ProximalFM: Amortized Proximal Causal Inference under Hidden Confounding
ProximalFM amortizes Bayesian proximal causal inference so a transformer estimates CATE posteriors under hidden confounding.
Standard causal methods fail when confounders are unobserved, while nonparametric proximal estimation of the conditional average treatment effect is unstable and data-hungry. ProximalFM trains prior-data fitted networks on synthetic structural causal models with oracle counterfactuals, turning the inversion into one transformer forward pass that estimates the Bayesian CATE posterior. It also models Monte Carlo error in the oracle labels and performs best when latent confounding is substantial and proxies are weakly informative.
- Uses proxy variables to identify effects under hidden confounding
- Amortizes Bayesian inversion with prior-data fitted networks
- Targets the CATE posterior, not only a point estimate
- Strongest when confounding is large and proxies are weak
Full article255 words · extracted from arxiv.org · click to collapse
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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2610.08078