Adaptive Lasso and group-Lasso for functional Poisson regression

Abstract

High dimensional Poisson regression has become a standard framework for the analysis ofmassive counts datasets. In this work we estimate the intensity function of the Poissonregression model by using a dictionary approach, which generalizes the classical basis ap-proach, combined with a Lasso or a group-Lasso procedure. Selection depends on penaltyweights that need to be calibrated. Standard methodologies developed in the Gaussianframework can not be directly applied to Poisson models due to heteroscedasticity. Here weprovide data-driven weights for the Lasso and the group-Lasso derived from concentrationinequalities adapted to the Poisson case. We show that the associated Lasso and group-Lassoprocedures are theoretically optimal in the oracle approach. Simulations are used to assessthe empirical performance of our procedure, and an original application to the analysis ofNext Generation Sequencing data is provided.nonnonouirechercheInternationa