# A Framework for Optimal Matching for Causal Inference

arXiv: https://arxiv.org/abs/1606.05188 · HTML: https://mlsanity.com/paper/1606.05188/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2016.

## Built on by (most cited first, 5 of 5)

- [Causality from Bottom to Top: A Survey](https://mlsanity.com/paper/2403.11219/) (2024)
- [Variable Importance Matching for Causal Inference](https://mlsanity.com/paper/2302.11715/) (2023)
- [Treatment Effect Estimation using Invariant Risk Minimization](https://mlsanity.com/paper/2103.07788/) (2021)
- [Estimating causal effects with optimization-based methods: A review and empirical comparison](https://mlsanity.com/paper/2203.00097/) (2022)
- [Retrospective Counterfactual Prediction by Conditioning on the Factual Outcome: A Cross-World Approach](https://mlsanity.com/paper/2603.27320/) (2026)

## Abstract (arXiv)

We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be expressed as optimal in this framework, including nearest-neighbor matching, coarsened exact matching, and mean-matched sampling. This reveals their motivation and aptness as structural priors formulated by embedding the effect in a particular functional space. This also gives rise to a range of new, kernel-based matching estimators that arise when one embeds the effect in a reproducing kernel Hilbert space. Depending on the case, these estimators can be found using either quadratic optimization or integer optimization. We show that estimators based on universal kernels are universally consistent without model specification. In empirical results using both synthetic and real data, the new, kernel-based estimators outperform all standard causal estimators in estimation error.