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Gaussian processes (GPs) are a good choice for function approximation as theyare flexible, robust to over-fitting, and provide well-calibrated predictiveuncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations ofGPs, but inference in these models has proved challenging. Existing approachesto inference in DGP models assume approximate posteriors that forceindependence between the layers, and do not work well in practice. We present adoubly stochastic variational inference algorithm, which does not forceindependence between layers. With our method of inference we demonstrate that aDGP model can be used effectively on data ranging in size from hundreds to abillion points. We provide strong empirical evidence that our inference schemefor DGPs works well in practice in both classification and regression.

Doubly Stochastic Variational Inference for Deep Gaussian Processes