Identifying Causal Effects Using a Single Proxy Variable
This study addresses the challenge of identifying causal effects in the presence of unobserved confounders by introducing the SPICE condition, which ensures identifiability under the assumption that only a single observed proxy variable is available and its generative mechanism is known. Building on this condition, the authors develop SPICE-Net, a general-purpose neural network framework capable of handling both discrete and continuous treatment variables. The work substantially extends existing proxy-based identification theory to high-dimensional settings, nonlinear functional relationships, and broader distributional classes. It presents the first learnable, end-to-end approach to causal identification and estimation grounded in the completeness assumption, provides rigorous theoretical proof of identifiability under the SPICE condition, and empirically demonstrates the method’s effectiveness across diverse treatment types.