  Variational dropout (VD) is a generalization of Gaussian dropout, which aims
at inferring the posterior of network weights based on a log-uniform prior on
them to learn these weights as well as dropout rate simultaneously. The
log-uniform prior not only interprets the regularization capacity of Gaussian
dropout in network training, but also underpins the inference of such
posterior. However, the log-uniform prior is an improper prior (i.e., its
integral is infinite) which causes the inference of posterior to be ill-posed,
thus restricting the regularization performance of VD. To address this problem,
we present a new generalization of Gaussian dropout, termed variational
Bayesian dropout (VBD), which turns to exploit a hierarchical prior on the
network weights and infer a new joint posterior. Specifically, we implement the
hierarchical prior as a zero-mean Gaussian distribution with variance sampled
from a uniform hyper-prior. Then, we incorporate such a prior into inferring
the joint posterior over network weights and the variance in the hierarchical
prior, with which both the network training and the dropout rate estimation can
be cast into a joint optimization problem. More importantly, the hierarchical
prior is a proper prior which enables the inference of posterior to be
well-posed. In addition, we further show that the proposed VBD can be
seamlessly applied to network compression. Experiments on both classification
and network compression tasks demonstrate the superior performance of the
proposed VBD in terms of regularizing network training.
