[图书][B] Metric algebraic geometry
P Breiding, K Kohn, B Sturmfels - 2024 - library.oapen.org
Metric algebraic geometry combines concepts from algebraic geometry and differential
geometry. Building on classical foundations, it offers practical tools for the 21st century …
geometry. Building on classical foundations, it offers practical tools for the 21st century …
Differential equations for Gaussian statistical models with rational maximum likelihood estimator
We study multivariate Gaussian statistical models whose maximum likelihood estimator
(MLE) is a rational function of the observed data. We establish a one-to-one correspondence …
(MLE) is a rational function of the observed data. We establish a one-to-one correspondence …
Gaussian likelihood geometry of projective varieties
S Di Rocco, L Gustafsson, L Schaffler - SIAM Journal on Applied Algebra and …, 2024 - SIAM
We explore the maximum likelihood degree of a homogeneous polynomial on a projective
variety,, which generalizes the concept of Gaussian maximum likelihood degree. We show …
variety,, which generalizes the concept of Gaussian maximum likelihood degree. We show …
Applications of intersection theory: from maximum likelihood to chromatic polynomials
RA Dinu, M Michałek, T Seynnaeve - arXiv preprint arXiv:2111.02057, 2021 - arxiv.org
Recently, we have witnessed tremendous applications of algebraic intersection theory to
branches of mathematics, that previously seemed very distant. In this article we review some …
branches of mathematics, that previously seemed very distant. In this article we review some …
Maximum likelihood estimation for nets of conics
We study the problem of maximum likelihood estimation for 3-dimensional linear spaces of 3
x 3 symmetric matrices from the point of view of algebraic statistics where we view these nets …
x 3 symmetric matrices from the point of view of algebraic statistics where we view these nets …
Geometry of the Gaussian graphical model of the cycle
RA Dinu, M Michałek, M Vodička - arXiv preprint arXiv:2111.02937, 2021 - arxiv.org
arXiv:2111.02937v1 [math.AG] 4 Nov 2021 Page 1 GEOMETRY OF THE GAUSSIAN
GRAPHICAL MODEL OF THE CYCLE RODICA ANDREEA DINU, MATEUSZ MICHA LEK, AND …
GRAPHICAL MODEL OF THE CYCLE RODICA ANDREEA DINU, MATEUSZ MICHA LEK, AND …
Conditional Euclidean distance optimization via relative tangency
S Di Rocco, L Gustafsson, L Sodomaco - arXiv preprint arXiv:2310.16766, 2023 - arxiv.org
We introduce a theory of relative tangency for projective algebraic varieties. The dual variety
$ X_Z^\vee $ of a variety $ X $ relative to a subvariety $ Z $ is the set of hyperplanes tangent …
$ X_Z^\vee $ of a variety $ X $ relative to a subvariety $ Z $ is the set of hyperplanes tangent …
Beyond linear algebra
B Sturmfels - Proceedings of the International Congress of …, 2022 - content.ems.press
Our title challenges the reader to venture beyond linear algebra in designing models and in
thinking about numerical algorithms for identifying solutions. This article accompanies the …
thinking about numerical algorithms for identifying solutions. This article accompanies the …
On the maximum likelihood degree for Gaussian graphical models
C Améndola, RA Dinu, M Michałek… - arXiv preprint arXiv …, 2024 - arxiv.org
In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a
detailed proof that the ML-degree behaves monotonically on induced subgraphs …
detailed proof that the ML-degree behaves monotonically on induced subgraphs …
Likelihood Correspondence of Statistical Models
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics
of the MLE problem for algebraic statistical models are reflected in the geometry of the …
of the MLE problem for algebraic statistical models are reflected in the geometry of the …