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).

提出了一种新方法 Ivy，用于合并仪器变量候选项，以在处理相关和无效候选项时进行有效估算，与 allele scores 相比，该方法的实验结果表明更可靠、准确性更高。