsekli · Alexandre Gramfort -
2016 Poster: GAP Safe Screening Rules for Sparse-Group Lasso »
Eugene Ndiaye · Olivier Fercoq · Alexandre Gramfort · Joseph Salmon -
2015 Poster: GAP Safe screening rules for sparse multi-task and multi-class models »
Eugene Ndiaye · Olivier Fercoq · Alexandre Gramfort · Joseph Salmon -
2010 Poster: Brain covariance selection: better individual functional connectivity models using population prior »
Gaël Varoquaux · Alexandre Gramfort · Jean-Baptiste Poline · Bertrand Thirion