Computing Maximum Likelihood Estimates for Gaussian Graphical Models with Macaulay2

1 code implementation • 21 Dec 2020 • Carlos Améndola, Luis David García-Puente, Roser Homs, Olga Kuznetsova, Harshit J. Motwani

We introduce the package "GraphicalModelsMLE" for computing the maximum likelihood estimates (MLEs) of a Gaussian graphical model in the computer algebra system Macaulay2.

Computation Commutative Algebra 14-04, 62R01, 62H22, 62F10

Toric invariant theory for maximum likelihood estimation in log-linear models

no code implementations • 14 Dec 2020 • Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal

We establish connections between invariant theory and maximum likelihood estimation for discrete statistical models.

Statistics Theory Algebraic Geometry Statistics Theory 14L24, 14P05, 20G45, 62F10, 62H22, 62R01

The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices

no code implementations • 1 Dec 2020 • Carlos Améndola, Lukas Gustafsson, Kathlén Kohn, Orlando Marigliano, Anna Seigal

We study multivariate Gaussian models that are described by linear conditions on the concentration matrix.

Algebraic Geometry Statistics Theory Statistics Theory 62R01, 14C17, 14Q15, 15A15

Structure Learning for Cyclic Linear Causal Models

no code implementations • 10 Jun 2020 • Carlos Améndola, Philipp Dettling, Mathias Drton, Federica Onori, Jun Wu

We consider the problem of structure learning for linear causal models based on observational data.