Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Alexandr, Yulia"'
Autor:
Alexandr, Yulia, Bakenhus, Miles, Curiel, Mark, Deshpande, Sameer K., Gross, Elizabeth, Gu, Yuqi, Hill, Max, Johnson, Joseph, Kagy, Bryson, Karwa, Vishesh, Li, Jiayi, Lyu, Hanbaek, Petrović, Sonja, Rodriguez, Jose Israel
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical statistics.
Externí odkaz:
http://arxiv.org/abs/2402.13961
We study mixtures of decomposable graphical models, focusing on their ideals and dimensions. For mixtures of clique stars, we characterize the ideals in terms of ideals of mixtures of independence models. We also give a recursive formula for their ML
Externí odkaz:
http://arxiv.org/abs/2401.15950
Autor:
Alexandr, Yulia, Hoşten, Serkan
We study the problem of maximizing information divergence from a new perspective using logarithmic Voronoi polytopes. We show that for linear models, the maximum is always achieved at the boundary of the probability simplex. For toric models, we pres
Externí odkaz:
http://arxiv.org/abs/2308.15598
The setting of this article is nonparametric algebraic statistics. We study moment varieties of conditionally independent mixture distributions on $\mathbb{R}^n$. These are the secant varieties of toric varieties that express independence in terms of
Externí odkaz:
http://arxiv.org/abs/2301.09068
We introduce a family of discrete context-specific models, which we call decomposable. We construct this family from the subclass of staged tree models known as CStree models. We give an algebraic and combinatorial characterization of all context-spe
Externí odkaz:
http://arxiv.org/abs/2210.11521
Autor:
Alexandr, Yulia, Hoşten, Serkan
We extend the theory of logarithmic Voronoi cells to Gaussian statistical models. In general, a logarithmic Voronoi cell at a point on a Gaussian model is a convex set contained in its log-normal spectrahedron. We show that for models of ML degree on
Externí odkaz:
http://arxiv.org/abs/2203.01487
Autor:
Alexandr, Yulia
Publikováno v:
Alg. Stat. 15 (2024) 1-13
We study logarithmic Voronoi cells for linear statistical models and partial linear models. The logarithmic Voronoi cells at points on such model are polytopes. To any $d$-dimensional linear model inside the probability simplex $\Delta_{n-1}$, we can
Externí odkaz:
http://arxiv.org/abs/2112.14384
Autor:
Alexandr, Yulia, Hoşten, Serkan
Publikováno v:
In Journal of Symbolic Computation May-June 2024 122
Autor:
Alexandr, Yulia, Heaton, Alexander
Publikováno v:
Alg. Stat. 12 (2021) 75-95
We study Voronoi cells in the statistical setting by considering preimages of the maximum likelihood estimator that tessellate an open probability simplex. In general, logarithmic Voronoi cells are convex sets. However, for certain algebraic models,
Externí odkaz:
http://arxiv.org/abs/2006.09431
The response matrix of a resistor network is the linear map from the potential at the boundary vertices to the net current at the boundary vertices. For circular planar resistor networks, Curtis, Ingerman, and Morrow have given a necessary and suffic
Externí odkaz:
http://arxiv.org/abs/1812.01517