# Synthetic Counterfactual Labels for Efficient Conformal Counterfactual Inference

arXiv: https://arxiv.org/abs/2509.04112 · HTML: https://mlsanity.com/paper/2509.04112/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [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)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Sionna: An Open-Source Library for Next-Generation Physical Layer Research](https://mlsanity.com/paper/2203.11854/) (2022)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [RealCause: Realistic Causal Inference Benchmarking](https://mlsanity.com/paper/2011.15007/) (2020)
- [Conformal Sensitivity Analysis for Individual Treatment Effects](https://mlsanity.com/paper/2112.03493/) (2021)
- [Conformal Meta-learners for Predictive Inference of Individual Treatment Effects](https://mlsanity.com/paper/2308.14895/) (2023)
- [Extending inferences from a randomized trial to a new target population](https://mlsanity.com/paper/1805.00550/) (2018)
- [Semi-Supervised Risk Control via Prediction-Powered Inference](https://mlsanity.com/paper/2412.11174/) (2024)
- [Adaptive Prediction-Powered AutoEval with Reliability and Efficiency Guarantees](https://mlsanity.com/paper/2505.18659/) (2025)
- [Learning-based Handover in Mobile Millimeter-wave Networks](https://mlsanity.com/paper/2003.11009/) (2020)
- [Calibrating doubly-robust estimators with unbalanced treatment assignment](https://mlsanity.com/paper/2403.01585/) (2024)
- [Statistical Decision Theory with Counterfactual Loss](https://mlsanity.com/paper/2505.08908/) (2025)

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

- [Confounding-Valid Conformal Inference for Counterfactual KPIs in Wireless Networks](https://mlsanity.com/paper/2609.05073/) (2026)
- [Conformal Individual Treatment Effect Estimation under Networked Interference](https://mlsanity.com/paper/2609.15254/) (2026)

## Abstract (arXiv)

This work addresses the problem of constructing reliable prediction intervals for individual counterfactual outcomes. Existing conformal counterfactual inference (CCI) methods provide marginal coverage guarantees but often produce overly conservative intervals, particularly under treatment imbalance when counterfactual samples are scarce. We introduce synthetic data-powered CCI (SP-CCI), a new framework that augments the calibration set with synthetic counterfactual labels generated by a pre-trained counterfactual model. To ensure validity, SP-CCI incorporates synthetic samples into a conformal calibration procedure based on risk-controlling prediction sets (RCPS) with a debiasing step informed by prediction-powered inference (PPI). We prove that SP-CCI achieves tighter prediction intervals while preserving marginal coverage, with theoretical guarantees under both exact and approximate importance weighting. Empirical results on different datasets confirm that SP-CCI consistently reduces interval width compared to standard CCI across all settings.