Deep Neural Networks as Point Estimates for Deep Gaussian Processes
This work bridges neural networks and Gaussian processes to combine their strengths, addressing uncertainty estimation and accuracy limitations in both methods.
The authors established an equivalence between neural network forward passes and deep sparse Gaussian processes by interpreting activation functions as interdomain inducing features, resulting in models that improve uncertainty prediction for neural networks or increase accuracy for Gaussian processes, with experimental validation on regression and classification datasets.
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.