Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo
This work addresses the problem of accurate and efficient inference for researchers and practitioners using Deep Gaussian Processes, establishing a new state-of-the-art method.
The paper tackled the challenge of intractable inference in Deep Gaussian Processes by applying Stochastic Gradient Hamiltonian Monte Carlo and introducing the Moving Window MCEM algorithm for hyperparameter optimization, resulting in significantly better predictions at lower computational cost than Variational Inference.
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.