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