45 citations · 87 across the 19 of their papers we have counts for
31 papers
Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles
Mathias Drton, Marina Garrote-López, Niko Nikov +2
The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the commo…
Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding
Daniela Schkoda, Elina Robeva, Mathias Drton
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possib…
Causal Structure Learning in Directed, Possibly Cyclic, Graphical Models
Pardis Semnani, Elina Robeva
We consider the problem of learning a directed graph from observational data. We assume that the distribution which gives rise to the samples is Markov and faithful to th…
Multivariate Super-Resolution without Separation
Bakytzhan Kurmanbek, Elina Robeva
In this paper we study the high-dimensional super-resolution imaging problem. Here we are given an image of a number of point sources of light whose locations and intensities are u…
Log-concave density estimation in undirected graphical models
Kaie Kubjas, Olga Kuznetsova, Elina Robeva +2
We study the problem of maximum likelihood estimation of densities that are log-concave and lie in the graphical model corresponding to a given undirected graph . We show that t…
Ultra-marginal Feature Importance: Learning from Data with Causal Guarantees
Joseph Janssen, Vincent Guan, Elina Robeva
Scientists frequently prioritize learning from data rather than training the best possible model; however, research in machine learning often prioritizes the latter. Marginal contr…
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…
Robust Eigenvectors of Symmetric Tensors
Tommi Muller, Elina Robeva, Konstantin Usevich
The tensor power method generalizes the matrix power method to higher order arrays, or tensors. Like in the matrix case, the fixed points of the tensor power method are the eigenve…
The Set of Orthogonal Tensor Trains
Pardis Semnani, Elina Robeva
In this paper we study the set of tensors that admit a special type of decomposition called an orthogonal tensor train decomposition. Finding equations defining varieties of low-ra…
Learning Linear Non-Gaussian Graphical Models with Multidirected Edges
Yiheng Liu, Elina Robeva, Huanqing Wang
In this paper we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model given observational data. We build on an algori…
Orthogonal Decomposition of Tensor Trains
Karim Halaseh, Tommi Muller, Elina Robeva
In this paper we study the problem of decomposing a given tensor into a tensor train such that the tensors at the vertices are orthogonally decomposable. When the tensor train has…
Bimonotone Subdivisions of Point Configurations in the Plane
Elina Robeva, Melinda Sun
Bimonotone subdivisions in two dimensions are subdivisions all of whose sides are either vertical or have nonnegative slope. They correspond to statistical estimates of probability…
Optimal Rates for Estimation of Two-Dimensional Totally Positive Distributions
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet +1
We study minimax estimation of two-dimensional totally positive distributions. Such distributions pertain to pairs of strongly positively dependent random variables and appear freq…
Multi-trek separation in Linear Structural Equation Models
Elina Robeva, Jean-Baptiste Seby
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non…
Convolutions of Totally Positive Distributions with applications to Kernel Density Estimation
Ali Zartash, Elina Robeva
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive d…
Estimation of Monge Matrices
Jan-Christian Hütter, Cheng Mao, Philippe Rigollet +1
Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such…
Maximum Likelihood Estimation for Totally Positive Log-Concave Densities
Elina Robeva, Bernd Sturmfels, Ngoc Tran +1
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP)…
Duality of Graphical Models and Tensor Networks
Elina Robeva, Anna Seigal
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor h…
Geometry of Log-Concave Density Estimation
Elina Robeva, Bernd Sturmfels, Caroline Uhler
Shape-constrained density estimation is an important topic in mathematical statistics. We focus on densities on that are log-concave, and we study geometric properti…
Determinantal Generalizations of Instrumental Variables
Luca Weihs, Bill Robinson, Emilie Dufresne +6
Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mix…
The degree of
Madeline Brandt, DJ Bruce, Taylor Brysiewicz +2
We provide a closed formula for the degree of over an algebraically closed field of characteristic zero. In addition, we describe symbolic and numerical techniques w…
Singular Vectors of Orthogonally Decomposable Tensors
Elina Robeva, Anna Seigal
Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable te…
Orthogonal and unitary tensor decomposition from an algebraic perspective
Ada Boralevi, Jan Draisma, Emil Horobet +1
While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogon…
Positive semidefinite rank and nested spectrahedra
Kaie Kubjas, Elina Robeva, Richard Z. Robinson
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general…