Interpretable deep Gaussian processes with moments
This work addresses interpretability and inference challenges in DGPs for machine learning researchers, offering incremental improvements through analytic approximations.
The authors tackled the problem of intractable inference and lack of interpretability in Deep Gaussian Processes (DGPs) by approximating DGPs as Gaussian Processes using exact moment calculations, which revealed heavy-tailed distributions and provided interpretable connections to neural networks and variational approximations, with results demonstrated on simulated and real data.
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.