Orthogonal Representation Learning for Estimating Causal Quantities

Abstract

End-to-end representation learning has become a powerful tool for estimating causal quantities from high-dimensional observational data, but its efficiency remained unclear. Here, we face a central tension: End-to-end representation learning methods often work well in practice but lack asymptotic optimality in the form of the quasi-oracle efficiency. In contrast, two-stage Neyman-orthogonal learners provide such a theoretical optimality property but do not explicitly benefit from the strengths of representation learning. In this work, we step back and ask two research questions: (1) When do representations strengthen existing Neyman-orthogonal learners? and (2) Can a balancing constraint - a commonly proposed technique in the representation learning literature - provide improvements to Neyman-orthogonality? We address these two questions through our theoretical and empirical analysis, where we introduce a unifying framework that connects representation learning with Neyman-orthogonal learners (namely, OR-learners). In particular, we show that, under the low-dimensional manifold hypothesis, the OR-learners can strictly improve the estimation error of the standard Neyman-orthogonal learners. At the same time, we find that the balancing constraint requires an additional inductive bias and cannot generally compensate for the lack of Neyman-orthogonality of the end-to-end approaches. Building on these insights, we offer guidelines for how users can effectively combine representation learning with the classical Neyman-orthogonal learners to achieve both practical performance and theoretical guarantees.