# Order-Independent Structure Learning of Multivariate Regression Chain Graphs

arXiv: https://arxiv.org/abs/1910.01067 · HTML: https://mlsanity.com/paper/1910.01067/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2019.

## Built on by (most cited first, 1 of 1)

- [Accelerating Recursive Partition-Based Causal Structure Learning](https://mlsanity.com/paper/2102.11545/) (2021)

## Abstract (arXiv)

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~na 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.