Liberty or Depth: Deep Bayesian Neural Nets Do Not Need Complex Weight Posterior Approximations
This provides a practical alternative for implementing Bayesian neural networks by reducing computational costs, though it appears incremental in addressing a specific methodological bottleneck.
The paper challenges the assumption that mean-field approximations are too restrictive for variational inference in Bayesian neural networks, showing that deep networks with simple weight posteriors can achieve similar function-space distributions as shallower networks with complex posteriors.
We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distributions in function-space to those induced by shallower networks with complex weight posteriors. We validate our theoretical contributions empirically, both through examination of the weight posterior using Hamiltonian Monte Carlo in small models and by comparing diagonal- to structured-covariance in large settings. Since complex variational posteriors are often expensive and cumbersome to implement, our results suggest that using mean-field variational inference in a deeper model is both a practical and theoretically justified alternative to structured approximations.