Gaussian Whittle-Matérn fields on metric graphs

Bolin, David; Simas, Alexandre B.; Wallin, Jonas

doi:10.48550/arxiv.2205.06163

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…Future work information about their position. To enable network-wide modeling that explicitly take space into account, we can model the processes spatially on a grid over the urban layout, or even directly over the bus network graph as recently proposed by Bolin et al (2022).…”

Section: Future Workmentioning

confidence: 99%

Bayesian Models for Spatiotemporal Data from Transportation Networks

Rodríguez-Déniz

2023

Linköping Studies in Statistics

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I express my gratitude to my supervisor, Mattias Villani, for his patience and support over the years since the very beginning of this journey. Learning the know-how of Bayesian modeling with him has been a privilege. I am grateful for his persistence in going beyond the call of duty to get the most out of every model and paper. Many thanks also to my co-supervisor, Augusto Voltes-Dorta, for useful discussions and support.The Division of Statistics and Machine Learning (STIMA) and the Department of Computer and Information Science (IDA) provided a nice and stable academic environment that I have really enjoyed. I am particularly grateful to Oleg Sysoev, José Peña, Jolanta Pielaszkiewicz and Fredrik Lindsten for their advice and support. The administrative staff in general, and Anne Moe and Karin Baardsen in particular, have done an excellent job throughout my studies. I also acknowledge the Knut and Alice Wallenberg Foundation for funding my doctorate through the WASP program.Since we met in late 2017 through WASP, John Törnblom has been my best friend here in Linköping. I am grateful for all the coffees, beers, concerts, and long conversations that made my time here more fun. Felipe Boeira supported me as well with his Brazilian cheerfulness and willingness to join to any non-academic activity. I also thank my fellow WASP PhD student, Caroline Svahn, for the many fikas and walks. Sarah Alsaadi was kind and supportive from the start, as well as Per Sidén and Josef Wilzén. Special thanks to the Ljusgården's PhD and postdoc gang, including

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Section: Future Workmentioning

confidence: 99%

Bayesian Models for Spatiotemporal Data from Transportation Networks

Rodríguez-Déniz

2023

Linköping Studies in Statistics

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“…proposed extrinsic framework for GP modeling on manifolds, which relies on embedding of the manifold into a Euclidean space and then constructing extrinsic kernels for GPs on their images. Dunson et al (2020) , Borovitskiy et al (2021) and Bolin et al (2022) focused on developing GPs on graphs and metric graphs formed by data observed on the manifold.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metrics

Niu¹,

Dai²,

Cheung³

et al. 2023

Preprint

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This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM ) in point clouds. In many real world applications, one often encounters high dimensional data (e.g.'point cloud data') centered around some lower dimensional unknown manifolds. The geometry of manifold is in general different from the usual Euclidean geometry. Naively applying traditional smoothing methods such as Euclidean Gaussian Processes (GPs) to manifold-valued data and so ignoring the geometry of the space can potentially lead to highly misleading predictions and inferences. A manifold embedded in a high dimensional Euclidean space can be well described by a probabilistic mapping function and the corresponding latent space. We investigate the geometrical structure of the unknown manifolds using the Bayesian Gaussian Processes latent variable models(B-GPLVM) and Riemannian geometry. The distribution of the metric tensor is learned using B-GPLVM. The boundary of the resulting manifold is defined based on the uncertainty quantification of the mapping. We use the the probabilistic metric tensor to simulate Brownian Motion paths on the unknown manifold. The heat kernel is estimated as the transition density of Brownian Motion and used as the covariance functions of GPUM . The applications of GPUM are illustrated in the simulation studies on the Swiss roll, high dimensional real datasets of WiFi signals and image data examples. Its performance is compared with the Graph Laplacian GP, Graph Matérn GP and Euclidean GP.

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Gaussian Whittle-Matérn fields on metric graphs

Cited by 2 publications

References 24 publications

Bayesian Models for Spatiotemporal Data from Transportation Networks

Bayesian Models for Spatiotemporal Data from Transportation Networks

Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metrics

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