Order-Independent Structure Learning of Multivariate Regression Chain Graphs
This addresses a reliability issue in structure learning for causal models, which is incremental but important for high-dimensional data analysis.
The paper identified that the PC-like algorithm for learning multivariate regression chain graphs is order-dependent, leading to variable results especially in high-dimensional settings, and proposed two modifications that improve performance, showing competitive results in low-dimensional and better results in high-dimensional scenarios.
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 Peña 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.