# Stabilized Inverse Probability Weighting via Isotonic Calibration

arXiv: https://arxiv.org/abs/2411.06342 · HTML: https://mlsanity.com/paper/2411.06342/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 10 Nov 2024.

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

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Distribution-free calibration guarantees for histogram binning without sample splitting](https://mlsanity.com/paper/2105.04656/) (2021)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Covariate Balancing Propensity Score by Tailored Loss Functions](https://mlsanity.com/paper/1601.05890/) (2016)
- [Augmented Minimax Linear Estimation](https://mlsanity.com/paper/1712.00038/) (2017)
- [Atlantic Causal Inference Conference (ACIC) Data Analysis Challenge 2017](https://mlsanity.com/paper/1905.09515/) (2019)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [The Balancing Act in Causal Inference](https://mlsanity.com/paper/2110.14831/) (2021)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts](https://mlsanity.com/paper/2402.01972/) (2024)
- [Causal isotonic calibration for heterogeneous treatment effects](https://mlsanity.com/paper/2302.14011/) (2023)
- [Self-Calibrating Conformal Prediction](https://mlsanity.com/paper/2402.07307/) (2024)
- [Minimax Linear Estimation of the Retargeted Mean](https://mlsanity.com/paper/1901.10296/) (2019)
- [Doubly robust inference via calibration](https://mlsanity.com/paper/2411.02771/) (2024)
- [Propensity score weighting under limited overlap and model misspecification](https://mlsanity.com/paper/2006.04038/) (2020)
- [On Adaptive Propensity Score Truncation in Causal Inference](https://mlsanity.com/paper/1707.05861/) (2017)
- [Isotonic propensity score matching](https://mlsanity.com/paper/2207.08868/) (2022)

## Built on by (most cited first, 9 of 9)

- [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)
- [Calibeating Prediction-Powered Inference](https://mlsanity.com/paper/2604.21260/) (2026)
- [Causal Judge Evaluation: Calibrated Surrogate Metrics for LLM Systems](https://mlsanity.com/paper/2512.11150/) (2025)
- [Bellman Calibration for V-Learning in Offline Reinforcement Learning](https://mlsanity.com/paper/2512.23694/) (2025)
- [Text Rationalization for Robust Causal Effect Estimation](https://mlsanity.com/paper/2512.05373/) (2025)
- [Tailoring Strictly Proper Scoring Rules for Downstream Tasks: An Application to Causal Inference](https://mlsanity.com/paper/2606.03332/) (2026)
- [Data-Poisoning Audits for Causal Effect Estimation](https://mlsanity.com/paper/2607.19692/) (2026)
- [Bellman Calibration for Marginalized Importance Weighting in Offline Reinforcement Learning](https://mlsanity.com/paper/2608.24858/) (2026)

## Abstract (arXiv)

Inverse weighting with an estimated propensity score is widely used by estimation methods in causal inference to adjust for confounding bias. However, directly inverting propensity score estimates can lead to instability, bias, and excessive variability due to large inverse weights, especially when treatment overlap is limited. In this work, we propose a post-hoc calibration algorithm for inverse propensity weights that generates well-calibrated, stabilized weights from user-supplied, cross-fitted propensity score estimates. Our approach employs a variant of isotonic regression with a loss function specifically tailored to the inverse propensity weights. Through theoretical analysis and empirical studies, we demonstrate that isotonic calibration improves the performance of doubly robust estimators of the average treatment effect.