{"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/automated-scalable-bayesian-inference-via","title":"Automated Scalable Bayesian Inference via Hilbert Coresets","arxiv_id":"1710.05053","date":"2017-10-13","proceeding":null,"authors":["Trevor Campbell","Tamara Broderick"],"abstract":"The automation of posterior inference in Bayesian data analysis has enabled\nexperts and nonexperts alike to use more sophisticated models, engage in faster\nexploratory modeling and analysis, and ensure experimental reproducibility.\nHowever, standard automated posterior inference algorithms are not tractable at\nthe scale of massive modern datasets, and modifications to make them so are\ntypically model-specific, require expert tuning, and can break theoretical\nguarantees on inferential quality. Building on the Bayesian coresets framework,\nthis work instead takes advantage of data redundancy to shrink the dataset\nitself as a preprocessing step, providing fully-automated, scalable Bayesian\ninference with theoretical guarantees. We begin with an intuitive reformulation\nof Bayesian coreset construction as sparse vector sum approximation, and\ndemonstrate that its automation and performance-based shortcomings arise from\nthe use of the supremum norm. To address these shortcomings we develop Hilbert\ncoresets, i.e., Bayesian coresets constructed under a norm induced by an\ninner-product on the log-likelihood function space. We propose two Hilbert\ncoreset construction algorithms---one based on importance sampling, and one\nbased on the Frank-Wolfe algorithm---along with theoretical guarantees on\napproximation quality as a function of coreset size. Since the exact\ncomputation of the proposed inner-products is model-specific, we automate the\nconstruction with a random finite-dimensional projection of the log-likelihood\nfunctions. The resulting automated coreset construction algorithm is simple to\nimplement, and experiments on a variety of models with real and synthetic\ndatasets show that it provides high-quality posterior approximations and a\nsignificant reduction in the computational cost of inference.","url_abs":"http://arxiv.org/abs/1710.05053v2","url_pdf":"http://arxiv.org/pdf/1710.05053v2.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":"automated-scalable-bayesian-inference-via","repo_url":"https://github.com/trevorcampbell/bayesian-coresets","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"automated-scalable-bayesian-inference-via","repo_url":"https://github.com/trevorcampbell/quasi-newton-coresets-experiments","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"}],"methods":[{"method_slug":"coresets","method_name":"Coresets"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1710.05053","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}