Third Order Moment Varieties of Non-Gaussian Graphical Models

We study non-Gaussian graphical models from a perspective of algebraic statistics. Our focus is on algebraic relations among second and third moments in graphical models given by linear structural equations.

We show that when the graph is a tree these relations form a toric ideal. From the covariance matrix and the third moment tensor, we construct explicit matrices (associated to treks and multi-treks) whose $2\times 2$ minors generate the vanishing ideal of the model.

This is a joint work with Carlos Améndola, Mathias Drton, Alexandros Grosdos and Elina Robeva.