Representation Learning Preserving Ignorability and Covariate Matching for Treatment Effects

Abstract: Estimating treatment effects from observational data is challenging due to two main reasons: (a) hidden confounding, and (b) covariate mismatch (control and treatment groups not having identical distributions). Long lines of works exist that address only either of these issues. To address the former, conventional techniques that require detailed knowledge in the form of causal graphs have been proposed. For the latter, covariate matching and importance weighting methods have been used. Recently, there has been progress in combining testable independencies with partial side information for tackling hidden confounding. A common framework to address both hidden confounding and selection bias is missing. We propose neural architectures that aim to learn a representation of pre-treatment covariates that is a valid adjustment and also satisfies covariate matching constraints. We combine two different neural architectures: one based on gradient matching across domains created by subsampling a suitable anchor variable that assumes causal side information, followed by the other, a covariate matching transformation. We prove that approximately invariant representations yield approximate valid adjustment sets which would enable an interval around the true causal effect. In contrast to usual sensitivity analysis, where an unknown nuisance parameter is varied, we have a testable approximation yielding a bound on the effect estimate. We also outperform various baselines with respect to ATE and PEHE errors on causal benchmarks that include IHDP, Jobs, Cattaneo, and an image-based Crowd Management dataset.