30 citations · 169 across the 28 of their papers we have counts for
6 papers · 1 filter
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…
The Identification Problem for Linear Rational Expectations Models
Majid M. Al-Sadoon, Piotr Zwiernik
This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary,…
Learning partial correlation graphs and graphical models by covariance queries
Gábor Lugosi, Jakub Truszkowski, Vasiliki Velona +1
We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often…
Total positivity in exponential families with application to binary variables
Steffen Lauritzen, Caroline Uhler, Piotr Zwiernik
We study exponential families of distributions that are multivariate totally positive of order 2 (MTP2), show that these are convex exponential families, and derive conditions for…
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…