Deep Gaussian Processes

TL;DR

This paper introduces deep Gaussian process models that extend standard GPs into deep hierarchies, enabling Bayesian inference and model selection even with small datasets, demonstrated on digit data.

Contribution

It presents a novel deep GP framework with variational inference, allowing Bayesian treatment and effective model selection for deep hierarchies.

Findings

A five-layer deep GP is justified for small digit datasets.

Variational inference provides a strict lower bound for model selection.

Deep GPs outperform standard GPs in modeling complex data hierarchies.

Abstract

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.