Proximal Causal Learning under Unmeasured Confounding

Ying Tang, Yi Wang

Estimating treatment effects from observational data typically relies on the No Unmeasured Confounding Assumption (NUCA), which rarely holds in practice. Proximal causal learning (PCL) addresses unmeasured confounding via proxy variables, yet existing methods require the proxy variables to be pre-specified. Thus, we propose PCL-U, a framework that learns proxy variables directly from observed covariates. PCL-U uses neural encoders to decompose covariates into treatment-inducing, outcome-inducing, and shared proxies, guided by minimax mutual information objectives, and obtains causal estimates through a practical moment-based risk function. Experiments on benchmarks show that PCL-U matches or outperforms existing baselines. Besides, there are two types of synthetic datasets with varying dimensions and confounding strengths that illustrate that our method maintains stable estimation accuracy.