The Bayesian Gaussian Process Latent Variable Model for Spatio-Temporal Stream Networks

TL;DR

This paper introduces a variational inference framework for Bayesian Gaussian process latent variable models tailored to spatio-temporal stream networks, effectively handling missing data and capturing complex dependencies.

Contribution

It develops a new family of models using sparse Gaussian processes, local variational methods, and stream-distance-based covariance functions for spatio-temporal stream networks.

Findings

Framework performs well in simulation-based case studies.

Models effectively handle missing data and censored observations.

Captures spatial and temporal dependencies using stream distance and process convolution.

Abstract

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data set subject to missing values, proceeds by maximising a secondary variational lower bound on the model log marginal likelihood using gradient-based optimisation. Consequently, the theoretical development for a new family of tails-up spatio-temporal stream network models is introduced which rely on the sparse Gaussian process inducing variable framework, the Bayesian Gaussian process latent variable model, and local variational methods. These spatio-temporal models use stream distance instead of Euclidean distance and capture spatial and temporal dependencies using auto/cross-correlation and process convolution, respectively, which allows for the development of valid separable spatio-temporal stream network-based covariance functions. Results from the simulation-based case studies indicate that the proposed framework performs well when considering benchmark comparisons and several performance metrics.