Tobias Boege: Colored Gaussian DAG models

Abstract

Colored Gaussian DAG models generalize linear structural equation models by allowing additional equalities to be specified among the error variances and regression coefficients. We show that these models are smooth manifolds and give a characterization of their vanishing ideals up to a saturation. We also initiate the study of faithfulness and structural identifiability. Our results are facilitated by an in-depth analysis of parameter identification maps for ordinary Gaussian DAG models and our techniques carry over easily to other classes of rationally identifiable statistical models. This is joint work with Kaie Kubjas, Pratik Misra and Liam Solus.