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We characterize tropical degenerations of the maximum likelihood estimation (MLE), we describe the log-normal polytopes, and we explore connections to determinantal point processes.<\/jats:p>","DOI":"10.1137\/25m1763998","type":"journal-article","created":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T09:00:26Z","timestamp":1775552426000},"page":"153-173","source":"Crossref","is-referenced-by-count":0,"title":["Squared Linear Models"],"prefix":"10.1137","volume":"10","author":[{"given":"Hannah","family":"Friedman","sequence":"first","affiliation":[{"name":"Mathematics, University of California, Berkeley, Berkeley, CA 94720 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6642-1479","authenticated-orcid":true,"given":"Bernd","family":"Sturmfels","sequence":"additional","affiliation":[{"name":"Mathematics, MPI-MiS Leipzig and UC Berkeley, Berkeley, CA 94720 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maximilian","family":"Wiesmann","sequence":"additional","affiliation":[{"name":"Center for Systems Biology Dresden, Dresden, 01307 Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,4,7]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2023.108863"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.2140\/astat.2024.15.1"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.2140\/astat.2021.12.75"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/23M1556174"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511586507"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/24M1656839"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-2010-01306-9"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-023-00557-2"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s44426-025-00007-x"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s13366-019-00481-8"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5350-1"},{"key":"ref12","first-page":"4463","volume":"153","author":"Friedman H.","year":"2025","journal-title":"Proc. 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Wang, Hypersurface arrangements with generic hypersurfaces added, preprint, arXiv:2412.20869."},{"key":"ref23","volume-title":"Basic Algebraic Geometry","volume":"1","author":"Shafarevich I.","year":"1994"}],"container-title":["SIAM Journal on Applied Algebra and Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/25M1763998","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:26:54Z","timestamp":1787236014000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1763998"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,7]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6,30]]}},"alternative-id":["10.1137\/25M1763998"],"URL":"https:\/\/doi.org\/10.1137\/25m1763998","relation":{},"ISSN":["2470-6566"],"issn-type":[{"value":"2470-6566","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,7]]}}}