  Uncertainty estimation in large deep-learning models is a computationally
challenging task, where it is difficult to form even a Gaussian approximation
to the posterior distribution. In such situations, existing methods usually
resort to a diagonal approximation of the covariance matrix despite, the fact
that these matrices are known to result in poor uncertainty estimates. To
address this issue, we propose a new stochastic, low-rank, approximate
natural-gradient (SLANG) method for variational inference in large, deep
models. Our method estimates a "diagonal plus low-rank" structure based solely
on back-propagated gradients of the network log-likelihood. This requires
strictly less gradient computations than methods that compute the gradient of
the whole variational objective. Empirical evaluations on standard benchmarks
confirm that SLANG enables faster and more accurate estimation of uncertainty
than mean-field methods, and performs comparably to state-of-the-art methods.
