OS Reelle Geometrie und Algebra: Likelihood Geometry of Reflexive Polytopes

Freitag, 1. Dezember 2023
13:30 bis 15 Uhr

F 426

Veranstaltet von
Philipp di Dio / Markus Schweighofer

Vortragende Person/Vortragende Personen:
Carlos Amendola (TU Berlin)

We study the problem of maximum likelihood (ML) estimation
for statistical models defined by reflexive polytopes. Our focus is on
the ML degree of these models as a way of measuring the algebraic
complexity of the corresponding optimization problem. We compute the
ML degrees of all 4319 classes of three-dimensional reflexive
polytopes and prove formulas for several general families, which
include the hypercube and the cross-polytope in any dimension. We find
some surprising behavior in terms of the gaps between ML degrees and
degrees of the associated toric varieties, and we encounter some
models of ML degree one.
This is joint work with Janike Oldekop.