Joint estimation of $K$ related regression models with simple $L_1$-norm penalties

Abstract

We propose a new approach, along with refinements, based on $L_1$ penalties and aimed at jointly estimating several related regression models. Its main interest is that it can be rewritten as a weighted lasso on a simple transformation of the original data set. In particular, it does not need new dedicated algorithms and is ready to implement under a variety of regression models, {\em e.g.}, using standard R packages. Moreover, asymptotic oracle properties are derived along with preliminary non-asymptotic results, suggesting good theoretical properties. Our approach is further compared with state-of-the-art competitors under various settings on synthetic data: these empirical results confirm that our approach performs at least similarly to its competitors. As a final illustration, an analysis of road safety data is provided.

arXiv comment33 pages, 7 figures

References in corpus (14)

• Discussion of "Least angle regression" by Efron et al
• Rejoinder to "Least angle regression" by Efron et al
• Least Angle Regression
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Discussion of "Least angle regression" by Efron et al
• Simultaneous analysis of Lasso and Dantzig selector
• On the conditions used to prove oracle results for the Lasso
• On the Prediction Performance of the Lasso
• A coordinate-wise optimization algorithm for the Fused Lasso

Cited by in corpus (1)

• A SAEM Algorithm for Fused Lasso Penalized Non Linear Mixed Effect Models: Application to Group Comparison in Pharmacokinetic