# Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding

arXiv: https://arxiv.org/abs/1810.02894 · HTML: https://mlsanity.com/paper/1810.02894/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2018.

## Built on by (most cited first, 30 of 51)

- [Causal machine learning for predicting treatment outcomes](https://mlsanity.com/paper/2410.08770/) (2024)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding](https://mlsanity.com/paper/2112.11449/) (2021)
- [B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding](https://mlsanity.com/paper/2304.10577/) (2023)
- [Sharp Bounds for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2305.16988/) (2023)
- [Long Story Short: Omitted Variable Bias in Causal Machine Learning](https://mlsanity.com/paper/2112.13398/) (2021)
- [Scalable Sensitivity and Uncertainty Analysis for Causal-Effect Estimates of Continuous-Valued Interventions](https://mlsanity.com/paper/2204.10022/) (2022)
- [Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation](https://mlsanity.com/paper/2311.11321/) (2023)
- [Estimating individual treatment effects under unobserved confounding using binary instruments](https://mlsanity.com/paper/2208.08544/) (2022)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Generalizing Off-Policy Learning under Sample Selection Bias](https://mlsanity.com/paper/2112.01387/) (2021)
- [What's the Harm? Sharp Bounds on the Fraction Negatively Affected by Treatment](https://mlsanity.com/paper/2205.10327/) (2022)
- [Estimating and Improving Dynamic Treatment Regimes With a Time-Varying Instrumental Variable](https://mlsanity.com/paper/2104.07822/) (2021)
- [Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders](https://mlsanity.com/paper/2302.00662/) (2023)
- [Model-Free and Model-Based Policy Evaluation when Causality is Uncertain](https://mlsanity.com/paper/2204.00956/) (2022)
- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Intact-VAE: Estimating Treatment Effects under Unobserved Confounding](https://mlsanity.com/paper/2101.06662/) (2021)
- [Causal Fairness under Unobserved Confounding: A Neural Sensitivity Framework](https://mlsanity.com/paper/2311.18460/) (2023)
- [Conformal Counterfactual Inference under Hidden Confounding](https://mlsanity.com/paper/2405.12387/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Individualized Decision-Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox](https://mlsanity.com/paper/2110.10961/) (2021)
- [Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding](https://mlsanity.com/paper/2212.09844/) (2022)
- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding](https://mlsanity.com/paper/2306.01157/) (2023)

## Abstract (arXiv)

We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for personalized assessments. Recent work has focused on how to learn CATE under unconfoundedness, i.e., when there are no unobserved confounders. Since CATE may not be identified when unconfoundedness is violated, we develop a functional interval estimator that predicts bounds on the individual causal effects under realistic violations of unconfoundedness. Our estimator takes the form of a weighted kernel estimator with weights that vary adversarially. We prove that our estimator is sharp in that it converges exactly to the tightest bounds possible on CATE when there may be unobserved confounders. Further, we study personalized decision rules derived from our estimator and prove that they achieve optimal minimax regret asymptotically. We assess our approach in a simulation study as well as demonstrate its application in the case of hormone replacement therapy by comparing conclusions from a real observational study and clinical trial.