We explore the maximum likelihood degree of a homogeneous polynomial $F$ on a projective variety $X$, $\mathrm{MLD}_F(X)$, which generalizes the concept of Gaussian maximum likelihood degree. We show that $\mathrm{MLD}_F(X)$ is equal to the count of critical points of a rational function on $X$, and give different geometric characterizations of it via topological Euler characteristic, dual varieties, and Chern classes.
Di Rocco, S., Gustafsson, L., Schaffler, L. (2024). Gaussian Likelihood Geometry of Projective Varieties. SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 8(1), 89-113 [10.1137/22m1526113].
Gaussian Likelihood Geometry of Projective Varieties
Schaffler, Luca
2024-01-01
Abstract
We explore the maximum likelihood degree of a homogeneous polynomial $F$ on a projective variety $X$, $\mathrm{MLD}_F(X)$, which generalizes the concept of Gaussian maximum likelihood degree. We show that $\mathrm{MLD}_F(X)$ is equal to the count of critical points of a rational function on $X$, and give different geometric characterizations of it via topological Euler characteristic, dual varieties, and Chern classes.File in questo prodotto:
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