Posterior Temperature Optimization in Variational Inference

Cold posteriors have been reported to perform better in practice in the context of Bayesian deep learning (Wenzel2020 et al., 2020). In variational inference, it is common to employ only a partially tempered posterior by scaling the complexity term in the log-evidence lower bound (ELBO). In this work, we first derive the ELBO for a fully tempered posterior in mean-field variational inference and subsequently use Bayesian optimization to automatically find the optimal posterior temperature. Choosing an appropriate posterior temperature leads to better predictive performance and improved uncertainty calibration, which we demonstrate for the task of denoising medical X-ray images.