Likelihood geometry of determinantal point processes
Copyright policy )Likelihood geometry of determinantal point processes
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.
11 pages
- University of California, Berkeley United States
- Max Planck Society Germany
- Max Planck Institute for Mathematics in the Sciences Germany
Random matrices (algebraic aspects), Probability (math.PR), maximum likelihood estimation, Mathematics - Statistics Theory, Statistics Theory (math.ST), Geometric aspects of numerical algebraic geometry, principal minors, Algebraic statistics, Mathematics - Algebraic Geometry, Statistics on algebraic and topological structures, numerical algebraic geometry, FOS: Mathematics, Algebraic Geometry (math.AG), Mathematics - Probability, hyperdeterminant
Random matrices (algebraic aspects), Probability (math.PR), maximum likelihood estimation, Mathematics - Statistics Theory, Statistics Theory (math.ST), Geometric aspects of numerical algebraic geometry, principal minors, Algebraic statistics, Mathematics - Algebraic Geometry, Statistics on algebraic and topological structures, numerical algebraic geometry, FOS: Mathematics, Algebraic Geometry (math.AG), Mathematics - Probability, hyperdeterminant
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