Effects of Nonparanormal Transform on PC and GES Search Accuracies
This work addresses a gap in simulation-based analysis for causal discovery methods, but it is incremental as it focuses on specific conditions for existing algorithms.
The study investigated how the nonparanormal transform affects the accuracy of PC and GES algorithms in graphical model searches, finding it generally ineffective but beneficial for GES in cases of moderate non-Gaussianity and non-linearity, with PC-GES performing equally well under strong linearity.
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.