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 BLOCKIN BLOCKIN aids—or BLOCKIN BLOCKIN harms—standard BLOCKIN BLOCKIN graphical BLOCKIN BLOCKIN model BLOCKIN BLOCKIN search BLOCKIN BLOCKIN procedures. BLOCKIN BLOCKIN We consider here how the transform affects the performance of two search algorithms in particular, PC (Spirtes BLOCKIN BLOCKIN et BLOCKIN 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 non-­‐linearity, another algorithm, PC-­‐GES (a combination of PC with GES), is equally effective. BLOCKIN developed BLOCKIN BLOCKIN a BLOCKIN BLOCKIN transformation BLOCKIN BLOCKIN of BLOCKIN BLOCKIN a BLOCKIN BLOCKIN class BLOCKIN BLOCKIN of BLOCKIN BLOCKIN non-­‐Gaussian BLOCKIN BLOCKIN 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 BLOCKIN We BLOCKIN BLOCKIN 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 non-­‐linearity, another algorithm, PC-­‐GES (a combination of PC with GES), is equally effective. The transform takes a column of data whose distribution is a smooth monotone function of N(0, 1) and renders it (using order statistics) as N(m, s 2) where m is the mean of the data and s 2 is the variance of the data, possibly with standardization. There are three questions. First, how does this transform affect data that is linear and Gaussian? Second, how does the transform affect analyses for data that are