Univariate-Guided Sparse Regression

TL;DR

This paper introduces UniLasso, a two-stage sparse regression method that improves stability and interpretability over Lasso, with proven support recovery and extensions to GLMs and Cox models.

Contribution

UniLasso is a novel two-stage sparse regression technique that preserves coefficient signs and magnitudes, enhancing model stability and interpretability.

Findings

Outperforms Lasso in sparsity and interpretability

Proves support recovery and MSE consistency

Effective in real-world datasets

Abstract

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.