Observational datasets frequently contain many baseline variables, yet investigators estimating causal effects may not know which variables to include in the adjustment set. Confounding information may also be distributed weakly across many variables. Propensity scores can simplify adjustment by reducing high-dimensional covariates to a scalar with binary treatment. Although the propensity score is the coarsest balancing score, this distributional optimality does not imply maximal specificity over causal graphs. We instead examine all causal graphs among a candidate score, treatment, and outcome while allowing latent variables. Under faithfulness, we identify the largest set of unconditional and conditional dependence relations whose truth is invariant to whether treatment causes the outcome, leaving treatment-effect estimation to the downstream analysis. This criterion defines the maximally specific graph class expressible through these relations. We then develop the proposed algorithm, which operationalizes the criterion through a generalized eigenvalue problem whose score space targets the span of a balancing coordinate and an outcome-guided coordinate. We show that sufficiently informative proxies can recover this span without direct observation of the adjustment variables, characterize the resulting estimation and causal errors, and establish bootstrap validity for the complete procedure. Simulations and a real-data application demonstrate superior performance over several alternatives.
Uplift modeling, crucial for estimating individual treatment effects (ITE), faces dual challenges: flexibly leveraging inter-group similarity to enhance discriminative power and debiasing under unobserved confounding scenarios. In this paper, we propose the Cross-Head Attention Uplift Network (CHAUN) and Robust Adversarial Inverse Propensity Score (RA-IPS) method to address these limitations. CHAUN employs shared feature embeddings and cross-head attention mechanisms to dynamically integrate treatment-specific and control-specific representations, enhancing inter-group correlation modeling. Theoretically, we prove that access to the true propensity scores ensures ITE identifiability even with unobserved confounders. For practical scenarios lacking true propensity scores, RA-IPS adversarially optimizes propensity weights within constrained uncertainty sets to mitigate bias from unobserved variables. Experiments on public datasets (CRITEO-UPLIFT, LAZADA) and a production e-commerce dataset demonstrate CHAUN's superiority over state-of-the-art uplift models, achieving relative improvements of up to 25.6% in QINI scores. RA-IPS further enhances robustness, outperforming standard IPS by 5.4% under unobserved confounding. The results validate the effectiveness of our proposed methods in real-world causal inference tasks.