6 papers
Tropical Fréchet Means: a polyhedral approach to exact optimization
Kamillo Ferry, Bo Lin, Carlos Améndola +2
The Fréchet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fréchet means…
Algebraic statistics of Hüsler-Reiss graphical models in multivariate extremes
Carlos Améndola, Jane Ivy Coons, Alexandros Grosdos +1
The field of extreme value statistics is concerned with modeling and predicting rare events. In a Hüsler-Reiss graphical model, a graph represents extremal conditional independenc…
Signature Varieties of Splines
Carlos Améndola, Felix Lotter, Leonard Schmitz
Splines are central objects for the interpolation of discrete data via piecewise smooth paths. Their iterated-integral signature is an infinite collection of tensors which characte…
Structural Identifiability of Graphical Continuous Lyapunov Models
Carlos Améndola, Tobias Boege, Benjamin Hollering +1
We prove two characterizations of model equivalence of acyclic graphical continuous Lyapunov models (GCLMs) with uncorrelated noise. The first result shows that two graphs are mode…
Tropical combinatorics of max-linear Bayesian networks
Carlos Améndola, Kamillo Ferry
A polytrope is a tropical polyhedron that is also classically convex. We study the tropical combinatorial types of polytropes associated to weighted directed acyclic graphs (DAGs).…
A PC Algorithm for Max-Linear Bayesian Networks
Carlos Améndola, Benjamin Hollering, Francesco Nowell
Max-linear Bayesian networks (MLBNs) are a relatively recent class of structural equation models which arise when the random variables involved have heavy-tailed distributions. Unl…