🤖 AI Summary
This study addresses the challenge of modeling spatiotemporal observational data with missing values in river network systems by proposing a novel Bayesian Gaussian process latent variable model tailored for upstream-to-downstream flow processes. The method constructs a separable spatiotemporal covariance function based on flow distance, integrating both autocorrelation and cross-correlation structures, and employs process convolution to capture complex dependencies inherent in stream networks. To enhance computational efficiency, the framework incorporates sparse inducing variables and local variational inference, enabling scalable training via gradient-based optimization. This work represents the first integration of Gaussian process latent variable models with river network topology, demonstrating superior modeling accuracy and predictive performance over existing benchmark methods in simulation experiments.
📝 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.