The goal of this paper is to contrast and survey the major advances in two of the most commonly used high-dimensional techniques, namely, the Lasso and horseshoe regularization. Lasso is a gold standard for predictor selection while horseshoe is a state-of-the-art Bayesian estimator for sparse signals. Lasso is fast and scalable and uses convex optimization whilst the horseshoe is nonconvex. Our novel perspective focuses on three aspects: (i) theoretical optimality in high-dimensional inference for the Gaussian sparse model and beyond, (ii) efficiency and scalability of computation and (iii) methodological development and performance.
"Lasso Meets Horseshoe: A Survey." Statist. Sci. 34 (3) 405 - 427, August 2019. https://doi.org/10.1214/19-STS700