A decomposition-based algorithm for learning the structure of multivariate regression chain graphs

We extend the decomposition approach for learning Bayesian networks (BNs) proposed by Xie et al. (2006) [54] to learning multivariate regression chain graphs (MVR CGs), which include BNs as a special case. The same advantages of this decomposition approach hold in the more general setting: reduced complexity and increased power of computational independence tests. Moreover, latent (hidden) variables can be represented in MVR CGs by using bidirected edges, and our algorithm correctly recovers any independence structure that is faithful to an MVR CG, thus greatly extending the range of applications of decomposition-based model selection techniques. Simulations under a variety of settings demonstrate the competitive performance of our method in comparison with the PC-like algorithm (Sonntag and Peña, 2012) [43]. In fact, the decomposition-based algorithm usually outperforms the PC-like algorithm except in running time. The performance of both algorithms is much better when the underlying graph is sparse.