Varieties with maximum likelihood degree one

TL;DR

This paper characterizes algebraic varieties with maximum likelihood degree one as images of A-discriminantal varieties under monomial maps, extending previous results to varieties of any codimension.

Contribution

It generalizes Kapranov's characterization of A-discriminantal hypersurfaces to varieties of arbitrary codimension with maximum likelihood degree one.

Findings

Varieties with ML degree one are images of A-discriminantal varieties.

Kapranov's Horn uniformization describes the ML estimator for these varieties.

The characterization extends to arbitrary codimension, not just hypersurfaces.

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.