Variational Bayesian dropout: pitfalls and fixes


Type
Conference Object
Change log
Authors
Matthews, Alexander G de G 
Ghahramani, Zoubin 
Abstract

Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.

Description
Keywords
stat.ML, stat.ML, cs.LG
Journal Title
Proceedings of Machine Learning Research
Conference Name
ICML 2018: 35th International Conference on Machine Learning
Journal ISSN
2640-3498
Volume Title
80
Publisher
Proceedings of Machine Learning Research
Sponsorship
EPSRC (via University of Sheffield) (143103)
Alan Turing Institute (EP/N510129/1)
Jiri Hron holds a Nokia CASE Studentship. Alexander Matthews and Zoubin Ghahramani acknowledge the support of EPSRC Grant EP/N014162/1 and EPSRC Grant EP/N510129/1 (The Alan Turing Institute).