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Variational Bayesian dropout: pitfalls and fixes
Jiri Hron · Alexander Matthews · Zoubin Ghahramani

Thu Jul 12 07:00 AM -- 07:20 AM (PDT) @ A4

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.

Author Information

Jiri Hron (University of Cambridge)
Alexander Matthews (University of Cambridge)

Research Associate at University of Cambridge Interested in Deep Learning, Gaussian Processes, Scalable Approximate Inference, Privacy in Machine Learning

Zoubin Ghahramani (University of Cambridge & Uber)

Zoubin Ghahramani is a Professor at the University of Cambridge, and Chief Scientist at Uber. He is also Deputy Director of the Leverhulme Centre for the Future of Intelligence, was a founding Director of the Alan Turing Institute and co-founder of Geometric Intelligence (now Uber AI Labs). His research focuses on probabilistic approaches to machine learning and AI. In 2015 he was elected a Fellow of the Royal Society.

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