MCMC to address model misspecification in Deep Learning classification of Radio Galaxies

The radio astronomy community is adopting deep learning techniques to deal with the huge data volumes expected from the next-generation of radio observatories. Bayesian neural networks (BNNs) provide a principled way to model uncertainty in the predictions made by deep learning models and will play an important role in extracting well-calibrated uncertainty estimates from the outputs of these models. However, most commonly used approximate Bayesian inference techniques such as variational inference and MCMC-based algorithms experience a "cold posterior effect (CPE)", according to which the posterior must be down-weighted in order to get good predictive performance. The CPE has been linked to several factors such as data augmentation or dataset curation leading to a misspecified likelihood and prior misspecification. In this work we use MCMC sampling to show that a Gaussian parametric family is a poor variational approximation to the true posterior and gives rise to the CPE previously observed in morphological classification of radio galaxies using variational inference based BNNs.