# Regularization and confounding in linear regression for treatment effect estimation

arXiv: https://arxiv.org/abs/1602.02176 · HTML: https://mlsanity.com/paper/1602.02176/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2016.

## Built on by (most cited first, 12 of 12)

- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Benchmarking Heterogeneous Treatment Effect Models through the Lens of Interpretability](https://mlsanity.com/paper/2206.08363/) (2022)
- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Hybrid Meta-learners for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2506.13680/) (2025)
- [FedECA: Federated External Control Arms for Causal Inference with Time-To-Event Data in Distributed Settings](https://mlsanity.com/paper/2311.16984/) (2023)
- [CausalKANs: interpretable treatment effect estimation with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2509.22467/) (2025)
- [Interpretable Deep Causal Learning for Moderation Effects](https://mlsanity.com/paper/2206.10261/) (2022)
- [Ablation Studies for Novel Treatment Effect Estimation Models](https://mlsanity.com/paper/2410.15560/) (2024)
- [A Bayesian Additive Regression Tree Model for Learning Conditional Average Treatment Effects in Regression Discontinuity Designs](https://mlsanity.com/paper/2503.00326/) (2025)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Generative Learner for Distributional Causal Effects](https://mlsanity.com/paper/2503.17894/) (2025)
- [Forests for Differences: Robust Causal Inference Beyond Parametric DiD](https://mlsanity.com/paper/2505.09706/) (2025)

## Abstract (arXiv)

This paper investigates the use of regularization priors in the context of treatment effect estimation using observational data where the number of control variables is large relative to the number of observations. First, the phenomenon of regularization-induced confounding is introduced, which refers to the tendency of regularization priors to adversely bias treatment effect estimates by over-shrinking control variable regression coefficients. Then, a simultaneous regression model is presented which permits regularization priors to be specified in a way that avoids this unintentional re-confounding. The new model is illustrated on synthetic and empirical data.