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Abstract:
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Weighting methods are an increasingly popular way to perform causal inference, especially ones that weight by the inverse propensity score. However, such weights suffer from increased variance and bias when the outcome and weighting models are both incorrect. To correct for this deficit, some more recent methods use weights that target covariate balance between treated and control units. But these techniques may rely too heavily on the mean of the covariates being sufficient to balance distributions between experimental groups. Instead, we propose a more robust method in terms of mean-squared error that relies on an interpolation between matching and weighting by using optimal transport weights. We simultaneously minimize the variance of the weights while minimizing Wasserstein distances between treated and non-treated units to achieve good performance both in well-specified and mis-specified settings. We apply our method in Frequentist and Bayesian settings and give results from an applied data example.
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