Bootstrapping the PC and CPC Algorithms to Improve Search Accuracy

By bootstrapping the output of the PC algorithm (Spirtes et al., 2000; Meek 1995), using larger conditioning sets informed by the current graph state, it is possible to define a novel algorithm, JPC, that improves accuracy of search for i.i.d. data drawn from linear, Gaussian, sparse to moderately dense models. The motivation for constructing sepsets using information in the current graph state is to highlight the differences between d-­‐separation information in the graph and conditional independence information extracted from the sample. The same idea can be pursued for any algorithm for which conditioning sets informed by the current graph state can be constructed and for which an orientation procedure capable of orienting undirected graphs can be extracted. Another plausible candidate for such retrofitting is the CPC algorithm (Ramsey et al, 2006), yielding an algorithm, JCPC, which, when the true graph is sparse is somewhat more accurate than JPC. The method is not feasible for discovery for models of categorical variables, i.e., traditional Bayes nets; with alternative tests for conditional independence it may extend to non-­‐linear or non-­‐Gaussian models, or both.