A New Measure of Conditional Dependence for Causal Structural Learning
Measuring the dependencies among the variables of a network is of great interest to many disciplines. This paper studies the limitations of the existing dependencies measures such as their shortcomings in detecting direct influences or their lack of ability for group selection in order to have effective interventions and introduces a new statistical influence measure to overcome them. This measure is inspired by Dobrushin's coefficients and has been developed based on the paradigm that the conditional distribution of the variable of interest given all the direct causes will not change by intervening on other variables in the system. We show the advantageous of this measure over the related measures in the literature. Moreover, we establish the connection between our measure and the integral probability metric (IPM) that helps to develop estimators for our measure with lower complexity compared to the other relevant information theoretic based measures. At the end, we show the performance of this measure through a numerical simulation.