  Conditional Mutual Information (CMI) is a measure of conditional dependence
between random variables X and Y, given another random variable Z. It can be
used to quantify conditional dependence among variables in many data-driven
inference problems such as graphical models, causal learning, feature selection
and time-series analysis. While k-nearest neighbor (kNN) based estimators as
well as kernel-based methods have been widely used for CMI estimation, they
suffer severely from the curse of dimensionality. In this paper, we leverage
advances in classifiers and generative models to design methods for CMI
estimation. Specifically, we introduce an estimator for KL-Divergence based on
the likelihood ratio by training a classifier to distinguish the observed joint
distribution from the product distribution. We then show how to construct
several CMI estimators using this basic divergence estimator by drawing ideas
from conditional generative models. We demonstrate that the estimates from our
proposed approaches do not degrade in performance with increasing dimension and
obtain significant improvement over the widely used KSG estimator. Finally, as
an application of accurate CMI estimation, we use our best estimator for
conditional independence testing and achieve superior performance than the
state-of-the-art tester on both simulated and real data-sets.
