Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Probabilistic ProgrammingSearch and Optimization: Sampling/Simulation-based Search
Propagating Surrogate Uncertainty in Bayesian Inverse Problems
🤖 AI Summary
This work addresses the challenge of surrogate-induced overconfidence in Bayesian inverse problems, where computationally expensive forward models are approximated by surrogates whose uncertainty is often neglected. The authors propose the Expected Posterior (EP) as a principled benchmark for propagating surrogate uncertainty, deriving it for the first time from decision-theoretic and modular Bayesian inference principles. They demonstrate that the commonly used heuristic Expected Utility Posterior (EUP) incurs systematic bias when surrogate uncertainty is non-uniform. To enable practical computation of EP, they develop a randomized kernel-preconditioned Crank–Nicolson (RKpCN) MCMC algorithm, which efficiently approximates the EP even with infinite-dimensional Gaussian process surrogates. This approach significantly enhances the reliability of posterior inference in high-dimensional settings.
Technology Category
Application Category
📝 Abstract
Standard Bayesian inference schemes are infeasible for inverse problems with computationally expensive forward models. A common solution is to replace the model with a cheaper surrogate. To avoid overconfident conclusions, it is essential to acknowledge the surrogate approximation by propagating its uncertainty. At present, a variety of distinct uncertainty propagation methods have been suggested, with little understanding of how they vary. To fill this gap, we propose a mixture distribution termed the expected posterior (EP) as a general baseline for uncertainty-aware posterior approximation, justified by decision theoretic and modular Bayesian inference arguments. We then investigate the expected unnormalized posterior (EUP), a popular heuristic alternative, analyzing when it may deviate from the EP baseline. Our results show that this heuristic can break down when the surrogate uncertainty is highly non-uniform over the design space, as can be the case when the log-likelihood is emulated by a Gaussian process. Finally, we present the random kernel preconditioned Crank-Nicolson (RKpCN) algorithm, an approximate Markov chain Monte Carlo scheme that provides practical EP approximation in the challenging setting involving infinite-dimensional Gaussian process surrogates.
Problem
Research questions and friction points this paper is trying to address.
Bayesian inverse problems
surrogate uncertainty
uncertainty propagation
posterior approximation
Gaussian process
Innovation
Methods, ideas, or system contributions that make the work stand out.
expected posterior
surrogate uncertainty
Bayesian inverse problems
Gaussian process emulation
RKpCN algorithm
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