Séance Séminaire

Séminaire de Probabilités et Statistique

Concomitant Lasso with Repetitions: smoothing nuclear norm to handle non homoscedastic noise

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such 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. 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.