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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21307 |
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| _version_ | 1866913149897146368 |
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| author | Basson, Marno Louw, Tobias M. Smith, Theresa R. |
| author_facet | Basson, Marno Louw, Tobias M. Smith, Theresa R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21307 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Bayesian Gaussian Process Latent Variable Model for Spatio-Temporal Stream Networks Basson, Marno Louw, Tobias M. Smith, Theresa R. Methodology 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. |
| title | The Bayesian Gaussian Process Latent Variable Model for Spatio-Temporal Stream Networks |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.21307 |