Varieties with maximum likelihood degree one

2013/01/12 by Huh, June · 2 citations
#14M25 #14N25 #62F10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1301.2732

Abstract

We show that algebraic varieties with maximum likelihood degree one are exactly the images of reduced A-discriminantal varieties under monomial maps with finite fibers. The maximum likelihood estimator corresponding to such a variety is Kapranov's Horn uniformization. This extends Kapranov's characterization of A-discriminantal hypersurfaces to varieties of arbitrary codimension.

Cited by

• One-dimensional Discrete Models of Maximum Likelihood Degree One
• Newton numbers, vanishing polytopes and algebraic degrees

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• Gaussian likelihood geometry of projective varieties
• Likelihood Geometry
• Bounding the maximum likelihood degree
• On Horn-Kapranov uniformisation of the discriminantal loci
• Likelihood Degenerations