Abstract

HTC-identifiable graphs are a large family of graphs known to be generically identifiable. We explore some algebraic properties of linear structural equation models that can be represented by an HTC-identifiable graph. In particular, we prove that all mixed graphs are HTC-identifiable if and only if all the regression coefficients can be recovered from the covariance matrix using straightforward linear algebra operations on specified equations. Furthermore, given an HTC-identifiable graph, we provide a set of polynomials that generates the ideal that encompasses all the equality constraints of the corresponding graphical model on the cone of positive definite matrices. We further prove that, for a subset of HTC-identifiable graphs, this set of polynomials are the minimal generators of said ideal.

Keywords

Mathematical Subject Classification

Milestones

Authors