Fast Computer Model Calibration using Annealed and Transformed Variational Inference

TL;DR

This paper introduces a novel variational inference framework with annealing and transformations that enhances calibration of complex computer models, achieving faster and more accurate results than traditional methods.

Contribution

It proposes a flexible, deep generative model-based VI approach with boundary-avoiding transformations and a temperature annealing scheme for improved model calibration.

Findings

Outperforms traditional VI and MCMC in speed and accuracy.

Effectively handles boundary issues in variational distributions.

Demonstrates success on infectious disease and geophysical models.

Abstract

Computer models play a crucial role in numerous scientific and engineering domains. To ensure the accuracy of simulations, it is essential to properly calibrate the input parameters of these models through statistical inference. While Bayesian inference is the standard approach for this task, employing Markov Chain Monte Carlo methods often encounters computational hurdles due to the costly evaluation of likelihood functions and slow mixing rates. Although variational inference (VI) can be a fast alternative to traditional Bayesian approaches, VI has limited applicability due to boundary issues and local optima problems. To address these challenges, we propose flexible VI methods based on deep generative models that do not require parametric assumptions on the variational distribution. We embed a surjective transformation in our framework to avoid posterior truncation at the boundary. Additionally, we provide theoretical conditions that guarantee the success of the algorithm. Furthermore, our temperature annealing scheme can prevent being trapped in local optima through a series of intermediate posteriors. We apply our method to infectious disease models and a geophysical model, illustrating that the proposed method can provide fast and accurate inference compared to its competitors.