Title: Enhancing Causal Uncertainty Quantification via Interventional Processes

Abstract:

Accurately quantifying uncertainty surrounding causal effects is a critical requirement for high-stakes decision-making, yet it presents significant difficulties when the objective is to characterize an entire function rather than a single scalar value. To address this challenge, we propose a Gaussian Process (GP)-based methodology for the uncertainty quantification of interventional functions. Our core strategy leverages recent theoretical advances that express interventional functions as the inner product of observational functions within a reproducing kernel Hilbert space (RKHS). By designing suitable GP priors for these functions and deriving posterior distributions from observational data, we achieve closed-form posterior moments alongside efficient training and inference processes. Notably, this framework circumvents the pathological issues associated with earlier GP prior constructions for RKHS functions. Additionally, we establish a practical method for calibrating posterior coverage. Evaluations across synthetic benchmarks, causal Bayesian optimization scenarios, and a large-scale real-world dataset demonstrate that our approach enhances uncertainty quantification while maintaining competitive performance in estimating causal effects.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC