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

Keywords: Gaussian processes, Deep Gaussian processes, variational inference

TL;DR: We show how to make a forward pass through a Deep Gaussian process equivalent to a DNN with standard activation functions. Another step towards unifying DGPs and DNNs.

Abstract: Neural networks and Gaussian processes are complementary in their strengths and weaknesses. Having a better understanding of their relationship comes with the promise to make each method benefit from the strengths of the other. In this work, we establish an equivalence between the forward passes of neural networks and (deep) sparse Gaussian process models. The theory we develop is based on interpreting activation functions as interdomain inducing features through a rigorous analysis of the interplay between activation functions and kernels. This results in models that can either be seen as neural networks with improved uncertainty prediction or deep Gaussian processes with increased prediction accuracy. These claims are supported by experimental results on regression and classification datasets.

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