A Wasserstein-based measure of conditional dependence
Abstract
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 betweenXandYgiven another variableZ, if and only if the conditional distribution ofYgiven$$X=x$$X=xand$$Z=z$$Z=zdoes not change whenXtakes another realization$$x'$$x′whileZtakes the same realizationz. 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 25, 2022
- Source ID
- 10.1007/s41237-022-00170-2
Entities
People
- Jalal Etesami
- Kun Zhang
- Negar Kiyavash
Organizations
- Office of Naval Research Global
- Swiss Federal Institute of Technology in Lausanne