A. Mendez Civieta, M. C. Aguilera-Morillo, R. E. Lillo Rodríguez

Quantile regression defines a set of models that allow a relaxation of the classical first two moment conditions over the model error, and that provides robust estimators capable of dealing with heteroscedasticity and outliers. In high-dimensional problems, sparsity constraints have proved to be very useful, improving prediction accuracy and interpretability. Sparse group LASSO (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. In this work, we propose a more complex 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.

Keywords: quantile regression; group variable selection; LASSO; high dimension; genetic dataset.


GT4-2 Multivariate Analysis and Classification
September 3, 2019  4:50 PM
I3L10. Georgina Blanes building

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