Deep Gaussian Processes for Regression using Approximate Expectation Propagation

TL;DR

This paper introduces a new approximate Bayesian learning method for Deep Gaussian Processes using Expectation Propagation, enabling scalable non-linear regression with improved accuracy and uncertainty estimation.

Contribution

It develops an efficient approximate Expectation Propagation algorithm for DGPs, allowing application to larger regression problems and outperforming existing methods.

Findings

Outperforms Gaussian process regression on eleven datasets.

Generally better than state-of-the-art Bayesian neural network methods.

Provides a comprehensive analysis of Bayesian training methods for neural networks.

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 nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. This paper develops a new approximate Bayesian learning scheme that enables DGPs to be applied to a range of medium to large scale regression problems for the first time. The new method uses an approximate Expectation Propagation procedure and a novel and efficient extension of the probabilistic backpropagation algorithm for learning. We evaluate the new method for non-linear regression on eleven real-world datasets, showing that it always outperforms GP regression and is almost always better than state-of-the-art deterministic and sampling-based approximate inference methods for Bayesian neural networks. As a by-product, this work provides a comprehensive analysis of six approximate Bayesian methods for training neural networks.