This paper introduces deep Gaussian process (GP) models, which are based on Gaussian process mappings and structured as a deep belief network. The data is modeled as the output of a multivariate GP, with the inputs to this GP governed by another GP. A single layer of the model is equivalent to a standard GP or a GP latent variable model (GP-LVM). The authors perform inference using approximate variational marginalization, which results in a strict lower bound on the marginal likelihood of the model. This lower bound is used for model selection, allowing the application of deep models even with scarce data. The paper demonstrates the effectiveness of deep GP models through experiments on toy data, human motion capture data, and handwritten digit images, showing that they can learn hierarchical representations and encode abstract information even with limited data. The variational lower bound also enables principled model selection, as shown in a digit data set with only 150 examples, where a five-layer hierarchy is justified.This paper introduces deep Gaussian process (GP) models, which are based on Gaussian process mappings and structured as a deep belief network. The data is modeled as the output of a multivariate GP, with the inputs to this GP governed by another GP. A single layer of the model is equivalent to a standard GP or a GP latent variable model (GP-LVM). The authors perform inference using approximate variational marginalization, which results in a strict lower bound on the marginal likelihood of the model. This lower bound is used for model selection, allowing the application of deep models even with scarce data. The paper demonstrates the effectiveness of deep GP models through experiments on toy data, human motion capture data, and handwritten digit images, showing that they can learn hierarchical representations and encode abstract information even with limited data. The variational lower bound also enables principled model selection, as shown in a digit data set with only 150 examples, where a five-layer hierarchy is justified.