56 citations · 161 across the 21 of their papers we have counts for
10 papers · 1 filter
One-dimensional Discrete Models of Maximum Likelihood Degree One
Carlos Améndola, Viet Duc Nguyen, Janike Oldekop
We settle a conjecture by Bik and Marigliano stating that the degree of a one-dimensional discrete model with rational maximum likelihood estimator is bounded above by a linear fun…
On the maximum likelihood degree for Gaussian graphical models
Carlos Améndola, Rodica Andreea Dinu, Mateusz Michałek +1
In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore,…
Likelihood Geometry of Reflexive Polytopes
Carlos Améndola, Janike Oldekop
We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the maximum likelihood degree of these models as a…
Identifiability in Continuous Lyapunov Models
Philipp Dettling, Roser Homs, Carlos Améndola +2
The recently introduced graphical continuous Lyapunov models provide a new approach to statistical modeling of correlated multivariate data. The models view each observation as a o…
Third-Order Moment Varieties of Linear Non-Gaussian Graphical Models
Carlos Améndola, Mathias Drton, Alexandros Grosdos +2
In this paper we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combina…
Likelihood Geometry of Correlation Models
Carlos Améndola, Piotr Zwiernik
Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of…
Toric invariant theory for maximum likelihood estimation in log-linear models
Carlos Améndola, Kathlén Kohn, Philipp Reichenbach +1
We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models. We show that norm minimization over a torus orbit is equivalent…
Invariant theory and scaling algorithms for maximum likelihood estimation
Carlos Améndola, Kathlén Kohn, Philipp Reichenbach +1
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation familie…
Maximum Likelihood Estimation of Toric Fano Varieties
Carlos Améndola, Dimitra Kosta, Kaie Kubjas
We study the maximum likelihood estimation problem for several classes of toric Fano models. We start by exploring the maximum likelihood degree for all -dimensional Gorenstein…
Maximum Number of Modes of Gaussian Mixtures
Carlos Améndola, Alexander Engström, Christian Haase
Gaussian mixture models are widely used in Statistics. A fundamental aspect of these distributions is the study of the local maxima of the density, or modes. In particular, it is n…