Variational inference (VI) is a popular approach for approximate Bayesian inference that is particularly promising for highly parameterized models such as deep neural networks.   A key challenge of variational inference is to approximate the posterior over model parameters with a distribution that is simpler and tractable yet sufficiently expressive. In this work, we propose a method for training highly flexible variational distributions by starting with a coarse approximation and iteratively refining it. Each refinement step makes cheap, local adjustments and only requires optimization of simple variational families. We demonstrate theoretically that our method always improves a bound on the approximation (the Evidence Lower BOund) and observe this empirically across a variety of benchmark tasks.   In experiments, our method consistently outperforms recent variational inference methods for deep learning in terms of log-likelihood and the ELBO.   We see that the gains are further amplified on larger scale models, significantly outperforming standard VI and deep ensembles on residual networks on CIFAR10.
The paper proposes an algorithm to increase the flexibility of the variational posterior in Bayesian neural networks through iterative optimization. A method for training flexible variational posterior distributions, applied to Bayesian neural nets to perform variation inference (VI) over the weights.