Likelihood Geometry of the Squared Grassmannian

2024/09/05 by Hannah Friedman, Friedman, Hannah · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2409.03730

openalex publication_date 2024/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study projection determinantal point processes and their connection to the squared Grassmannian. We prove that the log-likelihood function of this statistical model has (n - 1)!/2 critical points, all of which are real and positive, thereby settling a conjecture of Devriendt, Friedman, Reinke, and Sturmfels.

Cited by

• Squared Linear Models

Related

• Squared Linear Models
• Maximum likelihood estimation of determinantal point processes
• Duality induced by an embedding structure of determinantal point process
• Rates of estimation for determinantal point processes
• Maximum Likelihood Estimation on the Grassmannian of Lines