# Estimating causal effects with optimization-based methods: A review and empirical comparison

arXiv: https://arxiv.org/abs/2203.00097 · HTML: https://mlsanity.com/paper/2203.00097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 106 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 27 of 27)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [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)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training](https://mlsanity.com/paper/1802.05664/) (2018)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [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)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [FLAME: A Fast Large-scale Almost Matching Exactly Approach to Causal Inference](https://mlsanity.com/paper/1707.06315/) (2017)
- [Entropy balancing is doubly robust](https://mlsanity.com/paper/1501.03571/) (2015)
- [MALTS: Matching After Learning to Stretch](https://mlsanity.com/paper/1811.07415/) (2018)
- [Kernel Balancing: A flexible non-parametric weighting procedure for estimating causal effects](https://mlsanity.com/paper/1605.00155/) (2016)
- [Almost-Matching-Exactly for Treatment Effect Estimation under Network Interference](https://mlsanity.com/paper/2003.00964/) (2020)
- [Adaptive Hyper-box Matching for Interpretable Individualized Treatment Effect Estimation](https://mlsanity.com/paper/2003.01805/) (2020)
- [A Framework for Optimal Matching for Causal Inference](https://mlsanity.com/paper/1606.05188/) (2016)
- [Estimation and Inference on Nonlinear and Heterogeneous Effects](https://mlsanity.com/paper/1703.05849/) (2017)
- [A robust approach to quantifying uncertainty in matching problems of causal inference](https://mlsanity.com/paper/1812.02227/) (2018)
- [Optimal Estimation of Generalized Average Treatment Effects using Kernel Optimal Matching](https://mlsanity.com/paper/1908.04748/) (2019)
- [Interpretable Almost-Matching-Exactly With Instrumental Variables](https://mlsanity.com/paper/1906.11658/) (2019)
- [Matching Bounds: How Choice of Matching Algorithm Impacts Treatment Effects Estimates and What to Do about It](https://mlsanity.com/paper/2009.02776/) (2020)

## Built on by (most cited first, 1 of 1)

- [Improving uplift model evaluation on RCT data](https://mlsanity.com/paper/2210.02152/) (2022)

## Abstract (arXiv)

In the absence of randomized controlled and natural experiments, it is necessary to balance the distributions of (observable) covariates of the treated and control groups in order to obtain an unbiased estimate of a causal effect of interest; otherwise, a different effect size may be estimated, and incorrect recommendations may be given. To achieve this balance, there exist a wide variety of methods. In particular, several methods based on optimization models have been recently proposed in the causal inference literature. While these optimization-based methods empirically showed an improvement over a limited number of other causal inference methods in their relative ability to balance the distributions of covariates and to estimate causal effects, they have not been thoroughly compared to each other and to other noteworthy causal inference methods. In addition, we believe that there exist several unaddressed opportunities that operational researchers could contribute with their advanced knowledge of optimization, for the benefits of the applied researchers that use causal inference tools. In this review paper, we present an overview of the causal inference literature and describe in more detail the optimization-based causal inference methods, provide a comparative analysis of the prevailing optimization-based methods, and discuss opportunities for new methods.