Multiplicative Normalizing Flows for Variational Bayesian Neural Networks

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows (Rezende & Mohamed, 2015) while still allowing for local reparametrizations (Kingma et al., 2015) and a tractable lower bound (Ranganath et al., 2015; Maaløe et al., 2016). In experiments we show that with this new approximation we can significantly improve upon classical mean field for Bayesian neural networks on both predictive accuracy as well as predictive uncertainty.