Simulator Calibration under Covariate Shift with Kernels
This addresses calibration challenges in simulation applications like manufacturing, where covariate shift is common, though it appears incremental as it builds on existing kernel and Bayesian methods.
The authors tackled the problem of calibrating computer simulators under covariate shift, where training and test input distributions differ, by proposing a Bayesian inference method using kernel mean embeddings and importance-weighted kernels. They demonstrated its effectiveness in calibrating an industrial manufacturing simulator and for sensitivity analysis.
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of simulations. Our approach is based on Bayesian inference with kernel mean embedding of distributions, and on the use of an importance-weighted reproducing kernel for covariate shift adaptation. We provide a theoretical analysis for the proposed method, including a novel theoretical result for conditional mean embedding, as well as empirical investigations suggesting its effectiveness in practice. The experiments include calibration of a widely used simulator for industrial manufacturing processes, where we also demonstrate how the proposed method may be useful for sensitivity analysis of model parameters.