Posterior Temperature Optimization in Variational Inference for Inverse Problems

TL;DR

This paper introduces a method to optimize the posterior temperature in variational inference for inverse problems, enhancing predictive accuracy and uncertainty calibration in applications like sparse-view CT reconstruction.

Contribution

It proposes a Bayesian optimization approach to tune both prior parameters and posterior temperature, improving Bayesian inference performance in inverse problems.

Findings

Optimized posterior temperature improves predictive accuracy.

Better uncertainty calibration achieved with the method.

Enhanced results in sparse-view CT reconstruction.

Abstract

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice, this often results in a suboptimal posterior temperature and the full potential of the Bayesian approach is not realized. In this paper, we optimize both the parameters of the prior distribution and the posterior temperature using Bayesian optimization. Well-tempered posteriors lead to better predictive performance and improved uncertainty calibration, which we demonstrate for the task of sparse-view CT reconstruction.