Order-Independent Structure Learning of Multivariate Regression Chain Graphs

TL;DR

This paper investigates the order-dependence of the PC-like algorithm for learning multivariate regression chain graphs and proposes modifications to make it order-independent, improving stability especially in high-dimensional scenarios.

Contribution

The authors identify order-dependence issues in the PC-like algorithm for MVR CGs and introduce two modifications that enhance its robustness and performance in high-dimensional settings.

Findings

Modified algorithms reduce order-dependence effects.

Enhanced performance in high-dimensional structure learning.

Competitive results in low-dimensional scenarios.

Abstract

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.