Chain graph reduction into power chain graphs

Reduction of graphs is a class of procedures used to decrease the dimensionality of a given graphin which the properties of the reduced graph are to be induced from the properties of the largeroriginal graph. This paper introduces both a new method for reducing chain graphs to simplerdirected acyclic graphs (DAGs), that we call power chain graphs (PCG), as well as a procedure forstructure learning of this new type of graph from correlational data of a Gaussian graphical model.Adefinitionfor PCGs is given, directly followed by the reduction method. The structure learningprocedure is a two-step approach:first,the correlation matrix is used to cluster the variables; andthen, the averaged correlation matrix is used to discover the DAGs using the PC-stable algorithm.The results of simulations are provided to illustrate the theoretical proposal, which demonstrateinitial evidence for the validity of our procedure to recover the structure of power chain graphs.The paper ends with a discussion regarding suggestions for future studies as well as some practicalimplications