# Entropy balancing is doubly robust

arXiv: https://arxiv.org/abs/1501.03571 · HTML: https://mlsanity.com/paper/1501.03571/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2015.

## Built on by (most cited first, 13 of 13)

- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Deconfounding Scores: Feature Representations for Causal Effect Estimation with Weak Overlap](https://mlsanity.com/paper/2104.05762/) (2021)
- [End-to-End Balancing for Causal Continuous Treatment-Effect Estimation](https://mlsanity.com/paper/2107.13068/) (2021)
- [Covariate balancing using the integral probability metric for causal inference](https://mlsanity.com/paper/2305.13715/) (2023)
- [Debiased Collaborative Filtering with Kernel-Based Causal Balancing](https://mlsanity.com/paper/2404.19596/) (2024)
- [Outcome Assumptions and Duality Theory for Balancing Weights](https://mlsanity.com/paper/2203.09557/) (2022)
- [Differentially Private Covariate Balancing Causal Inference](https://mlsanity.com/paper/2410.14789/) (2024)
- [Collaborative Heterogeneous Causal Inference Beyond Meta-analysis](https://mlsanity.com/paper/2404.15746/) (2024)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Targeted Optimal Treatment Regime Learning Using Summary Statistics](https://mlsanity.com/paper/2201.06229/) (2022)
- [Estimating causal effects with optimization-based methods: A review and empirical comparison](https://mlsanity.com/paper/2203.00097/) (2022)
- [Temporal-Spatial Entropy Balancing for Causal Continuous Treatment-Effect Estimation](https://mlsanity.com/paper/2312.08670/) (2023)
- [Differentially Private Two-Stage Empirical Risk Minimization with Applications to Individualized Treatment Rule](https://mlsanity.com/paper/2602.12604/) (2026)

## Abstract (arXiv)

Covariate balance is a conventional key diagnostic for methods used estimating causal effects from observational studies. Recently, there is an emerging interest in directly incorporating covariate balance in the estimation. We study a recently proposed entropy maximization method called Entropy Balancing (EB), which exactly matches the covariate moments for the different experimental groups in its optimization problem. We show EB is doubly robust with respect to linear outcome regression and logistic propensity score regression, and it reaches the asymptotic semiparametric variance bound when both regressions are correctly specified. This is surprising to us because there is no attempt to model the outcome or the treatment assignment in the original proposal of EB. Our theoretical results and simulations suggest that EB is a very appealing alternative to the conventional weighting estimators that estimate the propensity score by maximum likelihood.