Deep Gaussian Processes for Regression using Approximate Expectation Propagation
This work enables more flexible and uncertainty-aware deep learning for regression tasks, though it is incremental as it builds on existing DGP and inference frameworks.
The paper tackled the challenge of applying deep Gaussian processes (DGPs) to medium-to-large scale regression problems by developing a new approximate Bayesian learning scheme using expectation propagation and probabilistic backpropagation. The result showed that this method outperformed GP regression and often beat state-of-the-art Bayesian neural network methods on eleven real-world datasets.
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.