Training Deep Gaussian Processes using Stochastic Expectation Propagation and Probabilistic Backpropagation

TL;DR

This paper introduces a scalable Bayesian training method for Deep Gaussian Processes using stochastic Expectation Propagation and probabilistic backpropagation, enhancing flexibility and uncertainty estimation in deep probabilistic models.

Contribution

It develops a novel extension of probabilistic backpropagation that incorporates stochastic Expectation Propagation for efficient training of DGPs.

Findings

Outperforms Gaussian process regression on real-world datasets

Automatically discovers input transformations like warping and compression

Provides better calibrated uncertainty estimates

Abstract

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. The focus of this paper is scalable approximate Bayesian learning of these networks. The paper develops a novel and efficient extension of probabilistic backpropagation, a state-of-the-art method for training Bayesian neural networks, that can be used to train DGPs. The new method leverages a recently proposed method for scaling Expectation Propagation, called stochastic Expectation Propagation. The method is able to automatically discover useful input warping, expansion or compression, and it is therefore is a flexible form of Bayesian kernel design. We demonstrate the success of the new method for supervised learning on several real-world datasets, showing that it typically outperforms GP regression and is never much worse.