Singularities of hypersurfaces in PC testing

This talk concerns Gaussian graphical models based on directed 
acyclic graphs (DAGs). The PC algorithm for learning the graph 
from data involves evaluating certain (almost-principal) 
subdeterminants of the sample covariance matrix. I will discuss
work by Lin-Uhler-Sturmfels-Bühlmann who argue that such a partial 
correlation test is more prone to errors when the hypersurface 
defined by the determinant has singularities, and I will present 
a positive answer to their question whether these hypersurfaces 
are *nonsingular* in the case of complete DAGS.