Deep Neural Networks as Point Estimates for Deep Gaussian Processes

Vincent Dutordoir
James Hensman
Mark van der Wilk
Carl Henrik Ek
Zoubin Ghahramani
Nicolas Durrande
Advances in Neural Information Processing Systems, Curran Associates, Inc.(2021)


Deep Gaussian processes (DGPs) have struggled for relevance in applications due to the challenges and cost associated with Bayesian inference. In this paper we propose a sparse variational approximation for DGPs for which the approximate posterior mean has the same mathematical structure as a Deep Neural Network (DNN). We make the forward pass through a DGP equivalent to a ReLU DNN by finding an interdomain transformation that represents the GP posterior mean as a sum of ReLU basis functions. This unification enables the initialisation and training of the DGP as a neural network, leveraging the well established practice in the deep learning community, and so greatly aiding the inference task. The experiments demonstrate improved accuracy and faster training compared to current DGP methods.

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