MALTS: Matching After Learning to Stretch

We introduce a flexible framework for matching in causal inference that produces high quality almost-exact matches. Most prior work in matching uses ad hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates that degrade the distance metric. In this work, we learn an interpretable distance metric used for matching, which leads to substantially higher quality matches. The distance metric can stretch continuous covariates and matches exactly on categorical covariates. The framework is flexible in that the user can choose the form of distance metric, the type of optimization algorithm, and the type of relaxation for matching. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for estimation of conditional average treatment effects.