# Generalized Optimal Matching Methods for Causal Inference

arXiv: https://arxiv.org/abs/1612.08321 · HTML: https://mlsanity.com/paper/1612.08321/

## Key facts

- Cited by 39 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 26 Dec 2016.

## Built on by (most cited first, 30 of 39)

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- [Towards Causal Foundation Model: on Duality between Causal Inference and Attention](https://mlsanity.com/paper/2310.00809/) (2023)
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- [NCoRE: Neural Counterfactual Representation Learning for Combinations of Treatments](https://mlsanity.com/paper/2103.11175/) (2021)
- [Black Box Causal Inference: Effect Estimation via Meta Prediction](https://mlsanity.com/paper/2503.05985/) (2025)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [Neural Score Matching for High-Dimensional Causal Inference](https://mlsanity.com/paper/2203.00554/) (2022)
- [Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency](https://mlsanity.com/paper/2301.06240/) (2023)
- [Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension](https://mlsanity.com/paper/2102.11076/) (2021)
- [Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves](https://mlsanity.com/paper/2111.03950/) (2021)
- [Outcome Assumptions and Duality Theory for Balancing Weights](https://mlsanity.com/paper/2203.09557/) (2022)
- [Matching for causal effects via multimarginal unbalanced optimal transport](https://mlsanity.com/paper/2112.04398/) (2021)
- [Estimating Average Treatment Effects with Support Vector Machines](https://mlsanity.com/paper/2102.11926/) (2021)
- [Robust Sample Weighting to Facilitate Individualized Treatment Rule Learning for a Target Population](https://mlsanity.com/paper/2105.00581/) (2021)
- [Instrument Space Selection for Kernel Maximum Moment Restriction](https://mlsanity.com/paper/2106.03340/) (2021)
- [Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection](https://mlsanity.com/paper/2111.05277/) (2021)
- [Case-based off-policy policy evaluation using prototype learning](https://mlsanity.com/paper/2111.11113/) (2021)
- [Estimating causal effects with optimization-based methods: A review and empirical comparison](https://mlsanity.com/paper/2203.00097/) (2022)
- [Matched Machine Learning: A Generalized Framework for Treatment Effect Inference With Learned Metrics](https://mlsanity.com/paper/2304.01316/) (2023)
- [Scalable kernel balancing weights in a nationwide observational study of hospital profit status and heart attack outcomes](https://mlsanity.com/paper/2311.00568/) (2023)
- [Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations](https://mlsanity.com/paper/2407.08494/) (2024)
- [Towards Representation Learning for Weighting Problems in Design-Based Causal Inference](https://mlsanity.com/paper/2409.16407/) (2024)
- [Federated Instrumental Variable Analysis via Federated Generalized Method of Moments](https://mlsanity.com/paper/2505.21012/) (2025)
- [De-confounding Representation Learning for Counterfactual Inference on Continuous Treatment via Generative Adversarial Network](https://mlsanity.com/paper/2307.12625/) (2023)
- [VLUCI: Variational Learning of Unobserved Confounders for Counterfactual Inference](https://mlsanity.com/paper/2308.00904/) (2023)

## Abstract (arXiv)

We develop an encompassing framework for matching, covariate balancing, and doubly-robust methods for causal inference from observational data called generalized optimal matching (GOM). The framework is given by generalizing a new functional-analytical formulation of optimal matching, giving rise to the class of GOM methods, for which we provide a single unified theory to analyze tractability, consistency, and efficiency. Many commonly used existing methods are included in GOM and, using their GOM interpretation, can be extended to optimally and automatically trade off balance for variance and outperform their standard counterparts. As a subclass, GOM gives rise to kernel optimal matching (KOM), which, as supported by new theoretical and empirical results, is notable for combining many of the positive properties of other methods in one. KOM, which is solved as a linearly-constrained convex-quadratic optimization problem, inherits both the interpretability and model-free consistency of matching but can also achieve the √n-consistency of well-specified regression and the efficiency and robustness of doubly robust methods. In settings of limited overlap, KOM enables a very transparent method for interval estimation for partial identification and robust coverage. We demonstrate these benefits in examples with both synthetic and real data