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# Ivy: Instrumental Variable Synthesis for Causal Inference

*Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics*, PMLR 108:398-410, 2020.

#### Abstract

A popular way to estimate the causal effect of a variable x on y from observational data is to use an instrumental variable (IV): a third variable z that affects y only through x. The more strongly z is associated with x, the more reliable the estimate is, but such strong IVs are difficult to find. Instead, practitioners combine more commonly available IV candidates—which are not necessarily strong, or even valid, IVs—into a single "summary" that is plugged into causal effect estimators in place of an IV. In genetic epidemiology, such approaches are known as allele scores. Allele scores require strong assumptions—independence and validity of all IV candidates—for the resulting estimate to be reliable. To relax these assumptions, we propose Ivy, a new method to combine IV candidates that can handle correlated and invalid IV candidates in a robust manner. Theoretically, we characterize this robustness, its limits, and its impact on the resulting causal estimates. Empirically, Ivy can correctly identify the directionality of known relationships and is robust against false discovery (median effect size <= 0.025) on three real-world datasets with no causal effects, while allele scores return more biased estimates (median effect size >= 0.118).