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Deep Gaussian Processes
Deep Gaussian ProcessesAndreas C. DamianouNeil D. LawrenceDept. of Computer Science & Sheffield Institute for Translational Neuroscience,University of Sheffield, UKAbstractIn this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief net-work based on Gaussian process mappings. Thedata is modeled as the output of a multivariateGP. The inputs to that Gaussian process are thengoverned by another GP. A single layer model isequivalent to a standard GP or the GP latent vari-able model (GP-LVM). We perform inference inthe model by approximate variational marginal-ization. This results in a strict lower bound on themarginal likelihood of the model which we usefor model selection (number of layers and nodesper layer). Deep belief networks are typically ap-plied to relatively large data sets using stochas-tic gradient descent for optimization.
outputs being placed in the leaves of the hierarchy. Gaus-sian processes govern the mappings between the layers. A single layer of the deep GP is effectively a Gaussian process latent variable model (GP-LVM), just as a single layer of a regular deep model is typically an RBM. [Tit-sias and Lawrence, 2010] have shown that latent variables
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