Comment on: Decomposition of structural learning about directed acyclic graphs [1]
This work is incremental, providing a clearer proof for a technical aspect in graphical model learning, primarily benefiting researchers in statistics and machine learning.
The authors tackled the problem of simplifying the proof for conditions that allow decomposing the search for d-separators and DAG skeleton construction into smaller subproblems based on a separation tree, resulting in a simpler proof compared to the original.
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).