  We extend the decomposition approach for learning Bayesian networks (BNs)
proposed by (Xie et. al.) 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 Pena). 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.
