# The Balancing Act in Causal Inference

arXiv: https://arxiv.org/abs/2110.14831 · HTML: https://mlsanity.com/paper/2110.14831/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2021.

## Built on by (most cited first, 20 of 20)

- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Covariate balancing using the integral probability metric for causal inference](https://mlsanity.com/paper/2305.13715/) (2023)
- [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)
- [Outcome Assumptions and Duality Theory for Balancing Weights](https://mlsanity.com/paper/2203.09557/) (2022)
- [Calibrated and Conformal Propensity Scores for Causal Effect Estimation](https://mlsanity.com/paper/2306.00382/) (2023)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [Scalable kernel balancing weights in a nationwide observational study of hospital profit status and heart attack outcomes](https://mlsanity.com/paper/2311.00568/) (2023)
- [Regularizing Extrapolation in Causal Inference](https://mlsanity.com/paper/2509.17180/) (2025)
- [De-paradox Tree: Breaking Down Simpson's Paradox via A Kernel-Based Partition Algorithm](https://mlsanity.com/paper/2603.02174/) (2026)
- [ConfHit: Conformal Generative Design with Oracle Free Guarantees](https://mlsanity.com/paper/2603.07371/) (2026)
- [Meta-analysis of individualized treatment rules via sign-coherency](https://mlsanity.com/paper/2211.15476/) (2022)
- [A Stable and Efficient Covariate-Balancing Estimator for Causal Survival Effects](https://mlsanity.com/paper/2310.02278/) (2023)
- [Causal rule ensemble approach for multi-arm data](https://mlsanity.com/paper/2504.17166/) (2025)
- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)
- [Fast Uncertainty Quantification for Kernel-Based Estimators in Large-Scale Causal Inference](https://mlsanity.com/paper/2603.13662/) (2026)
- [Two Approaches to Direct Estimation of Riesz Representers](https://mlsanity.com/paper/2603.20936/) (2026)
- [Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning](https://mlsanity.com/paper/2605.06386/) (2026)
- [Anytime-Valid Confirmation of Covariate Balance for Prespecified Corrections](https://mlsanity.com/paper/2607.23157/) (2026)

## Abstract (arXiv)

The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss two broad approaches to estimating these weights: the more traditional one, which fits a propensity score model and then uses the reciprocal of the estimated propensity score to construct weights, and the balancing approach, which estimates the inverse propensity weights essentially by the method of moments, finding weights that achieve balance in the sample. We review ideas from the causal inference, sample surveys, and semiparametric estimation literatures, with particular attention to the role of balance as a sufficient condition for robust inference. We focus on the inverse propensity weighting and augmented inverse propensity weighting estimators for the average treatment effect given strong ignorability and consider generalizations for a broader class of problems including policy evaluation and the estimation of individualized treatment effects.