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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).

even for simple prior densities like the Gaussian. In the GP-LVM [Lawrence, 2005] this problem is solved through 2They can also be treated as observed, e.g. in the upper most layer of the hierarchy where we might include the data label. maximizing with respect to the variables (instead of the pa-rameters, which are marginalized) and these ...

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  Densities, Gaussian

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