{"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/improving-quadrature-for-constrained","title":"Improving Quadrature for Constrained Integrands","arxiv_id":"1802.04782","date":"2018-02-13","proceeding":null,"authors":["Henry Chai","Roman Garnett"],"abstract":"We present an improved Bayesian framework for performing inference of affine\ntransformations of constrained functions. We focus on quadrature with\nnonnegative functions, a common task in Bayesian inference. We consider\nconstraints on the range of the function of interest, such as nonnegativity or\nboundedness. Although our framework is general, we derive explicit\napproximation schemes for these constraints, and argue for the use of a log\ntransformation for functions with high dynamic range such as likelihood\nsurfaces. We propose a novel method for optimizing hyperparameters in this\nframework: we optimize the marginal likelihood in the original space, as\nopposed to in the transformed space. The result is a model that better explains\nthe actual data. Experiments on synthetic and real-world data demonstrate our\nframework achieves superior estimates using less wall-clock time than existing\nBayesian quadrature procedures.","url_abs":"http://arxiv.org/abs/1802.04782v4","url_pdf":"http://arxiv.org/pdf/1802.04782v4.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":"improving-quadrature-for-constrained","repo_url":"https://github.com/hchai-wustl/mmlt","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}