  Measuring conditional dependencies among the variables of a network is of
great interest to many disciplines. This paper studies some shortcomings of the
existing dependency measures in detecting direct causal influences or their
lack of ability for group selection to capture strong dependencies and
accordingly introduces a new statistical dependency measure to overcome them.
This measure is inspired by Dobrushin's coefficients and based on the fact that
there is no dependency between $X$ and $Y$ given another variable $Z$, if and
only if the conditional distribution of $Y$ given $X=x$ and $Z=z$ does not
change when $X$ takes another realization $x'$ while $Z$ takes the same
realization $z$. We show the advantages 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 of the measure with lower complexity compared to other relevant
information theoretic based measures. Finally, we show the performance of this
measure through numerical simulations.
