# Horseshoe Regularization for Machine Learning in Complex and Deep Models

arXiv: https://arxiv.org/abs/1904.10939 · HTML: https://mlsanity.com/paper/1904.10939/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2019.

## Built on by (most cited first, 6 of 6)

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- [Deep Partial Least Squares for Empirical Asset Pricing](https://mlsanity.com/paper/2206.10014/) (2022)
- [Interpretable (not just posthoc-explainable) medical claims modeling for discharge placement to prevent avoidable all-cause readmissions or death](https://mlsanity.com/paper/2208.12814/) (2022)
- [Interpretable (not just posthoc-explainable) heterogeneous survivor bias-corrected treatment effects for assignment of postdischarge interventions to prevent readmissions](https://mlsanity.com/paper/2304.09981/) (2023)
- [Interpretable Latent Variables in Deep State Space Models](https://mlsanity.com/paper/2203.02057/) (2022)
- [False Discovery Rate Control via Frequentist-assisted Horseshoe](https://mlsanity.com/paper/2502.05460/) (2025)

## Abstract (arXiv)

Since the advent of the horseshoe priors for regularization, global-local shrinkage methods have proved to be a fertile ground for the development of Bayesian methodology in machine learning, specifically for high-dimensional regression and classification problems. They have achieved remarkable success in computation, and enjoy strong theoretical support. Most of the existing literature has focused on the linear Gaussian case; see Bhadra et al. (2019b) for a systematic survey. The purpose of the current article is to demonstrate that the horseshoe regularization is useful far more broadly, by reviewing both methodological and computational developments in complex models that are more relevant to machine learning applications. Specifically, we focus on methodological challenges in horseshoe regularization in nonlinear and non-Gaussian models; multivariate models; and deep neural networks. We also outline the recent computational developments in horseshoe shrinkage for complex models along with a list of available software implementations that allows one to venture out beyond the comfort zone of the canonical linear regression problems.