Améndola, C., Kosta, D. and Kubjas, K. (2020) Maximum likelihood estimation of toric Fano varieties. Algebraic Statistics, 11(1), pp. 5-30. (doi: 10.2140/astat.2020.11.5)
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Abstract
We study the maximum likelihood estimation problem for several classes of toric Fano models. We start by exploring the maximum likelihood degree for all 2-dimensional Gorenstein toric Fano varieties. We show that the ML degree is equal to the degree of the surface in every case except for the quintic del Pezzo surface with two singular points of type A1 and provide explicit expressions that allow to compute the maximum likelihood estimate in closed form whenever the ML degree is less than 5. We then explore the reasons for the ML degree drop using A-discriminants and intersection theory. Finally, we show that toric Fano varieties associated to 3-valent phylogenetic trees have ML degree one and provide a formula for the maximum likelihood estimate. We prove it as a corollary to a more general result about the multiplicativity of ML degrees of codimension zero toric fiber products, and it also follows from a connection to a recent result about staged trees.
Item Type: | Articles |
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Additional Information: | Part of this work was completed while D. Kosta was supported by a Daphne Jackson Trust Fellowship funded jointly by EPSRC and the University of Edinburgh. C. Améndola was partially supported by the Deutsche Forschungsgemeinschaft (DFG) in the context of the Emmy Noether junior research group KR 4512/1-1. K. Kubjas was supported by the European Union’s Horizon 2020 research and innovation programme: Marie Skłodowska-Curie grant agreement No. 748354, research carried out at LIDS, MIT and Team PolSys, LIP6, Sorbonne University. |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Kosta, Dr Dimitra |
Authors: | Améndola, C., Kosta, D., and Kubjas, K. |
Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Algebraic Statistics |
Journal Abbr.: | Astat |
Publisher: | Mathematical Sciences Publishers |
ISSN: | 2693-2997 |
ISSN (Online): | 2693-3004 |
Copyright Holders: | Copyright © 2020 Mathematical Science Publishers |
First Published: | First published in Algebraic Statistics 11(1):5-30 |
Publisher Policy: | Reproduced with the permission of the publisher |
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