Title: Model selection with lasso-zero tuned by quantile universal thresholding
Authors: Pascaline Descloux - University of Geneva (Switzerland) [presenting]
Sylvain Sardy - University of Geneva (Switzerland)
Abstract: When performing variable selection, controlling the false discovery rate (FDR) while maintaining high power is challenging. A new $\ell_1$-based estimator called lasso-zero is introduced for the linear regression problem. It relies on the repeated use of noise dictionaries concatenated to the design matrix for fitting the noise component. The threshold level is tuned by quantile universal thresholding, a general methodology that was introduced to select the regularization parameter of any thresholding estimator. The FDR is provably controlled for orthogonal designs, and empirically for independent Gaussian predictors. In case of correlated variables, simulations show that even though the FDR is no longer controlled, the proposed methodology exhibits a very good tradeoff between low FDR and high true positive rate.