# Conformal Counterfactual Inference under Hidden Confounding

arXiv: https://arxiv.org/abs/2405.12387 · HTML: https://mlsanity.com/paper/2405.12387/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 20 May 2024.

## Builds on (most cited first, 24 of 24)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (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)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Causal Inference in Natural Language Processing: Estimation, Prediction, Interpretation and Beyond](https://mlsanity.com/paper/2109.00725/) (2021)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [AutoDebias: Learning to Debias for Recommendation](https://mlsanity.com/paper/2105.04170/) (2021)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Learning Individual Causal Effects from Networked Observational Data](https://mlsanity.com/paper/1906.03485/) (2019)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Learning Causal Effects on Hypergraphs](https://mlsanity.com/paper/2207.04049/) (2022)
- [Conformal Off-Policy Prediction in Contextual Bandits](https://mlsanity.com/paper/2206.04405/) (2022)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [The Deconfounded Recommender: A Causal Inference Approach to Recommendation](https://mlsanity.com/paper/1808.06581/) (2018)

## Built on by (most cited first, 10 of 10)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [Counterfactually Fair Conformal Prediction](https://mlsanity.com/paper/2510.08724/) (2025)
- [Individualised Counterfactual Examples Using Conformal Prediction Intervals](https://mlsanity.com/paper/2505.22326/) (2025)
- [A Systematic Review of Conformal Inference Procedures for Treatment Effect Estimation: Methods and Challenges](https://mlsanity.com/paper/2509.21660/) (2025)
- [Causal Inference on Networks under Misspecified Exposure Mappings: A Partial Identification Framework](https://mlsanity.com/paper/2602.03459/) (2026)
- [Evaluating Uplift Modeling under Structural Biases: Insights into Metric Stability and Model Robustness](https://mlsanity.com/paper/2603.20775/) (2026)
- [Confounding-Valid Conformal Inference for Counterfactual KPIs in Wireless Networks](https://mlsanity.com/paper/2609.05073/) (2026)
- [Rethinking the Flow-Based Gradual Domain Adaptation: A Semi-Dual Optimal Transport Perspective](https://mlsanity.com/paper/2602.01179/) (2026)
- [Conformal Individual Treatment Effect Estimation under Networked Interference](https://mlsanity.com/paper/2609.15254/) (2026)

## Abstract (arXiv)

Personalized decision making requires the knowledge of potential outcomes under different treatments, and confidence intervals about the potential outcomes further enrich this decision-making process and improve its reliability in high-stakes scenarios. Predicting potential outcomes along with its uncertainty in a counterfactual world poses the foundamental challenge in causal inference. Existing methods that construct confidence intervals for counterfactuals either rely on the assumption of strong ignorability, or need access to un-identifiable lower and upper bounds that characterize the difference between observational and interventional distributions. To overcome these limitations, we first propose a novel approach wTCP-DR based on transductive weighted conformal prediction, which provides confidence intervals for counterfactual outcomes with marginal converage guarantees, even under hidden confounding. With less restrictive assumptions, our approach requires access to a fraction of interventional data (from randomized controlled trials) to account for the covariate shift from observational distributoin to interventional distribution. Theoretical results explicitly demonstrate the conditions under which our algorithm is strictly advantageous to the naive method that only uses interventional data. After ensuring valid intervals on counterfactuals, it is straightforward to construct intervals for individual treatment effects (ITEs). We demonstrate our method across synthetic and real-world data, including recommendation systems, to verify the superiority of our methods compared against state-of-the-art baselines in terms of both coverage and efficiency