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Title: A new approach to penalized quantile regression Authors:  Alvaro Mendez Civieta - Universidad Carlos III de Madrid (Spain) [presenting]
Rosa Lillo - Universidad Carlos III de Madrid (Spain)
M Carmen Aguilera-Morillo - Universidad Carlos III de Madrid (Spain)
Abstract: Along years, quantile regression has become a key technique used to obtain robust estimators that are able to deal with heteroscedasticity and outliers. In high-dimensional problems, sparsity constrains have shown a great improvement in interpretability and prediction accuracy. One of the best known constraints is the sparse group lasso (SGL). SGL is a penalization technique used in regression problems where the covariates have a natural grouped structure, providing solutions that are both between and within group sparse. We introduce a flexible version, the adaptive sparse group lasso (ASGL), that adds weights to the penalization. Usually, these weights are taken as a function of the original non-penalized model. This approach is only feasible in low-dimensional problems. We propose a solution that allows using adaptive weights in high-dimensional scenarios. We show the benefits of our proposal in a real genetic dataset.