{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/structured-bayesian-gaussian-process-latent","title":"Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion","arxiv_id":"1807.04302","date":"2018-07-11","proceeding":null,"authors":["Steven Atkinson","Nicholas Zabaras"],"abstract":"We introduce a methodology for nonlinear inverse problems using a variational\nBayesian approach where the unknown quantity is a spatial field. A structured\nBayesian Gaussian process latent variable model is used both to construct a\nlow-dimensional generative model of the sample-based stochastic prior as well\nas a surrogate for the forward evaluation. Its Bayesian formulation captures\nepistemic uncertainty introduced by the limited number of input and output\nexamples, automatically selects an appropriate dimensionality for the learned\nlatent representation of the data, and rigorously propagates the uncertainty of\nthe data-driven dimensionality reduction of the stochastic space through the\nforward model surrogate. The structured Gaussian process model explicitly\nleverages spatial information for an informative generative prior to improve\nsample efficiency while achieving computational tractability through Kronecker\nproduct decompositions of the relevant kernel matrices. Importantly, the\nBayesian inversion is carried out by solving a variational optimization\nproblem, replacing traditional computationally-expensive Monte Carlo sampling.\nThe methodology is demonstrated on an elliptic PDE and is shown to return\nwell-calibrated posteriors and is tractable with latent spaces with over 100\ndimensions.","url_abs":"http://arxiv.org/abs/1807.04302v1","url_pdf":"http://arxiv.org/pdf/1807.04302v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"structured-bayesian-gaussian-process-latent","repo_url":"https://github.com/cics-nd/sgplvm-inverse","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}