Interventional Processes For Causal Uncertainty Quantification

Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation.

When making decisions in areas like healthcare, economics, or public policy, it is often important not only to estimate the effect of an intervention, but also to know how uncertain that estimate is. This is especially difficult when the effect changes continuously across people or treatment levels, for example when estimating how a treatment effect varies with income, age, or dose. We introduce a new method for estimating these kinds of causal effects together with reliable uncertainty estimates. The method builds on recent mathematical tools that express causal effects using functions learned from observational data, and combines them with Gaussian processes, a standard tool for representing uncertainty over functions. Our approach is computationally tractable, avoids some problems with earlier related methods, and includes a calibration step to improve the reliability of the uncertainty intervals. Across several experiments, including synthetic examples, intervention-search tasks, and a large real dataset, our method gives better uncertainty estimates while remaining competitive in estimating the causal effects themselves.