Potential Conditional Mutual Information: Estimators, Properties and Applications
Abstract
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several applications, it is desirable to have a functional purely of the conditional distribution p_{Y|X,Z} rather than of the joint distribution p_{X,Y,Z}. We define the potential conditional mutual information as the conditional mutual information calculated with a modified joint distribution p_{Y|X,Z} q_{X,Z}, where q_{X,Z} is a potential distribution, fixed airport. We develop K nearest neighbor based estimators for this functional, employing importance sampling, and a coupling trick, and prove the finite k consistency of such an estimator. We demonstrate that the estimator has excellent practical performance and show an application in dynamical system inference.
Cite
@article{arxiv.1710.05012,
title = {Potential Conditional Mutual Information: Estimators, Properties and Applications},
author = {Arman Rahimzamani and Sreeram Kannan},
journal= {arXiv preprint arXiv:1710.05012},
year = {2017}
}