Adaptive Lasso and group-Lasso for functional Poisson regression - Archive ouverte HAL Access content directly
Journal Articles Journal of Machine Learning Research Year : 2016

Adaptive Lasso and group-Lasso for functional Poisson regression

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 satisfy fast and slow oracle inequalities. 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.
Fichier principal
Vignette du fichier
15-021.pdf (974.91 Ko) Télécharger le fichier
DJ-MSE-J-10.pdf (28.29 Ko) Télécharger le fichier
DJ-reconstruction-group-J-10.pdf (76.14 Ko) Télécharger le fichier
DJ-reconstruction-lasso-J-10.pdf (75.17 Ko) Télécharger le fichier
MSE-calibration-gamma.pdf (10.34 Ko) Télécharger le fichier
Ori-chr20.pdf (79.53 Ko) Télécharger le fichier
Ori-chrX.pdf (55.97 Ko) Télécharger le fichier
dF-calibration-gamma.pdf (9.85 Ko) Télécharger le fichier
simulation-notindict-reconstruction-J-10.pdf (77.61 Ko) Télécharger le fichier
simulation-notindict-tradeoff-frame-J-10.pdf (9.15 Ko) Télécharger le fichier
truebeta0-J-10.pdf (32.58 Ko) Télécharger le fichier
truebeta0-reconstruction-vanilla-lasso-J-10.pdf (10.41 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

hal-01097914 , version 1 (22-12-2014)
hal-01097914 , version 2 (08-06-2016)

Licence

Public Domain

Identifiers

Cite

Stéphane Ivanoff, Franck Picard, Vincent Rivoirard. Adaptive Lasso and group-Lasso for functional Poisson regression. Journal of Machine Learning Research, 2016, 17 (55), pp.1--46. ⟨hal-01097914v2⟩
215 View
604 Download

Altmetric

Share

Gmail Facebook X LinkedIn More