标题： 多变量回归链图的无序结构学习 显示英文标题

标题： Order-Independent Structure Learning of Multivariate Regression Chain Graphs

摘要： 本文研究了多变量回归链图（MVR CGs），由Cox和Wermuth [3,4]引入，用于表示具有相关误差的线性因果模型。 我们考虑了Sonntag和Peña在[18]中提出的类似于PC算法的结构学习方法，这是一种基于约束的方法。 我们证明了PC-like算法具有顺序依赖性，即输出可能依赖于变量给出的顺序。 在低维情况下，这种顺序依赖性是一个次要问题。 然而，在高维情况下，它可能会非常显著，导致结果高度可变。 我们提出了两种修改PC-like算法的方法，部分或全部消除了这种顺序依赖性。 在各种设定下的模拟表明，我们的算法在低维情况下与原始PC-like算法相比具有竞争力，在高维情况下则表现出改进的性能。 显示英文摘要

摘要： This paper deals with multivariate regression chain graphs (MVR CGs), which were introduced by Cox and Wermuth [3,4] to represent linear causal models with correlated errors. We consider the PC-like algorithm for structure learning of MVR CGs, which is a constraint-based method proposed by Sonntag and Pe\~{n}a in [18]. We show that the 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 is a minor issue in low-dimensional settings. However, it can be very pronounced in high-dimensional settings, where it can lead to highly variable results. We propose two modifications of the PC-like algorithm that remove part or all of this order-dependence. Simulations under a variety of settings demonstrate the competitive performance of our algorithms in comparison with the original PC-like algorithm in low-dimensional settings and improved performance in high-dimensional settings.