{"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/estimating-the-volumes-of-correlations-sets","title":"Estimating the volumes of correlations sets in causal networks","arxiv_id":"2311.08574","date":"2023-11-14","proceeding":null,"authors":["Giulio Camillo","Pedro Lauand","Davide Poderini","Rafael Rabelo","Rafael Chaves"],"abstract":"Causal networks beyond that in the paradigmatic Bell's theorem can lead to new kinds and applications of non-classical behavior. Their study, however, has been hindered by the fact that they define a non-convex set of correlations and only very incomplete or approximated descriptions have been obtained so far, even for the simplest scenarios. Here, we take a different stance on the problem and consider the relative volume of classical or non-classical correlations a given network gives rise to. Among many other results, we show instances where the inflation technique, arguably the most disseminated tool in the community, is unable to detect a significant portion of the non-classical behaviors. Interestingly, we also show that the use of interventions, a central tool in causal inference, can enhance substantially our ability to witness non-classicality.","url_abs":"https://arxiv.org/abs/2311.08574v1","url_pdf":"https://arxiv.org/pdf/2311.08574v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"estimating-the-volumes-of-correlations-sets","repo_url":"https://github.com/giuhcs/relative_volumes_tripartite","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}