1 citations · 3 across the 4 of their papers we have counts for
8 papers
Robust estimation of tree structured models
Marta Casanellas, Marina Garrote-López, Piotr Zwiernik
Consider the problem of learning undirected graphical models on trees from corrupted data. Recently Katiyar et al. showed that it is possible to recover trees from noisy binary dat…
Likelihood Geometry of Correlation Models
Carlos Améndola, Piotr Zwiernik
Correlation matrices are standardized covariance matrices. They form an affine space of symmetric matrices defined by setting the diagonal entries to one. We study the geometry of…
Dependence in elliptical partial correlation graphs
David Rossell, Piotr Zwiernik
The Gaussian model equips strong properties that facilitate studying and interpreting graphical models. Specifically it reduces conditional independence and the study of positive a…
Estimating linear covariance models with numerical nonlinear algebra
Bernd Sturmfels, Sascha Timme, Piotr Zwiernik
Numerical nonlinear algebra is applied to maximum likelihood estimation for Gaussian models defined by linear constraints on the covariance matrix. We examine the generic case as w…
Secant varieties of toric varieties arising from simplicial complexes
M. Azeem Khadam, Mateusz Michałek, Piotr Zwiernik
Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affin…
Brownian motion tree models are toric
Bernd Sturmfels, Caroline Uhler, Piotr Zwiernik
Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgeb…