Interventional Processes for Causal Uncertainty Quantification

TL;DR

This paper introduces IMPspec, a Gaussian process framework that effectively models and quantifies uncertainty in causal effects with continuous treatments, addressing key challenges in nonparametric causal inference.

Contribution

IMPspec leverages spectral representations of RKHSs to enable tractable inference and calibration, improving over previous GP-based methods for causal uncertainty quantification.

Findings

Achieves state-of-the-art performance in synthetic benchmarks

Demonstrates effectiveness in healthcare causal analysis

Provides reliable credible intervals for causal effects

Abstract

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.