Using the structure of d-connecting paths as a qualitative measure of the strength of dependence

TL;DR

This paper introduces a method to qualitatively assess the strength of dependence between variables in singly-connected Gaussian DAGs by analyzing the structure of d-connecting paths, enhancing understanding of conditional dependencies.

Contribution

It demonstrates that the form of d-connecting paths can be used to infer qualitative strength of dependence in Gaussian DAGs, a novel approach in graphical models.

Findings

Squared partial correlations can be ordered by analyzing d-connecting paths.

The structure of d-connecting paths provides qualitative insights into dependence strength.

Method applies specifically to singly-connected Gaussian DAGs.

Abstract

Pearls concept OF a d - connecting path IS one OF the foundations OF the modern theory OF graphical models : the absence OF a d - connecting path IN a DAG indicates that conditional independence will hold IN ANY distribution factorising according TO that graph. IN this paper we show that IN singly - connected Gaussian DAGs it IS possible TO USE the form OF a d - connection TO obtain qualitative information about the strength OF conditional dependence.More precisely, the squared partial correlations BETWEEN two given variables, conditioned ON different subsets may be partially ordered BY examining the relationship BETWEEN the d - connecting path AND the SET OF variables conditioned upon.