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Abstract
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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.
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Keywords
maximum likelihood estimation, hyperdeterminant, principal
minors, numerical algebraic geometry
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Mathematical Subject Classification
Primary: 14Q65, 15B52, 62R01
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Milestones
Received: 26 July 2023
Revised: 12 October 2023
Accepted: 14 October 2023
Published: 11 January 2024
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