# Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction

arXiv: https://arxiv.org/abs/2407.16037 · HTML: https://mlsanity.com/paper/2407.16037/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 82 references that are in the map.
- First posted on arXiv 22 Jul 2024.

## Builds on (most cited first, 23 of 23)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [Designing and Deploying Online Field Experiments](https://mlsanity.com/paper/1409.3174/) (2014)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Elastic Net Regularization Paths for All Generalized Linear Models](https://mlsanity.com/paper/2103.03475/) (2021)
- [Machine Learning for Variance Reduction in Online Experiments](https://mlsanity.com/paper/2106.07263/) (2021)
- [Causal isotonic calibration for heterogeneous treatment effects](https://mlsanity.com/paper/2302.14011/) (2023)
- [High-dimensional regression adjustments in randomized experiments](https://mlsanity.com/paper/1607.06801/) (2016)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Regression Adjustment for Estimating Distributional Treatment Effects in Randomized Controlled Trials](https://mlsanity.com/paper/2407.14074/) (2024)
- [Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes](https://mlsanity.com/paper/1608.05142/) (2016)
- [Quantile Treatment Effects in Difference in Differences Models under Dependence Restrictions and with only Two Time Periods](https://mlsanity.com/paper/1702.03618/) (2017)
- [Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations](https://mlsanity.com/paper/2105.14752/) (2021)

## Built on by (most cited first, 5 of 5)

- [On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization](https://mlsanity.com/paper/2506.05945/) (2025)
- [A Diffusion-Based Method for Learning the Multi-Outcome Distribution of Medical Treatments](https://mlsanity.com/paper/2506.01533/) (2025)
- [Beyond the Average: Distributional Causal Inference under Imperfect Compliance](https://mlsanity.com/paper/2509.15594/) (2025)
- [Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks](https://mlsanity.com/paper/2507.07738/) (2025)
- [Modeling Covariate Transition for Efficient Estimation of Longitudinal Treatment Effects in Randomized Experiments](https://mlsanity.com/paper/2605.31443/) (2026)

## Abstract (arXiv)

We propose a novel regression adjustment method designed for estimating distributional treatment effect parameters in randomized experiments. Randomized experiments have been extensively used to estimate treatment effects in various scientific fields. However, to gain deeper insights, it is essential to estimate distributional treatment effects rather than relying solely on average effects. Our approach incorporates pre-treatment covariates into a distributional regression framework, utilizing machine learning techniques to improve the precision of distributional treatment effect estimators. The proposed approach can be readily implemented with off-the-shelf machine learning methods and remains valid as long as the nuisance components are reasonably well estimated. Also, we establish the asymptotic properties of the proposed estimator and present a uniformly valid inference method. Through simulation results and real data analysis, we demonstrate the effectiveness of integrating machine learning techniques in reducing the variance of distributional treatment effect estimators in finite samples.