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Statistical Data Analysis in the Algebraic Geometry Age

Toric fiber product of two polytopes
The toric fiber product of two polytopes

In the past four decades, we have witnessed a change of paradigm in Statistical Data Analysis from the tools that were designed to run on more elementary machines to a new era where statistical inference is powered by sophisticated computation.  We can think of Statistical Data Analysis in the Algebraic Geometry Age similarly. In the sixties, the field of Algebraic Geometry was revolutionized by the foundational work of Grothendieck, and in recent decades it has seen enormous advances in terms of theory and, symbolic and numerical, computation. This revolution means that we can now solve problems in Statistics using tools from Algebraic Geometry.  The focus of this research group was to contribute to the theory and application of statistics by using as tools from Algebraic Geometry, Commutative Algebra, Combinatorics, and Discrete Geometry.

Scientist
09.03.17 31.05.20

Eliana Maria Duarte Gelvez

Otto-von-Guericke-Universität Magdeburg
Nonlinear Algebra External Website
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Multimedia resources

Publications

inJournal
2024
Yulia Alexandr et al.

Decomposable context-specific models

In: SIAM journal on applied algebra and geometry

BibTex

 DOI: 10.1137/23M1575111 ArXiv: 2210.11521
Preprint
2024
Michael Borinsky et al.

Bivariate exponential integrals and edge-bicolored graphs

BibTex

 ArXiv: 2409.18607 Code: mathrepo.mis.mpg.de
Preprint
2024
Thomas Kahle et al.

Arrangements and likelihood

BibTex

 ArXiv: 2411.09508 Code: mathrepo.mis.mpg.de
Preprint
2024
Kaie Kubjas et al.

Geometry of polynomial neural networks

BibTex

 ArXiv: 2402.00949 Code: mathrepo.mis.mpg.de
Preprint
2024
Simon Telen et al.

Euler stratifications of hypersurface families

BibTex

 ArXiv: 2407.18176 Code: mathrepo.mis.mpg.de
Preprint
2024
Maximilian Wiesmann et al.

Pathological regularization regimes in classification tasks

BibTex

 ArXiv: 2406.14731
inJournal
2023
Isobel Davies et al.

Families of polytopes with rational linear precision in higher dimensions

In: Foundations of computational mathematics

BibTex

 DOI: 10.1007/s10208-022-09583-7 ArXiv: 2109.08151
inJournal
2023
Eliana Duarte et al.

A new characterization of discrete decomposable graphical models

In: Proceedings of the American Mathematical Society

BibTex

 DOI: 10.1090/proc/16212 ArXiv: 2105.05907
Preprint
2023
Eliana Duarte et al.

Algebraic geometry of quantum graphical models

BibTex

 Code: mathrepo.mis.mpg.de
inBook
2023
Eliana Duarte et al.

Toric fiber products in geometric modeling

In: Geometric science of information : 6th international conference, GSI 2023, St. Malo, France, August 30 - September 1, 2023, proceedings, part I

BibTex

 DOI: 10.1007/978-3-031-38271-0_49 ArXiv: 2303.08754
inJournal
2021
Lamprini Ananiadi et al.

Gröbner bases for staged trees

In: Algebraic statistics

BibTex

 DOI: 10.2140/astat.2021.12.1 ArXiv: 1910.02721

MiS Preprint
inJournal
2021
Eliana Duarte et al.

Discrete statistical models with rational maximum likelihood estimator

In: Bernoulli

BibTex

 DOI: 10.3150/20-BEJ1231 ArXiv: 1903.06110

MiS Preprint
Preprint
2021
Eliana Duarte et al.

Representation of context-specific causal models with observational and interventional data

BibTex

 ArXiv: 2101.09271
inJournal
2021
Carlos Guerra et al.

Global projections of the soil microbiome in the Anthropocene

In: Global ecology and biogeography

BibTex

 DOI: 10.1111/geb.13273 Code: figshare.com
Preprint
2020
Eliana Duarte et al.

Algebraic geometry of discrete interventional models

BibTex

 ArXiv: 2012.03593
inJournal
2020
Eliana Duarte et al.

Implicitization of tensor product surfaces via virtual projective resolutions

In: Mathematics of computation

BibTex

 DOI: 10.1090/mcom/3548 ArXiv: 1908.02086

MiS Preprint
inJournal
2020
Christiane Görgen et al.

Equations defining probability tree models

In: Journal of symbolic computation

BibTex

 DOI: 10.1016/j.jsc.2019.04.001 ArXiv: 1802.04511

MiS Preprint
inJournal
2017
Eliana Duarte

Implicitization of tensor product surfaces in the presence of a generic set of basepoints

In: Journal of algebra and its applications

BibTex

 DOI: 10.1142/S0219498817501894 ArXiv: 1610.03820
inBook
2016
Eliana Duarte et al.

Polynomial GCDs by syzygies

In: SYNASC 2016 : 18th International symposium on symbolic and numeric algorithms for scientific computing, Timisoara, Romania, September 24-27, 2016 ; proceedings

BibTex

 DOI: 10.1109/SYNASC.2016.021
inJournal
2016
Eliana Duarte et al.

Tensor product surfaces and linear syzygies

In: Proceedings of the American Mathematical Society

BibTex

 DOI: 10.1090/proc/12703 ArXiv: 1402.6751
All Group Publications
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