Using the structure of d-connecting paths as a qualitative measure of the strength of dependence
This work provides a qualitative measure for dependence strength in graphical models, which is incremental as it builds on existing d-connection theory.
The paper tackles the problem of quantifying conditional dependence strength in singly-connected Gaussian DAGs by using the structure of d-connecting paths, resulting in a method to partially order squared partial correlations based on the relationship between the path and conditioning sets.
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.