Variational Bayesian Dropout with a Hierarchical Prior

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 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.

arXiv commentAccepted by CVPR 2019

References in corpus (13)

• Adam: A Method for Stochastic Optimization
• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Improving neural networks by preventing co-adaptation of feature detectors
• Understanding deep learning requires rethinking generalization
• Variational Dropout and the Local Reparameterization Trick
• Bayesian Compression for Deep Learning
• Variational Dropout Sparsifies Deep Neural Networks
• Structured Bayesian Pruning via Log-Normal Multiplicative Noise
• Compressing Neural Networks using the Variational Information Bottleneck
• Variational Gaussian Dropout is not Bayesian
• Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors
• Overpruning in Variational Bayesian Neural Networks
• Strong NP-Hardness for Sparse Optimization with Concave Penalty Functions