18 citations · 35 across the 24 of their papers we have counts for
25 papers
Trinomial containment in polynomial ideals is undecidable
Tobias Boege, Anna Hofer, Thomas Kahle
We prove that deciding whether an ideal in a polynomial ring contains a trinomial is impossible on a Turing machine. More precisely, from an integer polynomial we compute gener…
Recognition of algebraic matroids is undecidable
Tobias Boege, Geva Yashfe
We prove that the recognition problem for algebraic matroids is undecidable. Explicitly, this means that there is no algorithm that takes as input a finite set and a function $…
Sharp Inequalities for Products of Principal Minors of Positive Definite Matrices
Tobias Boege, Ludovick Bouthat
We study sharp inequalities for ratios of products of principal minors of real positive definite matrices. Our main result gives a closed-form solution to a family of nonconvex opt…
Algebraic Statistics in OSCAR
Tobias Boege, Antony Della Vecchia, Marina Garrote-López +1
We introduce the AlgebraicStatistics section of the OSCAR computer algebra system. We give an overview of its extensible design and highlight its features including serialization o…
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…
Polyhedral Aspects of Maxoids
Tobias Boege, Kamillo Ferry, Benjamin Hollering +1
The conditional independence (CI) relation of a distribution in a max-linear Bayesian network depends on its weight matrix through the -separation criterion. These CI~model…
On the Intersection and Composition properties of conditional independence
Tobias Boege
Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which sati…
The entropy profiles of a definable set over finite fields
Tobias Boege
A definable set in the first-order language of rings defines a family of random vectors: for each finite field , let the distribution be supported and uniform on…
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…
Sign patterns of principal minors of real symmetric matrices
Tobias Boege, Jesse Selover, Maksym Zubkov
We analyze a combinatorial rule satisfied by the signs of principal minors of a real symmetric matrix. The sign patterns satisfying this rule are equivalent to uniform oriented Lag…
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…
Self-adhesivity in lattices of abstract conditional independence models
Tobias Boege, Janneke H. Bolt, Milan Studený
We introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed…
Research-Data Management Planning in the German Mathematical Community
Tobias Boege, René Fritze, Christiane Görgen +13
In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized a…
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…
Selfadhesivity in Gaussian conditional independence structures
Tobias Boege
Selfadhesivity is a property of entropic polymatroids which guarantees that the polymatroid can be glued to an identical copy of itself along arbitrary restrictions such that the t…
No eleventh conditional Ingleton inequality
Tobias Boege
A rational probability distribution on four binary random variables is constructed which satisfies the conditional independence relations $[X \mathrel{\text{$\perp\mke…
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…
Construction Methods for Gaussoids
Tobias Boege, Thomas Kahle
The number of -gaussoids is shown to be a double exponential function in . The necessary bounds are achieved by studying construction methods for gaussoids that rely on presc…
The Geometry of Gaussoids
Tobias Boege, Alessio D'Alì, Thomas Kahle +1
A gaussoid is a combinatorial structure that encodes independence in probability and statistics, just like matroids encode independence in linear algebra. The gaussoid axioms of Ln…