{"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/beyond-the-chinese-restaurant-and-pitman-yor","title":"Beyond the Chinese Restaurant and Pitman-Yor processes: Statistical Models with Double Power-law Behavior","arxiv_id":"1902.04714","date":"2019-02-13","proceeding":null,"authors":["Fadhel Ayed","Juho Lee","François Caron"],"abstract":"Bayesian nonparametric approaches, in particular the Pitman-Yor process and the associated two-parameter Chinese Restaurant process, have been successfully used in applications where the data exhibit a power-law behavior. Examples include natural language processing, natural images or networks. There is also growing empirical evidence that some datasets exhibit a two-regime power-law behavior: one regime for small frequencies, and a second regime, with a different exponent, for high frequencies. In this paper, we introduce a class of completely random measures which are doubly regularly-varying. Contrary to the Pitman-Yor process, we show that when completely random measures in this class are normalized to obtain random probability measures and associated random partitions, such partitions exhibit a double power-law behavior. We discuss in particular three models within this class: the beta prime process (Broderick et al. (2015, 2018), a novel process called generalized BFRY process, and a mixture construction. We derive efficient Markov chain Monte Carlo algorithms to estimate the parameters of these models. Finally, we show that the proposed models provide a better fit than the Pitman-Yor process on various datasets.","url_abs":"https://arxiv.org/abs/1902.04714v2","url_pdf":"https://arxiv.org/pdf/1902.04714v2.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":"beyond-the-chinese-restaurant-and-pitman-yor","repo_url":"https://github.com/OxCSML-BayesNP/doublepowerlaw","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}