9 citations · 21 across the 11 of their papers we have counts for
12 papers
Computing the continuous symmetries of a parametrized variety
Benjamin Biaggi, Jan Draisma, Fulvio Gesmundo +2
We prove that the symmetry Lie algebra of a parametrized variety can be determined directly from the parametrization, without computing the vanishing ideal of the variety. We deriv…
Contrastive independent component analysis
Kexin Wang, Aida Maraj, Anna Seigal
In recent years, there has been growing interest in jointly analyzing a foreground dataset, representing an experimental group, and a background dataset, representing a control gro…
Maximum Likelihood Degrees of Brownian Motion Tree Models: Star Trees and Root Invariance
Jane Ivy Coons, Shelby Cox, Aida Maraj +1
A Brownian motion tree (BMT) model is a Gaussian model whose associated set of covariance matrices is linearly constrained according to common ancestry in a phylogenetic tree. We s…
Lawrence Lifts, Matroids, and Maximum Likelihood Degrees
Taylor Brysiewicz, Aida Maraj
We express the maximum likelihood (ML) degrees of a family toric varieties in terms of Mobius invariants of matroids. The family of interest are those parametrized by monomial maps…
Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics
Aida Maraj, Arpan Pal
The motivation for this paper is to detect when an irreducible projective variety V is not toric. We do this by analyzing a Lie group and a Lie algebra associated to V. If the dime…
Shift Invariant Algebras, Segre Products and Regular Languages
Aida Maraj, Uwe Nagel
Motivated by results on the rationality of equivariant Hilbert series of some hierarchical models in algebraic statistics we introduce the Segre product of formal languages and app…
Symmetrically colored Gaussian graphical models with toric vanishing ideal
Jane Ivy Coons, Aida Maraj, Pratik Misra +1
A colored Gaussian graphical model is a linear concentration model in which equalities among the concentrations are specified by a coloring of an underlying graph. The model is cal…
Staged tree models with toric structure
Christiane Görgen, Aida Maraj, Lisa Nicklasson
A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric…
Nonlinear Algebra and Applications
Paul Breiding, Türkü Özlüm Çelik, Timothy Duff +5
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, a…
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…
Generalized Cut Polytopes for Binary Hierarchical Models
Jane Ivy Coons, Joseph Cummings, Benjamin Hollering +1
Marginal polytopes are important geometric objects that arise in statistics as the polytopes underlying hierarchical log-linear models. These polytopes can be used to answer geomet…
Equivariant Hilbert series for hierarchical models
Aida Maraj, Uwe Nagel
Toric ideals to hierarchical models are invariant under the action of a product of symmetric groups. Taking the number of factors, say m, into account, we introduce and study invar…