Third-order moment varieties of linear non-Gaussian graphical models

• Carlos Améndola ^[1] ; Mathias Drton ^[1] ; Alexandros Grosdos ^[1] ; Roser Homs ^[1] ; Elina Robeva ^[2]
  1. [1] Technical University Munich

     Technical University Munich

     Kreisfreie Stadt München, Alemania

     
  2. [2] University of British Columbia

     University of British Columbia

     Canadá

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 43-46
• Idioma: inglés
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• Resumen

  • In this work we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The underlying directed causal graph can be identified uniquely via the set of second and third order moments of all random vectors that lie in the corresponding model. Our focus is on finding the algebraic relations among these moments for a given graph. We show that when the graph isa polytree these relations form a toric ideal. We construct explicit matrices associated to treks in the graph. Their entries are the covariances and third order moments, and their 2-minors define our model set-theoretically, and provide a generating set for the vanishing ideal of the model. Finally, we describe the polytopes of third order moments.