# Regression modeling on stratified data with the lasso

arXiv: https://arxiv.org/abs/1508.05476 · HTML: https://mlsanity.com/paper/1508.05476/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2015.

## Built on by (most cited first, 5 of 5)

- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Unified Transfer Learning Models in High-Dimensional Linear Regression](https://mlsanity.com/paper/2307.00238/) (2023)
- [Structured Estimation of Heterogeneous Time Series](https://mlsanity.com/paper/2311.08658/) (2023)
- [A cost-sensitive constrained Lasso](https://mlsanity.com/paper/2401.18023/) (2024)
- [Transfer Learning in ℓ1 Regularized Regression: Hyperparameter Selection Strategy based on Sharp Asymptotic Analysis](https://mlsanity.com/paper/2409.17704/) (2024)

## Abstract (arXiv)

We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a reference stratum. We show that the performance of a penalized version of this approach depends on this arbitrary choice. We propose a refined approach that bypasses this arbitrary choice, at almost no additional computational cost. Regarding model selection consistency, our proposal mimics the strategy based on an optimal and covariate-specific choice for the reference stratum. Results from an empirical study confirm that our proposal generally outperforms the basic approach in the identification and description of the interactions. An illustration on gene expression data is provided.