# Horseshoe Forests for High-Dimensional Causal Survival Analysis

arXiv: https://arxiv.org/abs/2507.22004 · HTML: https://mlsanity.com/paper/2507.22004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 115 references that are in the map.
- First posted on arXiv 29 Jul 2025.

## Builds on (most cited first, 30 of 32)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Bayesian Compression for Deep Learning](https://mlsanity.com/paper/1705.08665/) (2017)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations](https://mlsanity.com/paper/1309.4686/) (2013)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [Estimating heterogeneous treatment effects with right-censored data via causal survival forests](https://mlsanity.com/paper/2001.09887/) (2020)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Bayesian Causal Inference: A Critical Review](https://mlsanity.com/paper/2206.15460/) (2022)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [Lasso Meets Horseshoe : A Survey](https://mlsanity.com/paper/1706.10179/) (2017)
- [On Theory for BART](https://mlsanity.com/paper/1810.00787/) (2018)
- [Individualized Treatment Effects with Censored Data via Fully Nonparametric Bayesian Accelerated Failure Time Models](https://mlsanity.com/paper/1706.06611/) (2017)
- [Regularization and confounding in linear regression for treatment effect estimation](https://mlsanity.com/paper/1602.02176/) (2016)
- [Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score](https://mlsanity.com/paper/1812.08683/) (2018)
- [Estimating heterogeneous survival treatment effect in observational data using machine learning](https://mlsanity.com/paper/2008.07044/) (2020)
- [On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior](https://mlsanity.com/paper/1610.05559/) (2016)
- [The Graphical Horseshoe Estimator for Inverse Covariance Matrices](https://mlsanity.com/paper/1707.06661/) (2017)
- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [Dynamic Shrinkage Processes](https://mlsanity.com/paper/1707.00763/) (2017)
- [Variable Selection with ABC Bayesian Forests](https://mlsanity.com/paper/1806.02304/) (2018)
- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions](https://mlsanity.com/paper/2103.08195/) (2021)
- [Doubly robust matching estimators for high dimensional confounding adjustment](https://mlsanity.com/paper/1612.00424/) (2016)
- [A flexible parametric accelerated failure time model](https://mlsanity.com/paper/2006.06807/) (2020)
- [The central role of Bayes theorem for joint estimation of causal effects and propensity scores](https://mlsanity.com/paper/1308.5595/) (2013)
- [Averaging causal estimators in high dimensions](https://mlsanity.com/paper/1906.09303/) (2019)

## Built on by (most cited first, 1 of 1)

- [Bayesian fusion forests for heterogeneous treatment effects on survival from randomised and real-world data](https://mlsanity.com/paper/2607.29295/) (2026)

## Abstract (arXiv)

We develop a Bayesian tree ensemble model to estimate heterogeneous treatment effects in censored survival data with high-dimensional covariates. Instead of imposing sparsity through the tree structure, we place a horseshoe prior directly on the step heights to achieve adaptive global-local shrinkage. This strategy allows flexible regularisation and reduces noise. We develop a reversible jump Gibbs sampler to accommodate the non-conjugate horseshoe prior within the tree ensemble framework. We show through extensive simulations that the method accurately estimates treatment effects in high-dimensional covariate spaces, at various sparsity levels, and under non-linear treatment effect functions. We further illustrate the practical utility of the proposed approach by a re-analysis of pancreatic ductal adenocarcinoma (PDAC) survival data from The Cancer Genome Atlas.