Towards Improved Variational Inference for Deep Bayesian Models
Sebastian W. Ober
TL;DR
This thesis investigates improving variational inference for deep Bayesian models by addressing the limitations of partial Bayesian treatments and posterior symmetries. It introduces a unified, correlation-aware variational posterior that links Bayesian neural networks and deep Gaussian processes via global inducing points, and then reframes deep models in Gram-space with deep Wishart processes to remove rotational symmetries and enhance ELBOs. The work demonstrates substantial gains in calibration, uncertainty quantification, and predictive performance in benchmarks such as CIFAR-10, while also revealing contexts (e.g., heavy hyperparameter regimes) where standard marginal likelihood-based training can overfit. Collectively, these contributions advance practical, scalable Bayesian deep learning with improved uncertainty, model selection potential, and a principled path toward fully Bayesian deep kernel methods. The results highlight both the promise and remaining challenges in leveraging VI for robust deep probabilistic modeling in vision and beyond.
Abstract
Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it is well-known that deep models trained via maximum likelihood estimation tend to be overconfident and give poorly-calibrated predictions. Bayesian deep learning attempts to address this by placing priors on the model parameters, which are then combined with a likelihood to perform posterior inference. Unfortunately, for deep models, the true posterior is intractable, forcing the user to resort to approximations. In this thesis, we explore the use of variational inference (VI) as an approximation, as it is unique in simultaneously approximating the posterior and providing a lower bound to the marginal likelihood. If tight enough, this lower bound can be used to optimize hyperparameters and to facilitate model selection. However, this capacity has rarely been used to its full extent for Bayesian neural networks, likely because the approximate posteriors typically used in practice can lack the flexibility to effectively bound the marginal likelihood. We therefore explore three aspects of Bayesian learning for deep models: 1) we ask whether it is necessary to perform inference over as many parameters as possible, or whether it is reasonable to treat many of them as optimizable hyperparameters; 2) we propose a variational posterior that provides a unified view of inference in Bayesian neural networks and deep Gaussian processes; 3) we demonstrate how VI can be improved in certain deep Gaussian process models by analytically removing symmetries from the posterior, and performing inference on Gram matrices instead of features. We hope that our contributions will provide a stepping stone to fully realize the promises of VI in the future.