Primary Submission Category: Proximal Causal Learning
Extending Proxy Methods for Causal Identification: Comparing Bridge Equations and Completeness Conditions with Eigendecomposition Approaches
Authors: Helen Guo, Elizabeth Ogburn, Ilya Shpitser,
Presenting Author: Helen Guo*
Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. This work contrasts two prominent approaches within this framework: (1) methods that use bridge equations and completeness conditions to recover identifying representations and (2) eigendecomposition approaches that identify intermediate target distributions comprising the identifying representation, up to permutation of latent state labels. The former has been developed for settings involving unmeasured confounding or mediation (Miao et al., 2018; Cui et. al., 2023; Ghassami et al., 2024). The latter approach (Kuroki & Pearl, 2014) – which may be viewed as a special case of Kruskal’s uniqueness condition for the
Candecomp/Parafac decomposition (Kruskal, 1977; Stegeman & Sidiropoulos, 2007) – has been recently expanded to handle circumstances with unmeasured treatment (Zhou & Tchetgen Tchetgen, 2024). Comparing the model restrictions imposed by each approach for hidden confounding or mediation, we delineate scenarios where the models are equivalent and derive conditions for identifying the full joint distribution of the underlying causal graph. Furthermore, we extend proximal methods to simultaneously address unmeasured confounding and mediation together, and discuss assumptions under which identification is possible via different identifying representations.