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

TL;DR

This paper explores how representation learning can improve the estimation of weights in design-based causal inference, offering a flexible framework that enhances practical performance without relying on outcome data.

Contribution

It introduces a novel end-to-end method for learning representations that optimize weights in design-based causal inference, addressing errors from representation choices.

Findings

The proposed method is competitive across various causal inference tasks.

Representation learning reduces weight estimation errors.

The framework maintains promising theoretical properties.

Abstract

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.