198 citations · 713 across the 38 of their papers we have counts for
7 papers · 1 filter
Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
Bernd Sturmfels, Caroline Uhler
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the pro…
Open Problems in Algebraic Statistics
Bernd Sturmfels
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a l…
On the toric algebra of graphical models
Dan Geiger, Christopher Meek, Bernd Sturmfels
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or…
Conjunctive Bayesian networks
Niko Beerenwinkel, Nicholas Eriksson, Bernd Sturmfels
Conjunctive Bayesian networks (CBNs) are graphical models that describe the accumulation of events which are constrained in the order of their occurrence. A CBN is given by a parti…
Geometry of rank tests
Jason Morton, Lior Pachter, Anne Shiu +2
We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equi…
Solving the Likelihood Equations
Serkan Hosten, Amit Khetan, Bernd Sturmfels
Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all cr…