Proxy-HCD-IV: Bow-Capable Causal Discovery from Grouped Proxy Variables

We study causal discovery when observed variables can be related by both direct effects and shared hidden causes, including cases where both occur simultaneously. Although the hidden causes are not observed, we assume that each is measured indirectly by a group of proxy variables, such as multiple noisy sensors or assays of the same underlying quantity. We propose Proxy-HCD-IV, which uses these grouped proxies to recover both direct causal relationships and relationships induced by shared hidden causes. The method learns a causal order and divides the proxies for each hidden cause into two independent groups, using one group as noisy regressors and the other as instruments for joint structural estimation. We establish identification and false-addition control under stated conditions, with extensions to nonlinear mechanisms. Experiments include FCI/RFCI, RCD, FoundCause, and matched proxy-aware controls. On an independent 40-graph equal-information benchmark with high proxy noise, Proxy-HCD-IV reduces graphs containing any false direct or hidden-effect selection from 30/40 to 3/40 relative to its matched OLS control, while directed F1 increases from .898 to .913, with lower bidirected F1 (.914 to .733). A semi-synthetic experiment based on real clinical feature distributions shows a similar trade-off. These results demonstrate how grouped proxy variables can provide additional information for recovering direct and hidden-confounding structure while substantially reducing false structural selections.