Learning LWF Chain Graphs: an Order Independent Algorithm
  LWF chain graphs combine directed acyclic graphs and undirected graphs. We
present a PC-like algorithm that finds the structure of chain graphs under the
faithfulness assumption to resolve the problem of scalability of the proposed
algorithm by Studeny (1997). We prove that our PC-like algorithm is order
dependent, in the sense that the output can depend on the order in which the
variables are given. This order dependence can be very pronounced in
high-dimensional settings. We propose two modifications of the PC-like
algorithm that remove part or all of this order dependence. Simulation results
under a variety of settings demonstrate the competitive performance of the
PC-like algorithms in comparison with the decomposition-based method, called
LCD algorithm, proposed by Ma et al. (2008) in low-dimensional settings and
improved performance in high-dimensional settings.
