Effects of Nonparanormal Transform on PC and GES Search Accuracies
  Liu, et al., 2009 developed a transformation of a class of non-Gaussian
univariate distributions into Gaussian distributions. Liu and collaborators
(2012) subsequently applied the transform to search for graphical causal models
for a number of empirical data sets. To our knowledge, there has been no
published investigation by simulation of the conditions under which the
transform aids, or harms, standard graphical model search procedures. We
consider here how the transform affects the performance of two search
algorithms in particular, PC (Spirtes et al., 2000; Meek 1995) and GES (Meek
1997; Chickering 2002). We find that the transform is harmless but ineffective
for most cases but quite effective in very special cases for GES, namely, for
moderate non-Gaussianity and moderate non-linearity. For strong-linearity,
another algorithm, PC-GES (a combination of PC with GES), is equally effective.
