# Sensitivity analysis under the f-sensitivity models: a distributional robustness perspective

arXiv: https://arxiv.org/abs/2203.04373 · HTML: https://mlsanity.com/paper/2203.04373/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2022.

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

- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Distributionally Robust Policy Learning under Concept Drifts](https://mlsanity.com/paper/2412.14297/) (2024)
- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)
- [Minimax Regret Estimation for Generalizing Heterogeneous Treatment Effects with Multisite Data](https://mlsanity.com/paper/2412.11136/) (2024)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Multi-Distribution Robust Conformal Prediction](https://mlsanity.com/paper/2601.02998/) (2026)
- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Assessing the robustness of heterogeneous treatment effects in survival analysis under informative censoring](https://mlsanity.com/paper/2510.13397/) (2025)
- [Data Fusion for High-Resolution Estimation](https://mlsanity.com/paper/2508.14858/) (2025)

## Abstract (arXiv)

This paper introduces the f-sensitivity model, a new sensitivity model that characterizes the violation of unconfoundedness in causal inference. It assumes the selection bias due to unmeasured confounding is bounded "on average"; compared with the widely used point-wise sensitivity models in the literature, it is able to capture the strength of unmeasured confounding by not only its magnitude but also the chance of encountering such a magnitude. We propose a framework for sensitivity analysis under our new model based on a distributional robustness perspective. We first show that the bounds on counterfactual means under the f-sensitivity model are optimal solutions to a new class of distributionally robust optimization (DRO) programs, whose dual forms are essentially risk minimization problems. We then construct point estimators for these bounds by applying a novel debiasing technique to the output of the corresponding empirical risk minimization (ERM) problems. Our estimators are shown to converge to valid bounds on counterfactual means if any nuisance component can be estimated consistently, and to the exact bounds when the ERM step is additionally consistent. We further establish asymptotic normality and Wald-type inference for these estimators under slower-than-root-n convergence rates of the estimated nuisance components. Finally, the performance of our method is demonstrated with numerical experiments.