ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding

2026-10-06

AI Summary

This study addresses critical bottlenecks in nonparametric proximal causal inference under hidden confounding, including the ill-posedness of integral equations, strong data dependence, and optimization instability. To overcome these challenges, this work introduces Prior-data Fitted Networks (PFNs) to this domain for the first time. By training a Transformer on synthetic structural causal models, the proposed approach amortizes Bayesian inverse operations through a single forward pass, directly yielding the full posterior distribution of the conditional average treatment effect (CATE) while effectively suppressing stochastic errors inherent in Monte Carlo estimation. This contribution represents a paradigm shift from point estimation to posterior inference, enabling robust CATE estimation without task-specific tuning even under weak proxy variables and strong hidden confounding, alongside exceptionally fast inference.

Abstract

Standard causal identification methods often assume no unmeasured confounding and can fail when relevant confounders are unobserved. Proximal causal inference instead uses proxy variables to identify effects under hidden confounding. However, nonparametric proximal estimation can be challenging in practice: recovering causal estimands such as the conditional average treatment effect (CATE) requires solving an ill-posed integral equation that is data-hungry, hyperparameter-sensitive, and optimization-unstable. Bayesian inference for such models provides a desirable alternative, mitigating these difficulties by regularizing through the prior. However, computing a posterior is itself challenging, as a typical likelihood function will include latent variables. Following the recent success of tabular foundation models in backdoor, instrumental variable, and frontdoor settings, we propose that prior-data fitted networks (PFNs) are uniquely suited to resolve this bottleneck. Indeed, by training on synthetic data sampled from compliant structural causal models with access to oracle counterfactuals, we simplify the task substantially, amortizing the implied Bayesian operator inversion into a single transformer forward pass. Compared to prior literature that focuses primarily on point estimation, our model, ProximalFM, explicitly targets the Bayesian posterior distribution of the CATE. One unique aspect of this problem is that we need to provide Monte Carlo estimates of the oracle CATEs, leading to a novel variation of PFNs that accounts for the added stochastic error. Across a diverse suite of proximal regimes, ProximalFM achieves consistently strong CATE-estimation performance without dataset-specific tuning, with its largest advantage when latent confounding is substantial and the proxies are weakly informative; it also provides fast inference through a single amortized forward pass.

Problem

• proximal causal inference
• hidden confounding
• conditional average treatment effect
• ill-posed integral equation
• Bayesian posterior estimation

Innovation

• Proximal Causal Inference
• Prior-Data Fitted Networks
• Conditional Average Treatment Effect
• Hidden Confounding
• Amortized Bayesian Inference