Towards Representation Learning for Weighting Problems in Design-Based Causal Inference

Reweighting a distribution to minimize a distance to a target distribution is a powerful and flexible strategy for estimating a wide range of causal effects, but can be challenging in practice because optimal weights typically depend on knowledge of the underlying data generating process. In this paper, we focus on design-based weights, which do not incorporate outcome information; prominent examples include prospective cohort studies, survey weighting, and the weighting portion of augmented weighting estimators. In such applications, we explore the central role of representation learning in finding desirable weights in practice. Unlike the common approach of assuming a well-specified representation, we highlight the error due to the choice of a representation and outline a general framework for finding suitable representations that minimize this error. Building on recent work that combines balancing weights and neural networks, we propose an end-to-end estimation procedure that learns a flexible representation, while retaining promising theoretical properties. We show that this approach is competitive in a range of common causal inference tasks.

💡 Research Summary

The paper addresses the problem of constructing design‑based weights for causal inference, i.e., weights that are estimated without any use of outcome information. This setting arises in prospective cohort studies, survey sampling, transportability problems, and in doubly‑robust estimators where the weighting component must be outcome‑agnostic. Traditional approaches rely on propensity scores, balancing scores, or other handcrafted representations of the covariates. However, these methods assume that the chosen representation perfectly captures the relevant information for the unknown outcome model; when this assumption fails, the resulting weights can be severely biased, especially in high‑dimensional settings.

The authors propose to treat the choice of representation as a learnable component and to quantify the error introduced by any representation. They decompose the total bias of a weighting estimator into three distinct terms: (1) representation bias, which measures the loss of information when the true conditional outcome E