Learning Representations of Instruments for Partial Identification of Treatment Effects

TL;DR

This paper introduces a new method for estimating bounds on treatment effects using high-dimensional instruments, improving reliability and stability in observational studies where unconfoundedness may not hold.

Contribution

It proposes a novel approach for partial identification by mapping instruments to a discrete space and a neural partitioning method to obtain tight, stable bounds on treatment effects.

Findings

The method yields valid bounds with reduced estimation variance.

It performs well across various experimental settings.

The approach is applicable to high-dimensional instruments like Mendelian randomization.

Abstract

Reliable estimation of treatment effects from observational data is important in many disciplines such as medicine. However, estimation is challenging when unconfoundedness as a standard assumption in the causal inference literature is violated. In this work, we leverage arbitrary (potentially high-dimensional) instruments to estimate bounds on the conditional average treatment effect (CATE). Our contributions are three-fold: (1) We propose a novel approach for partial identification through a mapping of instruments to a discrete representation space so that we yield valid bounds on the CATE. This is crucial for reliable decision-making in real-world applications. (2) We derive a two-step procedure that learns tight bounds using a tailored neural partitioning of the latent instrument space. As a result, we avoid instability issues due to numerical approximations or adversarial training. Furthermore, our procedure aims to reduce the estimation variance in finite-sample settings to yield more reliable estimates. (3) We show theoretically that our procedure obtains valid bounds while reducing estimation variance. We further perform extensive experiments to demonstrate the effectiveness across various settings. Overall, our procedure offers a novel path for practitioners to make use of potentially high-dimensional instruments (e.g., as in Mendelian randomization).