Posterior Temperature Optimization in Variational Inference for Inverse Problems
This work addresses a specific bottleneck in Bayesian methods for inverse problems like tomographic reconstruction, offering incremental improvements in uncertainty calibration.
The paper tackles the suboptimal posterior temperature in variational inference for inverse problems, optimizing both prior parameters and posterior temperature via Bayesian optimization, resulting in better predictive performance and improved uncertainty calibration for sparse-view CT reconstruction.
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.