Interpretable deep Gaussian processes with moments

TL;DR

This paper introduces an interpretable approach to Deep Gaussian Processes by calculating exact moments, enabling better understanding of their expressivity and correlation structures, with applications demonstrated on simulated and real data.

Contribution

It proposes a novel method to approximate DGPs as GPs using moments, providing interpretability and insights into their correlation and expressivity.

Findings

Effective kernels derived for multiple DGP layers

Demonstrated interpretability through analytic forms

Showed advantages on simulated and real data

Abstract

Deep Gaussian Processes (DGPs) combine the expressiveness of Deep Neural Networks (DNNs) with quantified uncertainty of Gaussian Processes (GPs). Expressive power and intractable inference both result from the non-Gaussian distribution over composition functions. We propose interpretable DGP based on approximating DGP as a GP by calculating the exact moments, which additionally identify the heavy-tailed nature of some DGP distributions. Consequently, our approach admits interpretation as both NNs with specified activation functions and as a variational approximation to DGP. We identify the expressivity parameter of DGP and find non-local and non-stationary correlation from DGP composition. We provide general recipes for deriving the effective kernels for DGP of two, three, or infinitely many layers, composed of homogeneous or heterogeneous kernels. Results illustrate the expressiveness of our effective kernels through samples from the prior and inference on simulated and real data and demonstrate advantages of interpretability by analysis of analytic forms, and draw relations and equivalences across kernels.