# Balancing Covariates via Propensity Score Weighting

arXiv: https://arxiv.org/abs/1609.07494 · HTML: https://mlsanity.com/paper/1609.07494/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2016.

## Built on by (most cited first, 30 of 65)

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- [Towards Causal Foundation Model: on Duality between Causal Inference and Attention](https://mlsanity.com/paper/2310.00809/) (2023)
- [Generalization bound for estimating causal effects from observational network data](https://mlsanity.com/paper/2308.04011/) (2023)
- [End-to-End Balancing for Causal Continuous Treatment-Effect Estimation](https://mlsanity.com/paper/2107.13068/) (2021)
- [On the Distinction Between "Conditional Average Treatment Effects" (CATE) and "Individual Treatment Effects" (ITE) Under Ignorability Assumptions](https://mlsanity.com/paper/2108.04939/) (2021)
- [Adversarial De-confounding in Individualised Treatment Effects Estimation](https://mlsanity.com/paper/2210.10530/) (2022)
- [Covariate balancing using the integral probability metric for causal inference](https://mlsanity.com/paper/2305.13715/) (2023)
- [Neighborhood Adaptive Estimators for Causal Inference under Network Interference](https://mlsanity.com/paper/2212.03683/) (2022)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands](https://mlsanity.com/paper/2501.11868/) (2025)
- [Debiased Collaborative Filtering with Kernel-Based Causal Balancing](https://mlsanity.com/paper/2404.19596/) (2024)
- [Local Gaussian process extrapolation for BART models with applications to causal inference](https://mlsanity.com/paper/2204.10963/) (2022)
- [Differentially Private Covariate Balancing Causal Inference](https://mlsanity.com/paper/2410.14789/) (2024)
- [Estimating Average Treatment Effects with Support Vector Machines](https://mlsanity.com/paper/2102.11926/) (2021)
- [Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Population](https://mlsanity.com/paper/2105.00581/) (2021)
- [Calibrated and Conformal Propensity Scores for Causal Effect Estimation](https://mlsanity.com/paper/2306.00382/) (2023)
- [Causal Judge Evaluation: Calibrated Surrogate Metrics for LLM Systems](https://mlsanity.com/paper/2512.11150/) (2025)
- [Robust Causal Learning for the Estimation of Average Treatment Effects](https://mlsanity.com/paper/2209.01805/) (2022)
- [Federated Causal Inference from Multi-Site Observational Data via Propensity Score Aggregation](https://mlsanity.com/paper/2505.17961/) (2025)
- [A Two-armed Bandit Framework for A/B Testing](https://mlsanity.com/paper/2507.18118/) (2025)
- [Text Rationalization for Robust Causal Effect Estimation](https://mlsanity.com/paper/2512.05373/) (2025)
- [Generative Synthetic Data for Causal Inference: Pitfalls, Remedies, and Opportunities](https://mlsanity.com/paper/2604.23904/) (2026)
- [Case-based off-policy policy evaluation using prototype learning](https://mlsanity.com/paper/2111.11113/) (2021)
- [Estimating causal effects with optimization-based methods: A review and empirical comparison](https://mlsanity.com/paper/2203.00097/) (2022)
- [Generalized Balancing Weights via Deep Neural Networks](https://mlsanity.com/paper/2211.07533/) (2022)
- [Contagion Effect Estimation Using Proximal Embeddings](https://mlsanity.com/paper/2306.02479/) (2023)

## Abstract (arXiv)

Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit's weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.