Adaptive Lasso and group-Lasso for functional Poisson regression

TL;DR

This paper introduces adaptive Lasso and group-Lasso methods for high-dimensional Poisson regression, providing data-driven penalty weights and demonstrating their optimality and effectiveness through simulations and sequencing data analysis.

Contribution

It develops Poisson-specific penalty weights for Lasso and group-Lasso, extending regularization techniques to heteroscedastic Poisson models with theoretical guarantees.

Findings

Data-driven weights improve variable selection accuracy.

Methods achieve theoretical optimality in the oracle sense.

Successful application to Next Generation Sequencing data.

Abstract

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.