Generalized Optimal Matching Methods for Causal Inference

By Nathan Kallus. 2016

126 citations recorded by the source corpus.

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

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Citations in the corpus

Balanced Policy Evaluation and Learning (2017, positive): “This follows a general approach introduced by [22, 24] of finding optimal balancing weights that optimize a given CMSE objective directly rather than via a plug-in approach.”
The Balancing Act in Causal Inference (2021, methodology): “Ratkovic (2014), Kallus (2020), Li et al. (2018), Tan (2020), Wong and Chan (2018), Zhao (2019), and Zubizarreta (2015).”
Synthetic Difference In Differences (2018, unknown): “…some similarity to the work on “balancing” methods for program evaluation under unconfoundedness, including Athey, Imbens, and Wager ( 2018 ) ; Graham, Pinto, and Egel ( 2012 ) ; Hirshberg and Wager ( 2017 ) ; Imai and Ratkovic ( 2014 ) ; Kallus ( 2020 ) ; Zhao ( 2019 ); and Zubizarreta ( 2015 ) .”
Covariate balancing propensity score by tailored loss functions (2016, methodology): “To demonstrate the simplicity and effectiveness of the tailored loss function approach, we use the prominent simulation example of Kang and Schafer (2007). In this example, for each unit i = 1, .”
Augmented minimax linear estimation (2017, background): “In addition to strong conceptual support, estimators of the type have been found to perform well in practice across several application areas (Armstrong and Kolesár, 2018; Imbens and Wager, 2017; Kallus, 2016; Zubizarreta, 2015).”
Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations (2017, methodology): “Related methods that balance covariates approximately through a Lagrange relaxation of the balance constraints include those of Kallus (2017), Athey et al. (2018), Hirshberg & Wager (2019), Wong & Chan (2018) and Zhao (2019).”
Matching for Balance (2019, methodology): “Examples of these methods are Zubizarreta (2012), Diamond and Sekhon (2013), and Nikolaev et al. (2013); other related examples are Fogarty et al. (2015), Pimentel et al. (2015) and Kallus (2016).”