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Matroid stratification of ML degrees of independence models

Oliver Clarke, Serkan Hoşten, Nataliia Kushnerchuk and Janike Oldekop

Vol. 15 (2024), No. 2, 199–223
Abstract

We study the maximum likelihood (ML) degree of discrete exponential independence models and models defined by the second hypersimplex. For models with two independent variables, we show that the ML degree is an invariant of a matroid associated to the model. We use this description to explore ML degrees via hyperplane arrangements. For independence models with more variables, we investigate the connection between the vanishing of factors of its principal A-determinant and its ML degree. Similarly, for models defined by the second hypersimplex, we determine its principal A-determinant and give computational evidence towards a conjectured lower bound of its ML degree.

Keywords
maximum likelihood estimation, ML degrees, matroids
Mathematical Subject Classification
Primary: 13P15, 14M25, 62R01
Secondary: 05B35, 62F10
Milestones
Received: 12 February 2024
Accepted: 1 May 2024
Published: 3 December 2024
Authors
Oliver Clarke
University of Edinburgh
Edinburgh
United Kingdom
Serkan Hoşten
San Francisco State University
San Francisco, CA
United States
Nataliia Kushnerchuk
Aalto University
Aalto
Finland
Janike Oldekop
Technische Universität Berlin
Berlin
Germany