CausalGuard: Conformal Inference under Graph Uncertainty

Current methods for estimating treatment effects harbor a fundamental vulnerability: they demand a brittle, premature commitment to a single, uncertain causal graph. If the adjustment set is misspecified, standard conformal prediction frameworks fail silently by flawlessly calibrating a causally meaningless pseudo-outcome. We introduce CausalGuard, a proactive aggregate-before-calibrate paradigm that resolves this structural vulnerability. Rather than gambling on one graph, CausalGuard utilizes LLM-elicited priors and conditional-independence screening to construct a weighted family of valid adjustment strategies, elegantly collapsing redundant graphs into shared downstream estimators for maximum computational efficiency. By aggregating graph-conditional pseudo-outcomes and bounds before applying a single conformal correction, we mathematically eliminate the interval bloat inherent to naive averaging. We prove finite-sample marginal coverage for this aggregate and formally establish its convergence to the Conditional Average Treatment Effect (CATE). Empirical benchmarking demonstrates CausalGuard dramatically tightens efficiency at comparable operating points. Crucially, in a metadata-free collider stress test, CausalGuard autonomously prevents structural bias, collapsing CATE RMSE to $0.87$ compared to the catastrophic $3.10$ error of forced-adjustment baselines, proving that robust inference requires unifying predictive calibration with causal integrity.