# Uncertainty Quantification in Heterogeneous Treatment Effect Estimation with Gaussian-Process-Based Partially Linear Model

arXiv: https://arxiv.org/abs/2312.10435 · HTML: https://mlsanity.com/paper/2312.10435/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 16 Dec 2023.

## Builds on (most cited first, 8 of 8)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Benchmarking Framework for Performance-Evaluation of Causal Inference Analysis](https://mlsanity.com/paper/1802.05046/) (2018)
- [Bayesian Causal Inference: A Critical Review](https://mlsanity.com/paper/2206.15460/) (2022)

## Built on by (most cited first, 4 of 4)

- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Differentiable Pareto-Smoothed Weighting for High-Dimensional Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2404.17483/) (2024)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)

## Abstract (arXiv)

Estimating heterogeneous treatment effects across individuals has attracted growing attention as a statistical tool for performing critical decision-making. We propose a Bayesian inference framework that quantifies the uncertainty in treatment effect estimation to support decision-making in a relatively small sample size setting. Our proposed model places Gaussian process priors on the nonparametric components of a semiparametric model called a partially linear model. This model formulation has three advantages. First, we can analytically compute the posterior distribution of a treatment effect without relying on the computationally demanding posterior approximation. Second, we can guarantee that the posterior distribution concentrates around the true one as the sample size goes to infinity. Third, we can incorporate prior knowledge about a treatment effect into the prior distribution, improving the estimation efficiency. Our experimental results show that even in the small sample size setting, our method can accurately estimate the heterogeneous treatment effects and effectively quantify its estimation uncertainty.