# Causal isotonic calibration for heterogeneous treatment effects

arXiv: https://arxiv.org/abs/2302.14011 · HTML: https://mlsanity.com/paper/2302.14011/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 81 references that are in the map.
- First posted on arXiv 27 Feb 2023.

## Builds on (most cited first, 18 of 18)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Uncertainty Quantification and Deep Ensembles](https://mlsanity.com/paper/2007.08792/) (2020)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Distribution-free binary classification: prediction sets, confidence intervals and calibration](https://mlsanity.com/paper/2006.10564/) (2020)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [Distribution-free calibration guarantees for histogram binning without sample splitting](https://mlsanity.com/paper/2105.04656/) (2021)
- [Evaluating Treatment Prioritization Rules via Rank-Weighted Average Treatment Effects](https://mlsanity.com/paper/2111.07966/) (2021)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [Stable discovery of interpretable subgroups via calibration in causal studies](https://mlsanity.com/paper/2008.10109/) (2020)
- [Calibration Error for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2203.13364/) (2022)
- [From controlled to undisciplined data: estimating causal effects in the era of data science using a potential outcome framework](https://mlsanity.com/paper/2012.06865/) (2020)
- [A Calibration Approach to Transportability and Data-Fusion with Observational Data](https://mlsanity.com/paper/2008.06615/) (2020)

## Built on by (most cited first, 16 of 16)

- [Self-Calibrating Conformal Prediction](https://mlsanity.com/paper/2402.07307/) (2024)
- [Stabilized Inverse Probability Weighting via Isotonic Calibration](https://mlsanity.com/paper/2411.06342/) (2024)
- [Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands](https://mlsanity.com/paper/2501.11868/) (2025)
- [Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction](https://mlsanity.com/paper/2502.05676/) (2025)
- [Orthogonal Causal Calibration](https://mlsanity.com/paper/2406.01933/) (2024)
- [On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization](https://mlsanity.com/paper/2506.05945/) (2025)
- [Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction](https://mlsanity.com/paper/2407.16037/) (2024)
- [Improving the Finite Sample Estimation of Average Treatment Effects using Double/Debiased Machine Learning with Propensity Score Calibration](https://mlsanity.com/paper/2409.04874/) (2024)
- [Orthogonal Representation Learning for Estimating Causal Quantities](https://mlsanity.com/paper/2502.04274/) (2025)
- [Calibrated and Conformal Propensity Scores for Causal Effect Estimation](https://mlsanity.com/paper/2306.00382/) (2023)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Robust CATE Estimation Using Novel Ensemble Methods](https://mlsanity.com/paper/2407.03690/) (2024)
- [Attenuated Heterogeneity in Fixed-Effects Causal Forests, and a Cross-Fitted Correction](https://mlsanity.com/paper/2607.22896/) (2026)
- [An analysis of binary isotonic regression: degrees of freedom and implications for calibration](https://mlsanity.com/paper/2607.27301/) (2026)
- [Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning](https://mlsanity.com/paper/2608.24858/) (2026)

## Abstract (arXiv)

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.