Title: Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo,
Abstract: Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian
Processes that combine well calibrated uncertainty estimates with the high
flexibility of multilayer models. One of the biggest challenges with these
models is that exact inference is intractable. The current state-of-the-art
inference method, Variational Inference (VI), employs a Gaussian approximation
to the posterior distribution. This can be a potentially poor unimodal
approximation of the generally multimodal posterior. In this work, we provide
evidence for the non-Gaussian nature of the posterior and we apply the
Stochastic Gradient Hamiltonian Monte Carlo method to generate samples. To
efficiently optimize the hyperparameters, we introduce the Moving Window MCEM
algorithm. This results in significantly better predictions at a lower
computational cost than its VI counterpart. Thus our method establishes a new
state-of-the-art for inference in DGPs.