{"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/bayesian-hierarchical-stacking","title":"Bayesian hierarchical stacking: Some models are (somewhere) useful","arxiv_id":"2101.08954","date":"2021-01-22","proceeding":null,"authors":["Yuling Yao","Gregor Pirš","Aki Vehtari","Andrew Gelman"],"abstract":"Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can further improve the stacked mixture with a hierarchical model. We generalize stacking to Bayesian hierarchical stacking. The model weights are varying as a function of data, partially-pooled, and inferred using Bayesian inference. We further incorporate discrete and continuous inputs, other structured priors, and time series and longitudinal data. To verify the performance gain of the proposed method, we derive theory bounds, and demonstrate on several applied problems.","url_abs":"https://arxiv.org/abs/2101.08954v2","url_pdf":"https://arxiv.org/pdf/2101.08954v2.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":"bayesian-hierarchical-stacking","repo_url":"https://github.com/yao-yl/hierarchical-stacking-code","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2101.08954","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}