Learning Representations of Instruments for Partial Identification of Treatment Effects

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).

Estimating how a treatment affects individuals using only observational data is crucial in fields like medicine, but standard methods break down when hidden factors influence both treatment and outcome. To address this, we use variables called “instruments”—for example, genetic markers—that affect treatment but not directly the outcome, even if these instruments are complex and high-dimensional. Our method transforms these instruments into a simple, discrete form that guarantees valid upper and lower bounds on the treatment effect for each person, ensuring we never make overconfident claims. To do so, we train a two-step neural network that learns the tightest possible bounds while avoiding instability from hard numerical approximations or adversarial techniques; this also reduces uncertainty when data are limited. We prove that our approach always produces correct bounds and yields less variance than existing methods. Through extensive experiments, we show that our method works well across different settings. By making it practical to use complicated instruments, such as genetic data in Mendelian randomization, our work helps researchers and clinicians make safer, evidence-based decisions when unmeasured confounding is a concern.