# Covariate balancing using the integral probability metric for causal inference

arXiv: https://arxiv.org/abs/2305.13715 · HTML: https://mlsanity.com/paper/2305.13715/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [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)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [The Balancing Act in Causal Inference](https://mlsanity.com/paper/2110.14831/) (2021)
- [Learning fair representation with a parametric integral probability metric](https://mlsanity.com/paper/2202.02943/) (2022)
- [Adaptive Metric Dimensionality Reduction](https://mlsanity.com/paper/1302.2752/) (2013)
- [Entropy balancing is doubly robust](https://mlsanity.com/paper/1501.03571/) (2015)
- [Covariate Distribution Balance via Propensity Scores](https://mlsanity.com/paper/1810.01370/) (2018)

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

- [Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metrics](https://mlsanity.com/paper/2505.06435/) (2025)
- [Differentially Private Covariate Balancing Causal Inference](https://mlsanity.com/paper/2410.14789/) (2024)
- [SSL Framework for Causal Inconsistency between Structures and Representations](https://mlsanity.com/paper/2310.18634/) (2023)
- [ReLU integral probability metric and its applications](https://mlsanity.com/paper/2504.18897/) (2025)
- [TSCAN: Context-Aware Uplift Modeling via Two-Stage Training for Online Merchant Business Diagnosis](https://mlsanity.com/paper/2504.18881/) (2025)
- [RepFlow: Representation Enhanced Flow Matching for Causal Effect Estimation](https://mlsanity.com/paper/2605.05890/) (2026)
- [A nonparametric two-sample test using a parametric integral probability metric](https://mlsanity.com/paper/2606.16941/) (2026)
- [Testing Distributions Against Bounded Distinguishers](https://mlsanity.com/paper/2607.15645/) (2026)
- [Weighted Spline-Expanded Networks with Distributional Balancing for Continuous Treatment Effects](https://mlsanity.com/paper/2609.33740/) (2026)

## Abstract (arXiv)

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.