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Likelihood geometry of determinantal point processes

Hannah Friedman, Bernd Sturmfels and Maksym Zubkov

Vol. 15 (2024), No. 1, 15–25

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.

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