18 citations · 35 across the 24 of their papers we have counts for
10 papers · 1 filter
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…
Real birational implicitization for statistical models
Tobias Boege, Liam Solus
We derive an implicit description of the image of a semialgebraic set under a birational map, provided that the denominators of the map are positive on the set. For statistical mod…
Conditional Independence in Stationary Diffusions
Tobias Boege, Mathias Drton, Benjamin Hollering +3
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by…
Colored Gaussian directed acyclic graphical models
Tobias Boege, Kaie Kubjas, Pratik Misra +1
We study submodels of Gaussian DAG models defined by partial homogeneity constraints imposed on the model error variances and structural coefficients. We represent these models wit…
Algebra in probabilistic reasoning
Tobias Boege
This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates…
Marginal Independence Models
Tobias Boege, Sonja Petrović, Bernd Sturmfels
We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex. Following work of Kirkup and Sullivant, such marginal independence models can be made…
The geometry of Gaussian double Markovian distributions
Tobias Boege, Thomas Kahle, Andreas Kretschmer +1
Gaussian double Markovian models consist of covariance matrices constrained by a pair of graphs specifying zeros simultaneously in the covariance matrix and its inverse. We study t…
Incidence geometry in the projective plane via almost-principal minors of symmetric matrices
Tobias Boege
We present an encoding of a polynomial system into vanishing and non-vanishing constraints on almost-principal minors of a symmetric, principally regular matrix, such that the solv…
Gaussoids are two-antecedental approximations of Gaussian conditional independence structures
Tobias Boege
The gaussoid axioms are conditional independence inference rules which characterize regular Gaussian CI structures over a three-element ground set. It is known that no finite set o…
Reciprocal Maximum Likelihood Degrees of Brownian Motion Tree Models
Tobias Boege, Jane Ivy Coons, Christopher Eur +2
We give an explicit formula for the reciprocal maximum likelihood degree of Brownian motion tree models. To achieve this, we connect them to certain toric (or log-linear) models, a…