Variational Bayesian Dropout With a Hierarchical Prior 

                           Yuhang Liu, Wenyong Dong, Lei Zhang, Dong Gong, and Qinfeng Shi

Abstract 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 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 classification and network compression demonstrate the superior performance of the proposed VBD in regularizing network training.

Experiments

References 

[1] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever and Ruslan Salakhutdinov, Dropout: A Simple Way to Prevent Neural Networks from Overfitting, JMLR 2014. 

[2] Wang Sida and Christopher Manning. Fast dropout training, ICML 2013 

[3] Diederik Kingma, Tim Salimans and Max Welling. Variational dropout and the local reparameterization trick, NIPS, 2015. 

[4] Jiri Hron, Alexander GG Matthews, and Zoubin Ghahramani. Variational bayesian dropout: pitfalls and fixes. ICML, 2018. 

[Code]