38 citations · 62 across the 23 of their papers we have counts for
27 papers
Euclidean Distance Optimization Within the Grassmannian
Hannah Friedman, Serkan Hoşten, Andrea Rosana
Given a subvariety of the Grassmannian and a data point, we seek to find a point on the subvariety minimizing the Euclidean distance to the data point. The number of complex critic…
Equations of Tree Tensor Network Varieties
Serkan Hoşten, Niharika Chakrabarty Paul, Otto T. P. Schmidt +1
We show that tree tensor network varieties, including tensor train varieties, are general Markov models associated to spaced trees. This allows us to prove that the prime ideals of…
Grassmann and Flag Varieties in Linear Algebra, Optimization, and Statistics: An Algebraic Perspective
Hannah Friedman, Serkan Hoşten
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics…
Uniqueness of size-2 positive semidefinite matrix factorizations
Kristen Dawson, Serkan Hoşten, Kaie Kubjas +1
We characterize when a size-2 positive semidefinite (psd) factorization of a positive matrix of rank 3 and psd rank 2 is unique. The characterization is obtained using tools from r…
Tropical toric maximum likelihood estimation
Emma Boniface, Karel Devriendt, Serkan Hoşten
We consider toric maximum likelihood estimation over the field of Puiseux series and study critical points of the likelihood function using tropical methods. This problem translate…
Maximum information divergence from linear and toric models
Yulia Alexandr, Serkan Hoşten
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…