56 citations · 161 across the 21 of their papers we have counts for
22 papers
Learning Barycenters from Signature Matrices
Carlos Améndola, Leonard Schmitz
The expected signature of a family of paths need not be a signature of a path itself. Motivated by this, we consider the notion of a Lie group barycenter introduced by Buser and Ka…
The Maximum Likelihood Degree of Toric Models is Monotonic
Carlos Améndola, Janike Oldekop, Maximilian Wiesmann
We settle a conjecture by Coons and Sullivant stating that the maximum likelihood (ML) degree of a facial submodel of a toric model is at most the ML degree of the model itself. We…
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…
Computing Path Signature Varieties in Macaulay2
Carlos Améndola, Angelo El Saliby, Felix Lotter +1
The signature of a path is a non-commutative power series whose coefficients are given by certain iterated integrals over the path coordinates. This series almost uniquely characte…
Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks
Oskar Henriksson, Carlos Améndola, Jose Israel Rodriguez +1
A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the ma…
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…
Convex Hulls of Curves: Volumes and Signatures
Carlos Améndola, Darrick Lee, Chiara Meroni
Taking the convex hull of a curve is a natural construction in computational geometry. On the other hand, path signatures, central in stochastic analysis, capture geometric propert…
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…
Estimating Gaussian mixtures using sparse polynomial moment systems
Julia Lindberg, Carlos Améndola, Jose Israel Rodriguez
The method of moments is a classical statistical technique for density estimation that solves a system of moment equations to estimate the parameters of an unknown distribution. A…
An Invitation to Tropical Alexandrov Curvature
Carlos Améndola, Anthea Monod
We study Alexandrov curvature in the tropical projective torus with respect to the tropical metric, which has been useful in various statistical analyses, particularly in phylogeno…
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…
Computing Maximum Likelihood Estimates for Gaussian Graphical Models with Macaulay2
Carlos Améndola, Luis David García Puente, Roser Homs +2
We introduce the package "GraphicalModelsMLE" for computing the maximum likelihood estimates (MLEs) of a Gaussian graphical model in the computer algebra system Macaulay2. This pac…
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…
The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices
Carlos Améndola, Lukas Gustafsson, Kathlén Kohn +2
We study multivariate Gaussian models that are described by linear conditions on the concentration matrix. We compute the maximum likelihood (ML) degrees of these models. That is,…
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…
Computing Tropical Varieties in Macaulay2
Carlos Améndola, Kathlén Kohn, Sara Lamboglia +5
We introduce a package for doing tropical computations in Macaulay2. The package draws on the functionality of Gfan and Polymake while making the process as simple as possible for…
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…
Solving Parameterized Polynomial Systems with Decomposable Projections
Carlos Améndola, Julia Lindberg, Jose Israel Rodriguez
The Galois group of a parameterized polynomial system of equations encodes the structure of the solutions. This monodromy group acts on the set of solutions for a general set of pa…
Moment Varieties of Gaussian Mixtures
Carlos Améndola, Jean-Charles Faugère, Bernd Sturmfels
The points of a moment variety are the vectors of all moments up to some order of a family of probability distributions. We study this variety for mixtures of Gaussians. Following…