Generalized Optimal Matching Methods for Causal Inference

Abstract

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 $\sqrt{n}$-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

References in corpus (3)

• Matching Methods for Causal Inference: A Review and a Look Forward
• Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique
• Kernel-based Conditional Independence Test and Application in Causal Discovery

Cited by in corpus (10)

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• DeepMatch: Balancing Deep Covariate Representations for Causal Inference Using Adversarial Training
• Q* Approximation Schemes for Batch Reinforcement Learning: A Theoretical Comparison
• More robust estimation of sample average treatment effects using Kernel Optimal Matching in an observational study of spine surgical interventions
• Off-policy Evaluation in Infinite-Horizon Reinforcement Learning with Latent Confounders
• Policy Evaluation with Latent Confounders via Optimal Balance
• Characterization of Overlap in Observational Studies
• A Balancing Weight Framework for Estimating the Causal Effect of General Treatments
• Optimal Estimation of Generalized Average Treatment Effects using Kernel Optimal Matching
• Quantifying Error in the Presence of Confounders for Causal Inference