Mutual Information Based Matching for Causal Inference with Observational Data

Lei Sun; Alexander G. Nikolaev

This paper presents an information theory-driven matching methodology for making causal inference from observational data. The paper adopts a âpotential outcomes frameworkâ view on evaluating the strength of cause-effect relationships: the population-wide average effects of binary treatments are estimated by comparing two groups of units -- the treated and untreated (control). To reduce the bias in such treatment effect estimation, one has to compose a control group in such a way that across the compared groups of units, treatment is independent of the units' covariates. This requirement gives rise to a subset selection / matching problem. This paper presents the models and algorithms that solve the matching problem by minimizing the mutual information (MI) between the covariates and the treatment variable. Such a formulation becomes tractable thanks to the derived optimality conditions that tackle the non-linearity of the sample-based MI function. Computational experiments with mixed integer-programming formulations and four matching algorithms demonstrate the utility of MI based matching for causal inference studies. The algorithmic developments culminate in a matching heuristic that allows for balancing the compared groups in polynomial (close to linear) time, thus allowing for treatment effect estimation with large data sets.

Mutual Information Based Matching for Causal Inference with Observational Data

Abstract