Partially Observable Gaussian Process Network and Doubly Stochastic Variational Inference

TL;DR

This paper introduces the Partially Observable Gaussian Process Network (POGPN), a model that handles indirect, noisy, and incomplete observations in process networks, improving inference and predictive performance in real-world applications.

Contribution

The work extends deep Gaussian processes by incorporating partial observations into POGPN, enabling better modeling of real-world systems with incomplete data.

Findings

Incorporating partial observations improves predictive accuracy.

Two training methods enable inference on the entire network.

Application to benchmark problems demonstrates practical effectiveness.

Abstract

To reduce the curse of dimensionality for Gaussian processes (GP), they can be decomposed into a Gaussian Process Network (GPN) of coupled subprocesses with lower dimensionality. In some cases, intermediate observations are available within the GPN. However, intermediate observations are often indirect, noisy, and incomplete in most real-world systems. This work introduces the Partially Observable Gaussian Process Network (POGPN) to model real-world process networks. We model a joint distribution of latent functions of subprocesses and make inferences using observations from all subprocesses. POGPN incorporates observation lenses (observation likelihoods) into the well-established inference method of deep Gaussian processes. We also introduce two training methods for POPGN to make inferences on the whole network using node observations. The application to benchmark problems demonstrates how incorporating partial observations during training and inference can improve the predictive performance of the overall network, offering a promising outlook for its practical application.