Interventional Processes for Causal Uncertainty Quantification
This addresses a crucial challenge in causal inference for applications like healthcare, offering a novel method for uncertainty quantification.
The paper tackles the problem of reliable uncertainty quantification for causal effects under continuous treatments in nonparametric models, introducing IMPspec, a Gaussian process framework that achieves state-of-the-art performance in synthetic benchmarks and healthcare applications.
Reliable uncertainty quantification for causal effects is crucial in various applications, but remains difficult in nonparametric models, particularly for continuous treatments. We introduce IMPspec, a Gaussian process (GP) framework for modeling uncertainty over interventional causal functions under continuous treatments, which can be represented using reproducing Kernel Hilbert Spaces (RKHSs). By using principled function class expansions and a spectral representation of RKHS features, IMPspec yields tractable training and inference, a spectral algorithm to calibrate posterior credible intervals, and avoids the underfitting and variance collapse pathologies of earlier GP-on-RKHS methods. Across synthetic benchmarks and an application in healthcare, IMPspec delivers state-of-the-art performance in causal uncertainty quantification and downstream causal Bayesian optimization tasks.