Causal Inference on Networks under Misspecified Exposure Mappings: A Partial Identification Framework
Maresa Schröder, Miruna Oprescu, Stefan Feuerriegel, Nathan Kallus
TL;DR
This work addresses causal inference on networks under misspecified exposure mappings by introducing a model-agnostic partial identification framework that yields sharp upper and lower bounds on conditional average potential outcomes $\mu^{\pm}(t,z,\mathbf{x})$. It derives closed-form CAPO bounds using exposure-misspecification bounds $b^{\pm}(z,\mathbf{x})$, and provides an orthogonal two-stage estimator with cross-fitting, achieving quasi-oracle rates and valid inference under nuisance-estimation error. The framework is instantiated for three canonical exposure mappings (weighted means, thresholds, and higher-order spillovers) and backed by theoretical guarantees of sharpness and robustness, including kernel-localized results for continuous $Z$. Experiments on synthetic networks show informative bounds that remain valid under misspecification and demonstrate faster convergence for the orthogonal estimator compared to plug-in approaches, enabling robust decision-making when exposure mappings are uncertain. Overall, the paper offers a principled, flexible approach to sensitivity analysis in network causal inference with strong theoretical and empirical support for robustness and practicality.
Abstract
Estimating treatment effects in networks is challenging, as each potential outcome depends on the treatments of all other nodes in the network. To overcome this difficulty, existing methods typically impose an exposure mapping that compresses the treatment assignments in the network into a low-dimensional summary. However, if this mapping is misspecified, standard estimators for direct and spillover effects can be severely biased. We propose a novel partial identification framework for causal inference on networks to assess the robustness of treatment effects under misspecifications of the exposure mapping. Specifically, we derive sharp upper and lower bounds on direct and spillover effects under such misspecifications. As such, our framework presents a novel application of causal sensitivity analysis to exposure mappings. We instantiate our framework for three canonical exposure settings widely used in practice: (i) weighted means of the neighborhood treatments, (ii) threshold-based exposure mappings, and (iii) truncated neighborhood interference in the presence of higher-order spillovers. Furthermore, we develop orthogonal estimators for these bounds and prove that the resulting bound estimates are valid, sharp, and efficient. Our experiments show the bounds remain informative and provide reliable conclusions under misspecification of exposure mappings.