{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:04:30Z","timestamp":1750309470415,"version":"3.41.0"},"reference-count":5,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p>Marginal independence models are often studied by associating a combinatorial structure to describe the independence relations between random variables. For instance, Drton and Richardson [3] used bidirected graphs to develop a family of marginal independence models for discrete random variables, and Boege, Petrov\u00edc, and Sturmfels [1] used simplicial complexes. The marginal independence models of [3] fit more broadly into the class of graphical models [4, 5]. Each of these structures describes a very different family of models, with very little overlap between them. In both cases it had been shown that when we restrict to discrete random variables, we obtain toric models after a linear change of coordinates. However, there are collections of marginal independence statements that cannot be expressed either as graphs or simplicial complexes. This motivates the proposal of a more general combinatorial structure which we use in our treatment of marginal independence.<\/jats:p>","DOI":"10.1145\/3717582.3717585","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:41:51Z","timestamp":1739306511000},"page":"62-66","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Marginal Independence and Partial Set Partitions"],"prefix":"10.1145","volume":"58","author":[{"given":"Francisco Ponce","family":"Carri\u00f3n","sequence":"first","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Raleigh, NC"}]},{"given":"Seth","family":"Sullivant","sequence":"additional","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Raleigh, NC"}]}],"member":"320","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","author":"Boege Tobias","year":"2021","unstructured":"Tobias Boege, Sonja Petrov\u00edc, and Bernd Sturmfels. Marginal independence models. Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, 2021."},{"key":"e_1_2_1_2_1","volume-title":"Marginal independence and partial set partitions. Preprint. arXiv:2402.16292","author":"Carri\u00f3n Francisco Ponce","year":"2024","unstructured":"Francisco Ponce Carri\u00f3n and Seth Sullivant. Marginal independence and partial set partitions. Preprint. arXiv:2402.16292, 2024."},{"key":"e_1_2_1_3_1","volume-title":"Binary models for marginal independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(2):287--309","author":"Drton Mathias","year":"2008","unstructured":"Mathias Drton and Thomas S. Richardson. Binary models for marginal independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(2):287--309, 2008."},{"key":"e_1_2_1_4_1","volume-title":"Oxford Statistical Science Series","author":"Lauritzen S.L.","year":"1996","unstructured":"S.L. Lauritzen. Graphical Models. Oxford Statistical Science Series. Clarendon Press, 1996."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/194"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717585","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3717582.3717585","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:15Z","timestamp":1750295835000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717585"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1145\/3717582.3717585"],"URL":"https:\/\/doi.org\/10.1145\/3717582.3717585","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"2025-02-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}