# Lasso Meets Horseshoe : A Survey

arXiv: https://arxiv.org/abs/1706.10179 · HTML: https://mlsanity.com/paper/1706.10179/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2017.

## Built on by (most cited first, 17 of 17)

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- [Sparse Bayesian Lasso via a Variable-Coefficient ℓ1 Penalty](https://mlsanity.com/paper/2211.05089/) (2022)
- [T-LoHo: A Bayesian Regularization Model for Structured Sparsity and Smoothness on Graphs](https://mlsanity.com/paper/2107.02510/) (2021)
- [Bayesian Cox model with graph-structured variable selection priors for multi-omics biomarker identification](https://mlsanity.com/paper/2503.13078/) (2025)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Bayesian Pliable Lasso with Horseshoe Prior for Interaction Effects in GLMs with Missing Responses](https://mlsanity.com/paper/2509.07501/) (2025)
- [Decoupling Shrinkage and Selection for the Bayesian Quantile Regression](https://mlsanity.com/paper/2107.08498/) (2021)
- [Autoencoded sparse Bayesian in-IRT factorization, calibration, and amortized inference for the Work Disability Functional Assessment Battery](https://mlsanity.com/paper/2210.10952/) (2022)
- [False Discovery Rate Control via Frequentist-assisted Horseshoe](https://mlsanity.com/paper/2502.05460/) (2025)
- [Bayesian Meta-Analyses Could Be More: A Case Study in Trial of Labor After a Cesarean-section Outcomes and Complications](https://mlsanity.com/paper/2601.10089/) (2026)
- [Sparse Regression under Correlation and Weak Signals: A Reproducible Benchmark of Classical and Bayesian Methods](https://mlsanity.com/paper/2605.00835/) (2026)
- [Horseshoe Priors for Spatial Small Area Estimation: Regular Variation, Tail Robustness, and Deep Learning](https://mlsanity.com/paper/2606.30659/) (2026)
- [Sparsity by Default: The Theory and Practice of ARD in Gaussian Process Regression for Variable Selection](https://mlsanity.com/paper/2609.33550/) (2026)

## Abstract (arXiv)

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 non-convex. 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.