Publications: MPI-CBG

^* joint first author ^# joint corresponding author

2025

Kexin Wang, Aida Maraj, Anna Seigal
Contrastive independent component analysis for salient patterns and dimensionality reduction.
Proc Natl Acad Sci U.S.A., 122(50) Art. No. e2425119122 (2025)
Open Access DOI

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 group. The goal of such contrastive investigations is to identify salient features in the experimental group relative to the control. Independent component analysis (ICA) is a powerful tool for learning independent patterns in a dataset. We generalize it to contrastive ICA (cICA). For this purpose, we devise a linear algebra-based tensor decomposition algorithm, which is more expressive but just as efficient and identifiable as other linear algebra-based algorithms. We establish the identifiability of cICA and demonstrate its performance in finding patterns and visualizing data, using synthetic, semisynthetic, and real-world datasets, comparing the approach to existing methods.

Taylor Brysiewicz^#, Aida Maraj^#
Lawrence lifts, matroids, and maximum likelihood degrees.
Algebr Stat, 16(2) 217-242 (2025)
DOI

We express the maximum likelihood (ML) degrees of a family of toric varieties in terms of Möbius invariants of matroids. The family of interest are those parametrized by monomial maps given by Lawrence lifts of totally unimodular matrices with even circuits. Specifying these matrices to be vertex-edge incidence matrices of bipartite graphs gives the ML degrees of some hierarchical models and three dimensional quasi-independence models. Included in this list are the no-three-way interaction models with one binary random variable, for which we give closed formulae.

Jane Ivy Coons, Shelby Cox, Aida Maraj, Ikenna Nometa
ML degrees of Brownian motion tree models: Star trees and root invariance.
J Symb Comput, 132 Art. No. 102482 (2025)
DOI

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 study the complexity of inferring the maximum likelihood (ML) estimator for a BMT model by computing its ML-degree. Our main result is that the ML-degree of the BMT model on a star tree with n + 1 leaves is 2n+1-2n-3, which was previously conjectured by Am & eacute;ndola and Zwiernik. We also prove that the ML-degree of a BMT model is independent of the choice of the root. The proofs rely on the toric geometry of concentration matrices in a BMT model. Toward this end, we produce a combinatorial formula for the determinant of the concentration matrix of a BMT model, which generalizes the Cayley-Pr & uuml;fer theorem to complete graphs with weights given by a tree. (c) 2025 Published by Elsevier Ltd.

2024

Toric Multivariate Gaussian Models from Symmetries in a Tree with Emma Cardwell and Alvaro Ribot, (arxiv.org:407.02357)

Contrastive Independent Component Analysis with Kexin Wang and Anna Seigal, (https://arxiv.org/abs/2412.00895)

Maximum Likelihood Degrees of Brownian Motion Tree Models: Star Trees and Root Invariance with Jane Ivy Coons, Shelby Cox, Ikenna Nometa (https://arxiv.org/abs/2402.10322)

2023

Lawrence Lifts, Matroids, and Maximum Likelihood Degrees with Taylor Brysiewicz (arXiv:2310.13064)

Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics with Arpan Pal (arXiv:2309.10741)

2022

Shift Invariant Algebras, Segre Products and Regular Languages with Uwe Nagel, Journal of Algebra, Volume 631, 236-266, 2023 (arXiv:2204.07849)

2021

Symmetrically Colored Gaussian Graphical Models with Toric Vanishing Ideals with Jane Ivy Coons, Pratik Misra, and Miruna-Stefana Sorea, SIAM Journal of Applied Algebra and Geometry 7(1), 2023 (arXiv:2111.14817)

Staged Tree Models with Toric Structure with Christiane Gorgen and Lisa Nicklasson, Journal of Symbolic Computation 113, 242-268, 2022 (arXiv:2107.04516).

Nonlinear Algebra and Applications with Paul Breiding, Türkü Özlüm Çelik, Timothy Duff, Alexander Heaton, Anna-Laura Sattelberger, Lorenzo Venturello, Oğuzhan Yürük, Numerical Algebra, Control and Optimization, 2021 (arXiv:2103.16300).

2020

Reciprocal Maximum Likelihood Degrees of Brownian Motion Tree Models with Tobias Boege, Jane Ivy Coons, Christopher Eur, and Frank Rottger, Le Matematiche 76 (2), 383-398, 2021, special issue on Linear Spaces of Symmetric Matrices (arXiv:2009.11849).

Generalized Cut Polytopes for Binary Hierarchical Models with Jane Ivy Coons, Joseph Cummings, and Ben Hollering, Algebraic Statistics Vol. 14 (2023), No. 1, 17–36, 2023 (arXiv:2008.00043).

Algebraic and Geometric Properties of Hierarchical Models, Ph.D. Thesis, https://doi.org/10.13023/etd.2020.232.

2019

Equivariant Hilbert Series for Hierarchical Models with Uwe Nagel, Algebraic Statistics 12(1), 21–42, 2021 (arXiv:1909.13026).