  We show how to use Stein variational gradient descent (SVGD) to carry out
inference in Gaussian process (GP) models with non-Gaussian likelihoods and
large data volumes. Markov chain Monte Carlo (MCMC) is extremely
computationally intensive for these situations, but the parametric assumptions
required for efficient variational inference (VI) result in incorrect inference
when they encounter the multi-modal posterior distributions that are common for
such models. SVGD provides a non-parametric alternative to variational
inference which is substantially faster than MCMC. We prove that for GP models
with Lipschitz gradients the SVGD algorithm monotonically decreases the
Kullback-Leibler divergence from the sampling distribution to the true
posterior. Our method is demonstrated on benchmark problems in both regression
and classification, a multimodal posterior, and an air quality example with
550,134 spatiotemporal observations, showing substantial performance
improvements over MCMC and VI.
