# Distributionally Robust Causal Inference with Observational Data

arXiv: https://arxiv.org/abs/2210.08326 · HTML: https://mlsanity.com/paper/2210.08326/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 15 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [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)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap](https://mlsanity.com/paper/1711.11286/) (2017)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach](https://mlsanity.com/paper/2002.02579/) (2020)
- [Safe Policy Learning through Extrapolation: Application to Pre-trial Risk Assessment](https://mlsanity.com/paper/2109.11679/) (2021)
- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)
- [Safe Policy Learning under Regression Discontinuity Designs with Multiple Cutoffs](https://mlsanity.com/paper/2208.13323/) (2022)
- [Studentized sensitivity analysis for the sample average treatment effect in paired observational studies](https://mlsanity.com/paper/1609.02112/) (2016)
- [Model-assisted sensitivity analysis for treatment effects under unmeasured confounding via regularized calibrated estimation](https://mlsanity.com/paper/2209.11383/) (2022)
- [Sensitivity Analysis for matched pair analysis of binary data: From worst case to average case analysis](https://mlsanity.com/paper/1707.09549/) (2017)

## Built on by (most cited first, 2 of 2)

- [Distributionally Robust Skeleton Learning of Discrete Bayesian Networks](https://mlsanity.com/paper/2311.06117/) (2023)
- [Learning Risk Scores Robust to Unobserved Confounders](https://mlsanity.com/paper/2609.27144/) (2026)

## Abstract (arXiv)

We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first specify the maximal degree to which the distribution of unobserved potential outcomes may deviate from that of observed outcomes. We then derive sharp bounds on the average treatment effects under this assumption. Our framework encompasses the popular marginal sensitivity model as a special case, and we demonstrate how the proposed methodology can address a primary challenge of the marginal sensitivity model that it produces uninformative results when unobserved confounders substantially affect treatment and outcome. Specifically, we develop an alternative sensitivity model, called the distributional sensitivity model, under the assumption that heterogeneity of treatment effect due to unobserved variables is relatively small. Unlike the marginal sensitivity model, the distributional sensitivity model allows for potential lack of overlap and often produces informative bounds even when unobserved variables substantially affect both treatment and outcome. Finally, we show how to extend the distributional sensitivity model to difference-in-differences designs and settings with instrumental variables. Through simulation and empirical studies, we demonstrate the applicability of the proposed methodology.