Title: Variational Bayesian dropout: pitfalls and fixes,
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.