14 citations · 35 across the 13 of their papers we have counts for
15 papers
Algebraic Distance Optimization in Polyhedral Norms
Eliana Duarte, Nidhi Kaihnsa, Julia Lindberg +2
We consider the distance minimization problem to a real algebraic variety $X \subseteq \RR^n$ when the metric is induced by a polyhedral norm. Each point in the variety has a Voron…
Learning Linear Gaussian Polytree Models with Interventions
D. Tramontano, L. Waldmann, M. Drton +1
We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known interve…
Algebraic Geometry of Quantum Graphical Models
Eliana Duarte, Dmitrii Pavlov, Maximilian Wiesmann
Algebro-geometric methods have proven to be very successful in the study of graphical models in statistics. In this paper we introduce the foundations to carry out a similar study…
Toric Fiber Products in Geometric Modeling
Eliana Duarte, Benjamin Hollering, Maximilian Wiesmann
An important challenge in Geometric Modeling is to classify polytopes with rational linear precision. Equivalently, in Algebraic Statistics one is interested in classifying scaled…
Decomposable context-specific models
Yulia Alexandr, Eliana Duarte, Julian Vill
We introduce a family of discrete context-specific models, which we call decomposable. We construct this family from the subclass of staged tree models known as CStree models. We g…
Families of polytopes with rational linear precision in higher dimensions
Isobel Davies, Eliana Duarte, Irem Portakal +1
In this article we introduce a new family of lattice polytopes with rational linear precision. For this purpose, we define a new class of discrete statistical models that we call m…
A new characterization of discrete decomposable models
Eliana Duarte, Liam Solus
Decomposable graphical models, also known as perfect DAG models, play a fundamental role in standard approaches to probabilistic inference via graph representations in modern machi…
Representation of Context-Specific Causal Models with Observational and Interventional Data
Eliana Duarte, Liam Solus
We address the problem of representing context-specific causal models based on both observational and experimental data collected under general (e.g. hard or soft) interventions by…
Algebraic geometry of discrete interventional models
Eliana Duarte, Liam Solus
We investigate the algebra and geometry of general interventions in discrete DAG models. To this end, we introduce a theory for modeling soft interventions in the more general fami…
Gröbner bases for staged trees
Lamprini Ananiadi, Eliana Duarte
In this article we consider the problem of finding generators of the toric ideal associated to a combinatorial object called a staged tree. Our main theorem states that toric ideal…
Implicitization of tensor product surfaces via virtual projective resolutions
Eliana Duarte, Alexandra Seceleanu
We derive the implicit equations for certain parametric surfaces in three-dimensional projective space termed tensor product surfaces. Our method computes the implicit equation for…
Discrete Statistical Models with Rational Maximum Likelihood Estimator
Eliana Duarte, Orlando Marigliano, Bernd Sturmfels
A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator (MLE) is a retraction from that simplex onto the model. We characterize all mode…
Equations defining probability tree models
Eliana Duarte, Christiane Görgen
Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class…
Implicitization of tensor product surfaces in the presence of a generic set of basepoints
Eliana Duarte
Given a -dimensional vector subspace of , a tensor product surface, denoted by , is…
Tensor product surfaces and linear syzygies
Eliana Duarte, Hal Schenck
Let U be a basepoint free four-dimensional subpace of the space of sections of bidegree (a,b) on X = P^1 x P^1, with a and b at least 2. The sections corresponding to U determine a…