Learning LWF Chain Graphs: an Order Independent Algorithm
This work provides a more scalable method for learning chain graphs, which is important for researchers in causal inference and graphical models, though it is incremental as it builds on existing PC-like algorithms.
The authors tackled the problem of learning LWF chain graphs by developing a PC-like algorithm that addresses scalability issues of previous methods, demonstrating competitive performance in low-dimensional settings and improved performance in high-dimensional settings compared to existing approaches.
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.