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Likelihood geometry of determinantal point processes

Hannah Friedman, Bernd Sturmfels and Maksym Zubkov

Vol. 15 (2024), No. 1, 15–25
DOI: 10.2140/astat.2024.15.15
Abstract

We study determinantal point processes (DPP) through the lens of algebraic statistics. We count the critical points of the log-likelihood function, and we compute them for small models, thereby disproving a conjecture of Brunel, Moitra, Rigollet and Urschel.

Keywords
maximum likelihood estimation, hyperdeterminant, principal minors, numerical algebraic geometry
Mathematical Subject Classification
Primary: 14Q65, 15B52, 62R01
Milestones
Received: 26 July 2023
Revised: 12 October 2023
Accepted: 14 October 2023
Published: 11 January 2024
Authors
Hannah Friedman
University of California Berkeley
Berkeley, CA
United States
Bernd Sturmfels
Max Planck Institute for Mathematics in the Sciences
Leipzig
Germany
Maksym Zubkov
University of California Berkeley
Berkeley, CA
United States