From the 1 of 13 linked papers with an AI index.
13 papers
Recognition of algebraic matroids is undecidable
Tobias Boege, Geva Yashfe
The paper shows that there is no algorithm to decide whether a given rank function defines an algebraic matroid, proving the recognition problem undecidable by reducing from Diopha…
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…
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…
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…
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…
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…