Univariate-Guided Sparse Regression

In this article, we introduce "uniLasso," a novel statistical method for 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 data sets, 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.