Effects of Nonparanormal Transform on PC and GES Search Accuracies

TL;DR

This paper investigates how the nonparanormal transform influences the accuracy of PC and GES graphical model search algorithms, finding it generally harmless but beneficial in specific moderate non-Gaussian and non-linear cases.

Contribution

It provides the first simulation-based analysis of the transform's impact on PC and GES, identifying conditions where it improves search accuracy.

Findings

Transform is harmless in most cases.

Transform is effective for moderate non-Gaussianity and non-linearity with GES.

PC-GES performs well under strong linearity.

Abstract

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.