Maximum likelihood estimation of toric Fano varieties

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)

[img] Text
214549.pdf - Published Version


Publisher's URL:


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
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.
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 (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
Related URLs:

University Staff: Request a correction | Enlighten Editors: Update this record