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While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders, and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more carefully about the prior specification for their models and to provide them with some inspiration in this regard.
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. Recent work has
Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, such simplistic priors are unlikely to either accurately reflect our true beliefs about the weight distributions, or to give optimal performanc
We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we formulate th
Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropr
Evaluation of Bayesian deep learning (BDL) methods is challenging. We often seek to evaluate the methods robustness and scalability, assessing whether new tools give `better uncertainty estimates than old ones. These evaluations are paramount for pra