Inference in Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo

TL;DR

This paper introduces a novel inference method for Deep Gaussian Processes using Stochastic Gradient Hamiltonian Monte Carlo, which better captures the complex posterior distribution and improves prediction accuracy over traditional Variational Inference.

Contribution

The paper demonstrates the effectiveness of SGHMC for DGP inference and introduces the Moving Window MCEM algorithm for efficient hyperparameter optimization.

Findings

SGHMC captures non-Gaussian, multimodal posteriors more effectively.

The proposed method outperforms Variational Inference in predictive accuracy.

Computational cost is reduced compared to existing state-of-the-art methods.

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.