{"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/scalable-levy-process-priors-for-spectral","title":"Scalable Lévy Process Priors for Spectral Kernel Learning","arxiv_id":"1802.00530","date":"2018-02-02","proceeding":null,"authors":["Phillip A. Jang","Andrew E. Loeb","Matthew B. Davidow","Andrew Gordon Wilson"],"abstract":"Gaussian processes are rich distributions over functions, with generalization\nproperties determined by a kernel function. When used for long-range\nextrapolation, predictions are particularly sensitive to the choice of kernel\nparameters. It is therefore critical to account for kernel uncertainty in our\npredictive distributions. We propose a distribution over kernels formed by\nmodelling a spectral mixture density with a L\\'evy process. The resulting\ndistribution has support for all stationary covariances--including the popular\nRBF, periodic, and Mat\\'ern kernels--combined with inductive biases which\nenable automatic and data efficient learning, long-range extrapolation, and\nstate of the art predictive performance. The proposed model also presents an\napproach to spectral regularization, as the L\\'evy process introduces a\nsparsity-inducing prior over mixture components, allowing automatic selection\nover model order and pruning of extraneous components. We exploit the algebraic\nstructure of the proposed process for $\\mathcal{O}(n)$ training and\n$\\mathcal{O}(1)$ predictions. We perform extrapolations having reasonable\nuncertainty estimates on several benchmarks, show that the proposed model can\nrecover flexible ground truth covariances and that it is robust to errors in\ninitialization.","url_abs":"http://arxiv.org/abs/1802.00530v1","url_pdf":"http://arxiv.org/pdf/1802.00530v1.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":"scalable-levy-process-priors-for-spectral","repo_url":"https://github.com/pjang23/levy-spectral-kernel-learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"pruning","method_name":"Pruning"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1802.00530","atlas_url":"https://app.syntology.ai/?focus=1802.00530","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}