# Varieties with maximum likelihood degree one

@article{Huh2013VarietiesWM, title={Varieties with maximum likelihood degree one}, author={June Huh}, journal={arXiv: Algebraic Geometry}, year={2013} }

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.

## 24 Citations

Moment maps, strict linear precision, and maximum likelihood degree one

- MathematicsAdvances in Mathematics
- 2020

Likelihood Geometry

- Mathematics
- 2013

We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that…

Maximum Likelihood Degree, Complete Quadrics, and ℂ*-Action

- MathematicsSIAM J. Appl. Algebra Geom.
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An explicit, basic, albeit of high computational complexity, formula is provided for the maximum likelihood degree of linear concentration models in algebraic statistics by relating an intersection problem on the variety of complete quadrics.

Maximum likelihood degree, complete quadrics and ${\mathbb C}^*$-action

- Mathematics
- 2020

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on a smooth compact moduli space of orbits of a ${\mathbb…

Maximum likelihood degree and space of orbits of a ${\mathbb C}^*$ action

- Mathematics
- 2020

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on a smooth compact moduli space of orbits of a ${\mathbb…

Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective

- Mathematics
- 2021

In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their…

Geometry of the Gaussian graphical model of the cycle

- Mathematics
- 2021

We prove a conjecture due to Sturmfels and Uhler concerning the degree of the projective variety associated to the Gaussian graphical model of the cycle. We involve new methods based on the…

Discrete statistical models with rational maximum likelihood estimator

- Mathematics, Computer Science
- 2019

This work presents an algorithm for constructing models with rational MLE, and demonstrates it on a range of instances of models familiar to statisticians, like Bayesian networks, decomposable graphical models, and staged trees.

A note on Maximum Likelihood Estimation for cubic and quartic canonical toric del Pezzo Surfaces

- Mathematics
- 2016

This article focuses on the study of toric algebraic statistical models which correspond to toric Del Pezzo surfaces with Du Val singularities. A closed-form for the Maximum Likelihood Estimate of…

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