Simulator Calibration under Covariate Shift with Kernels

TL;DR

This paper introduces a Bayesian kernel-based calibration method for computer simulators that effectively handles covariate shift, improving calibration accuracy and enabling sensitivity analysis in industrial applications.

Contribution

It presents a novel kernel mean embedding approach with importance weighting for covariate shift, along with theoretical analysis and practical validation.

Findings

Effective calibration under covariate shift demonstrated in industrial simulator

Theoretical results for conditional mean embedding established

Method improves sensitivity analysis of model parameters

Abstract

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.