{"year":"2016","date_published":"2016-01-07T00:00:00Z","abstract":[{"lang":"eng","text":"Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials. "}],"quality_controlled":"1","oa":1,"status":"public","day":"07","doi":"10.1112/plms/pdv066","department":[{"_id":"CaUh"}],"publication":"Proceedings of the London Mathematical Society","oa_version":"Preprint","issue":"1","citation":{"ama":"Michałek M, Sturmfels B, Uhler C, Zwiernik P. Exponential varieties. *Proceedings of the London Mathematical Society*. 2016;112(1):27-56. doi:10.1112/plms/pdv066","mla":"Michałek, Mateusz, et al. “Exponential Varieties.” *Proceedings of the London Mathematical Society*, vol. 112, no. 1, Oxford University Press, 2016, pp. 27–56, doi:10.1112/plms/pdv066.","ieee":"M. Michałek, B. Sturmfels, C. Uhler, and P. Zwiernik, “Exponential varieties,” *Proceedings of the London Mathematical Society*, vol. 112, no. 1. Oxford University Press, pp. 27–56, 2016.","short":"M. Michałek, B. Sturmfels, C. Uhler, P. Zwiernik, Proceedings of the London Mathematical Society 112 (2016) 27–56.","ista":"Michałek M, Sturmfels B, Uhler C, Zwiernik P. 2016. Exponential varieties. Proceedings of the London Mathematical Society. 112(1), 27–56.","chicago":"Michałek, Mateusz, Bernd Sturmfels, Caroline Uhler, and Piotr Zwiernik. “Exponential Varieties.” *Proceedings of the London Mathematical Society*. Oxford University Press, 2016. https://doi.org/10.1112/plms/pdv066.","apa":"Michałek, M., Sturmfels, B., Uhler, C., & Zwiernik, P. (2016). Exponential varieties. *Proceedings of the London Mathematical Society*. Oxford University Press. https://doi.org/10.1112/plms/pdv066"},"title":"Exponential varieties","date_created":"2018-12-11T11:52:16Z","language":[{"iso":"eng"}],"author":[{"first_name":"Mateusz","full_name":"Michałek, Mateusz","last_name":"Michałek"},{"first_name":"Bernd","full_name":"Sturmfels, Bernd","last_name":"Sturmfels"},{"id":"49ADD78E-F248-11E8-B48F-1D18A9856A87","full_name":"Uhler, Caroline","first_name":"Caroline","last_name":"Uhler","orcid":"0000-0002-7008-0216"},{"first_name":"Piotr","full_name":"Zwiernik, Piotr","last_name":"Zwiernik"}],"publication_status":"published","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1480","month":"01","publist_id":"5714","main_file_link":[{"url":"http://arxiv.org/abs/1412.6185","open_access":"1"}],"date_updated":"2021-01-12T06:51:02Z","publisher":"Oxford University Press","volume":112,"intvolume":" 112","page":"27 - 56","type":"journal_article","scopus_import":1}