# Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects

arXiv: https://arxiv.org/abs/2202.12891 · HTML: https://mlsanity.com/paper/2202.12891/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 94 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 30 of 38)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Multi-Task Deep Neural Networks for Natural Language Understanding](https://mlsanity.com/paper/1901.11504/) (2019)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders](https://mlsanity.com/paper/1902.00450/) (2019)
- [On Inductive Biases for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2106.03765/) (2021)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Learning Weighted Representations for Generalization Across Designs](https://mlsanity.com/paper/1802.08598/) (2018)
- [Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap](https://mlsanity.com/paper/1711.11286/) (2017)
- [Semi-Supervised Learning by Augmented Distribution Alignment](https://mlsanity.com/paper/1905.08171/) (2019)
- [Combining multiple observational data sources to estimate causal effects](https://mlsanity.com/paper/1801.00802/) (2018)
- [Combining Observational and Experimental Datasets Using Shrinkage Estimators](https://mlsanity.com/paper/2002.06708/) (2020)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)

## Built on by (most cited first, 30 of 32)

- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [Transfer Learning on Heterogeneous Feature Spaces for Treatment Effects Estimation](https://mlsanity.com/paper/2210.06183/) (2022)
- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Estimating Conditional Average Treatment Effects with Missing Treatment Information](https://mlsanity.com/paper/2203.01422/) (2022)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Efficient and robust transfer learning of optimal individualized treatment regimes with right-censored survival data](https://mlsanity.com/paper/2301.05491/) (2023)
- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Heterogeneous Treatment Effect with Trained Kernels of the Nadaraya-Watson Regression](https://mlsanity.com/paper/2207.09139/) (2022)
- [Improving the Generation and Evaluation of Synthetic Data for Downstream Medical Causal Inference](https://mlsanity.com/paper/2510.18768/) (2025)
- [Transfer Learning for Causal Effect Estimation](https://mlsanity.com/paper/2305.09126/) (2023)
- [Causal Effect Estimation from Observational and Interventional Data Through Matrix Weighted Linear Estimators](https://mlsanity.com/paper/2306.06002/) (2023)
- [Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data](https://mlsanity.com/paper/2406.06452/) (2024)
- [Long-term Causal Inference via Modeling Sequential Latent Confounding](https://mlsanity.com/paper/2502.18994/) (2025)
- [BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect](https://mlsanity.com/paper/2211.10793/) (2022)
- [Assessing Electricity Service Unfairness with Transfer Counterfactual Learning](https://mlsanity.com/paper/2310.03258/) (2023)
- [Estimating treatment effects from single-arm trials via latent-variable modeling](https://mlsanity.com/paper/2311.03002/) (2023)
- [Combining Incomplete Observational and Randomized Data for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2410.21343/) (2024)
- [Robust estimation of heterogeneous treatment effects in randomized trials leveraging external data](https://mlsanity.com/paper/2507.03681/) (2025)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Accounting for Missing Covariates in Heterogeneous Treatment Estimation](https://mlsanity.com/paper/2410.15655/) (2024)
- [A Partial Initialization Strategy to Mitigate the Overfitting Problem in CATE Estimation with Hidden Confounding](https://mlsanity.com/paper/2501.08888/) (2025)
- [Deconfounded Warm-Start Thompson Sampling with Applications to Precision Medicine](https://mlsanity.com/paper/2505.17283/) (2025)
- [Uncovering Bias Mechanisms in Observational Studies](https://mlsanity.com/paper/2506.01191/) (2025)
- [Conditional Average Treatment Effect Estimation Under Hidden Confounders](https://mlsanity.com/paper/2506.12304/) (2025)
- [Mitigating Hidden Confounding by Progressive Confounder Imputation via Large Language Models](https://mlsanity.com/paper/2507.02928/) (2025)
- [Augmenting Limited and Biased RCTs through Pseudo-Sample Matching-Based Observational Data Fusion Method](https://mlsanity.com/paper/2509.18148/) (2025)
- [Testing Effect Homogeneity and Confounding in High-Dimensional Experimental and Observational Studies](https://mlsanity.com/paper/2602.19703/) (2026)

## Abstract (arXiv)

Estimating heterogeneous treatment effects is an important problem across many domains. In order to accurately estimate such treatment effects, one typically relies on data from observational studies or randomized experiments. Currently, most existing works rely exclusively on observational data, which is often confounded and, hence, yields biased estimates. While observational data is confounded, randomized data is unconfounded, but its sample size is usually too small to learn heterogeneous treatment effects. In this paper, we propose to estimate heterogeneous treatment effects by combining large amounts of observational data and small amounts of randomized data via representation learning. In particular, we introduce a two-step framework: first, we use observational data to learn a shared structure (in form of a representation); and then, we use randomized data to learn the data-specific structures. We analyze the finite sample properties of our framework and compare them to several natural baselines. As such, we derive conditions for when combining observational and randomized data is beneficial, and for when it is not. Based on this, we introduce a sample-efficient algorithm, called CorNet. We use extensive simulation studies to verify the theoretical properties of CorNet and multiple real-world datasets to demonstrate our method's superiority compared to existing methods.