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Title: An iterative sparse-group lasso Authors:  Juan Carlos Laria de la Cruz - Carlos III University of Madrid (Spain) [presenting]
Rosa Lillo - Universidad Carlos III de Madrid (Spain)
M Carmen Aguilera-Morillo - Universidad Carlos III de Madrid (Spain)
Abstract: Regression models with a sparsity constraint on the solution have become very popular in high dimensional problems. The Sparse-group Lasso (SGL) has gained a lot of attention in last years. Under its simplest formulation, SGL leads to a solution depending on two weight parameters, which control the penalization on the coefficients of the solution. Selecting these weight parameters is still an open problem. In most of the applications of the SGL this problem is left aside, and the parameters are either fixed based on a prior information about the data, or chosen to minimize some error function in a grid of possible values. However, an appropriate election of the parameters deserves more attention, considering that it plays a key role in the structure and interpretation of the solution. In this sense, we present a gradient-free coordinate descent algorithm that automatically selects both penalty parameters of the SGL. The advantages of our approach are illustrated using both real and synthetic data sets.