# Conformal Prediction for Causal Effects of Continuous Treatments

arXiv: https://arxiv.org/abs/2407.03094 · HTML: https://mlsanity.com/paper/2407.03094/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 64 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 30 of 36)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Identifying Causal-Effect Inference Failure with Uncertainty-Aware Models](https://mlsanity.com/paper/2007.00163/) (2020)
- [Conditional Density Estimation with Bayesian Normalising Flows](https://mlsanity.com/paper/1802.04908/) (2018)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Is MC Dropout Bayesian?](https://mlsanity.com/paper/2110.04286/) (2021)
- [Nonparametric causal effects based on incremental propensity score interventions](https://mlsanity.com/paper/1704.00211/) (2017)
- [Bayesian Neural Controlled Differential Equations for Treatment Effect Estimation](https://mlsanity.com/paper/2310.17463/) (2023)
- [Conformal Off-Policy Prediction in Contextual Bandits](https://mlsanity.com/paper/2206.04405/) (2022)
- [Probabilistically robust conformal prediction](https://mlsanity.com/paper/2307.16360/) (2023)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)

## Built on by (most cited first, 19 of 19)

- [Conformal Generative Modeling with Improved Sample Efficiency through Sequential Greedy Filtering](https://mlsanity.com/paper/2410.01660/) (2024)
- [Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner](https://mlsanity.com/paper/2411.03387/) (2024)
- [Stabilized Neural Prediction of Potential Outcomes in Continuous Time](https://mlsanity.com/paper/2410.03514/) (2024)
- [What If We Had Used a Different App? Reliable Counterfactual KPI Analysis in Wireless Systems](https://mlsanity.com/paper/2410.00150/) (2024)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [Differentially Private Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2503.03486/) (2025)
- [Uplift modeling with continuous treatments: A predict-then-optimize approach](https://mlsanity.com/paper/2412.09232/) (2024)
- [Multi-Condition Conformal Selection](https://mlsanity.com/paper/2510.08075/) (2025)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [Counterfactually Fair Conformal Prediction](https://mlsanity.com/paper/2510.08724/) (2025)
- [Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects](https://mlsanity.com/paper/2507.12581/) (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)
- [Prediction Intervals for Individual Treatment Effects in a Multiple Decision Point Framework using Conformal Inference](https://mlsanity.com/paper/2512.08828/) (2025)
- [Debiased Machine Learning for Conformal Prediction of Counterfactual Outcomes Under Runtime Confounding](https://mlsanity.com/paper/2604.03772/) (2026)
- [Set-Valued Policy Learning](https://mlsanity.com/paper/2605.19830/) (2026)
- [Attention-Based Estimation of the Individual Treatment Benefit Probability under Dose Variation](https://mlsanity.com/paper/2606.13821/) (2026)
- [Conformal Bayes under Continuous Label Shift: Sensitivity Analysis and the Limits of Exact Validity](https://mlsanity.com/paper/2609.27976/) (2026)
- [GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation](https://mlsanity.com/paper/2609.28895/) (2026)

## Abstract (arXiv)

Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic finite-sample guarantees. Yet, existing methods for conformal prediction of causal effects are limited to binary/discrete treatments and make highly restrictive assumptions such as known propensity scores. In this work, we provide a novel conformal prediction method for potential outcomes of continuous treatments. We account for the additional uncertainty introduced through propensity estimation so that our conformal prediction intervals are valid even if the propensity score is unknown. Our contributions are three-fold: (1) We derive finite-sample prediction intervals for potential outcomes of continuous treatments. (2) We provide an algorithm for calculating the derived intervals. (3) We demonstrate the effectiveness of the conformal prediction intervals in experiments on synthetic and real-world datasets. To the best of our knowledge, we are the first to propose conformal prediction for continuous treatments when the propensity score is unknown and must be estimated from data.