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.

我们扩展了 Xie 等人提出的用于学习贝叶斯网络 (BN) 的分解方法。(2006) [54] 学习多元回归链图 (MVR CG)，其中包括 BN 作为特例。这种分解方法的相同优点在更一般的设置中保持不变：降低计算独立性测试的复杂性并增加其能力。此外，潜在（隐藏）变量可以通过使用双向边在 MVR CG 中表示，并且我们的算法正确恢复了忠实于 MVR CG 的任何独立结构，从而大大扩展了基于分解的模型选择技术的应用范围。各种设置下的模拟证明了我们的方法与类似 PC 的方法相比的竞争性能算法（Sonntag 和 Peña，2012 年）[43]。事实上，除运行时间外，基于分解的算法通常优于类PC算法。当底层图稀疏时，两种算法的性能都要好得多。