# Univariate-Guided Sparse Regression

arXiv: https://arxiv.org/abs/2501.18360 · HTML: https://mlsanity.com/paper/2501.18360/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2025.

## Built on by (most cited first, 4 of 4)

- [Stability Selection via Variable Decorrelation](https://mlsanity.com/paper/2505.20864/) (2025)
- [Statistical Learning for Heterogeneous Treatment Effects: Pretraining, Prognosis, and Prediction](https://mlsanity.com/paper/2505.00310/) (2025)
- [A Stable Lasso](https://mlsanity.com/paper/2511.02306/) (2025)
- [TinyBayes: Closed-Form Bayesian Inference via Jacobi Prior for Real-Time Image Classification on Edge Devices](https://mlsanity.com/paper/2605.06333/) (2026)

## Abstract (arXiv)

In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive for stability and interpretation of the model. Through comprehensive simulations and applications to real-world datasets, we demonstrate that UniLasso outperforms Lasso in various settings, particularly in terms of sparsity and model interpretability. We prove asymptotic support recovery and mean-squared error consistency under a set of conditions different from the well-known irrepresentability conditions for the Lasso. Extensions to generalized linear models (GLMs) and Cox regression are also discussed.