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# Deep Gaussian Processes

*Proceedings of the Sixteenth International Workshop on Artificial Intelligence and Statistics*, PMLR 31:207-215, 2013.

#### 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.