Comment on: Decomposition of structural learning about directed acyclic graphs [1]

TL;DR

This paper presents a simplified proof for the conditions needed to decompose the process of learning DAG structures into smaller problems, improving understanding and potentially efficiency.

Contribution

It offers a simpler proof for decomposing DAG structure learning, applicable to d-separators and skeleton construction, building on previous work.

Findings

Simpler proof for DAG decomposition conditions

Applicable to d-separators and skeleton building

Influences structure learning algorithms

Abstract

We propose an alternative proof concerning necessary and sufficient conditions to split the problem of searching for d-separators and building the skeleton of a DAG into small problems for every node of a separation tree T. The proof is simpler than the original [1]. The same proof structure has been used in [2] for learning the structure of multivariate regression chain graphs (MVR CGs).