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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. Our fullyBayesian treatment allows for the application ofdeep models even when data is scarce.

led to other families of methods, in particular kernel meth-ods such as the support vector machine (SVM), to be con-sidered for the domain of data classification. Almost con-temporaneously to the SVM, Gaussian process (GP) mod-els [Rasmussen and Williams, 2006] were introduced as a fully probabilistic substitute for the multilayer perceptron

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  Process, Kernel, Gaussian, Gaussian process

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