Towards representation learning for general weighting problems in causal inference

Weighting problems in treatment effect estimation can be solved by minimising an appropriate probability distance. However, choosing which distance to minimise is uneasy as it depends on the unknown data generating process (DGP). A workaround consists in choosing a distance depending on a suitable representation of covariates. In this work, we give errors that quantify how much bias is added to the weighting estimator when using a representation, giving clear objectives to minimise when learning the representation and generalising a large body of previous work on deconfounding, prognostic, balancing and propensity scores. We further outline a method minimising such objectives, and show promising numerical results on a high-dimensional dataset.