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This paper introduces ProximalFM, a novel approach for amortized proximal causal inference that addresses the challenges of nonparametric estimation under hidden confounding by leveraging prior-data fitted networks (PFNs). By training on synthetic data with oracle counterfactuals, ProximalFM amortizes the Bayesian posterior inference of conditional average treatment effects (CATEs) into a single transformer forward pass, overcoming the data-hungriness and instability of traditional methods. The model demonstrates strong CATE estimation performance across various proximal regimes, particularly when latent confounding is significant and proxies are weak, offering fast inference without dataset-specific tuning.
Amortized Bayesian causal inference for hidden confounding is now possible via a single transformer pass, achieving state-of-the-art CATE estimation without hyperparameter tuning.
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.
ETH