Discrete Statistical Models with Rational Maximum Likelihood Estimator

03/14/2019
by   Eliana Duarte, et al.
0

A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator (MLE) is a retraction from that simplex onto the model. We characterize all models for which this retraction is a rational function. This is a contribution via real algebraic geometry which rests on results due to Huh and Kapranov on Horn uniformization. We present an algorithm for constructing models with rational MLE, and we demonstrate it on a range of instances. Our focus lies on models familiar to statisticians, like Bayesian networks, decomposable graphical models, and staged trees.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

05/19/2022

Classifying one-dimensional discrete models with maximum likelihood degree one

We propose a classification of all one-dimensional discrete statistical ...
04/13/2022

Bayesian Integrals on Toric Varieties

We explore the positive geometry of statistical models in the setting of...
09/16/2021

Families of polytopes with rational linear precision in higher dimensions

In this article we introduce a new family of lattice polytopes with rati...
06/01/2022

Rational partition models under iterative proportional scaling

In this work we investigate partition models, the subset of log-linear m...
09/02/2019

Estimating linear covariance models with numerical nonlinear algebra

Numerical nonlinear algebra is applied to maximum likelihood estimation ...
09/15/2017

Mixtures and products in two graphical models

We compare two statistical models of three binary random variables. One ...
12/09/2020

Likelihood Equations and Scattering Amplitudes

We relate scattering amplitudes in particle physics to maximum likelihoo...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.