Variational Bayesian dropout: pitfalls and fixes

By Jiri Hron, Alexander G. de G. Matthews, Zoubin Ghahramani. 2018

70 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence

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Citations in the corpus

Safe Imitation Learning via Fast Bayesian Reward Inference from Preferences (2020, background): “Future work should examine more sophisticated applications of dropout to uncertainty estimation that seek to solve the theoretical and practical problems with vanilla MC Dropout (Hron et al., 2018).”
Hands-On Bayesian Neural Networks—A Tutorial for Deep Learning Users (2020, background): “Variational Dropout has been criticized as not being Bayesian [34], mainly due to the fact that the authors have chosen an objective function where Gaussian Dropout is the only form of regularization used.”
Uncertainty Weighted Actor-Critic for Offline Reinforcement Learning (2021, methodology): “MC-dropout uncertainty estimation is a simple method with minimal overhead and has been thoroughly studied in many traditional supervised learning tasks in deep learning (Gal & Ghahramani, 2016a; Hron et al., 2018; Kingma et al., 2015; Gal & Ghahramani, 2016b).”