{"_id":"1092","status":"public","abstract":[{"lang":"eng","text":"A graphical model encodes conditional independence relations via the Markov properties. For an undirected graph these conditional independence relations can be represented by a simple polytope known as the graph associahedron, which can be constructed as a Minkowski sum of standard simplices. We show that there is an analogous polytope for conditional independence relations coming from a regular Gaussian model, and it can be defined using multiinformation or relative entropy. For directed acyclic graphical models we give a construction of this polytope as a Minkowski sum of matroid polytopes. Finally, we apply this geometric insight to construct a new ordering-based search algorithm for causal inference via directed acyclic graphical models. "}],"type":"journal_article","extern":"1","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"id":"2C29581E-F248-11E8-B48F-1D18A9856A87","first_name":"Fatemeh","full_name":"Mohammadi, Fatemeh","last_name":"Mohammadi"},{"first_name":"Caroline","last_name":"Uhler","full_name":"Uhler, Caroline","id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7008-0216"},{"last_name":"Wang","full_name":"Wang, Charles","first_name":"Charles"},{"first_name":"Josephine","last_name":"Yu","full_name":"Yu, Josephine"}],"publisher":"SIAM","publication":"SIAM Journal on Discrete Mathematics","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.01814"}],"day":"01","page":"64-93","language":[{"iso":"eng"}],"issue":"1","year":"2018","oa":1,"volume":32,"title":"Generalized permutohedra from probabilistic graphical models","intvolume":"        32","date_created":"2018-12-11T11:50:06Z","date_updated":"2021-01-12T06:48:13Z","month":"01","doi":"10.1137/16M107894X","citation":{"short":"F. Mohammadi, C. Uhler, C. Wang, J. Yu, SIAM Journal on Discrete Mathematics 32 (2018) 64–93.","mla":"Mohammadi, Fatemeh, et al. “Generalized Permutohedra from Probabilistic Graphical Models.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 1, SIAM, 2018, pp. 64–93, doi:<a href=\"https://doi.org/10.1137/16M107894X\">10.1137/16M107894X</a>.","ista":"Mohammadi F, Uhler C, Wang C, Yu J. 2018. Generalized permutohedra from probabilistic graphical models. SIAM Journal on Discrete Mathematics. 32(1), 64–93.","ieee":"F. Mohammadi, C. Uhler, C. Wang, and J. Yu, “Generalized permutohedra from probabilistic graphical models,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 32, no. 1. SIAM, pp. 64–93, 2018.","ama":"Mohammadi F, Uhler C, Wang C, Yu J. Generalized permutohedra from probabilistic graphical models. <i>SIAM Journal on Discrete Mathematics</i>. 2018;32(1):64-93. doi:<a href=\"https://doi.org/10.1137/16M107894X\">10.1137/16M107894X</a>","chicago":"Mohammadi, Fatemeh, Caroline Uhler, Charles Wang, and Josephine Yu. “Generalized Permutohedra from Probabilistic Graphical Models.” <i>SIAM Journal on Discrete Mathematics</i>. SIAM, 2018. <a href=\"https://doi.org/10.1137/16M107894X\">https://doi.org/10.1137/16M107894X</a>.","apa":"Mohammadi, F., Uhler, C., Wang, C., &#38; Yu, J. (2018). Generalized permutohedra from probabilistic graphical models. <i>SIAM Journal on Discrete Mathematics</i>. SIAM. <a href=\"https://doi.org/10.1137/16M107894X\">https://doi.org/10.1137/16M107894X</a>"},"date_published":"2018-01-01T00:00:00Z","publication_status":"published","quality_controlled":"1","oa_version":"Preprint","publist_id":"6284"}