Paper ID: 2410.14483 • Published Oct 18, 2024
Spectral Representations for Accurate Causal Uncertainty Quantification with Gaussian Processes
Hugh Dance, Peter Orbanz, Arthur Gretton
TL;DR
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Accurate uncertainty quantification for causal effects is essential for
robust decision making in complex systems, but remains challenging in
non-parametric settings. One promising framework represents conditional
distributions in a reproducing kernel Hilbert space and places Gaussian process
priors on them to infer posteriors on causal effects, but requires restrictive
nuclear dominant kernels and approximations that lead to unreliable uncertainty
estimates. In this work, we introduce a method, IMPspec, that addresses these
limitations via a spectral representation of the Hilbert space. We show that
posteriors in this model can be obtained explicitly, by extending a result in
Hilbert space regression theory. We also learn the spectral representation to
optimise posterior calibration. Our method achieves state-of-the-art
performance in uncertainty quantification and causal Bayesian optimisation
across simulations and a healthcare application.