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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).

representational power of a Gaussian process in the same role is significantly greater than that of an RBM. For the GP the corresponding likelihood is over a continuous vari-able, but it is a nonlinear function of the inputs, p(yjx) = N yjf(x);˙2; where N j ;˙2 is a Gaussian density with mean and variance ˙2. In this case the likelihood is ...

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  Process, Gaussian, Gaussian process

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