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Poster
Handling correlated and repeated measurements with the smoothed multivariate square-root Lasso
Quentin Bertrand · Mathurin Massias · Alexandre Gramfort · Joseph Salmon

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #43
in Algorithms -- Sparsity and Compressed Sensing »

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.

Keywords: Convex Optimization · Brain Imaging · Neuroscience and Cognitive Science · Algorithms -> Sparsity and Compressed Sensing; Optimization
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Author Information

Quentin Bertrand (INRIA)
Mathurin Massias (Inria)
Alexandre Gramfort (INRIA)
Joseph Salmon (Université de Montpellier)

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