  Given independent samples generated from the joint distribution
$p(\mathbf{x},\mathbf{y},\mathbf{z})$, we study the problem of Conditional
Independence (CI-Testing), i.e., whether the joint equals the CI distribution
$p^{CI}(\mathbf{x},\mathbf{y},\mathbf{z})= p(\mathbf{z})
p(\mathbf{y}|\mathbf{z})p(\mathbf{x}|\mathbf{z})$ or not. We cast this problem
under the purview of the proposed, provable meta-algorithm, "Mimic and
Classify", which is realized in two-steps: (a) Mimic the CI distribution close
enough to recover the support, and (b) Classify to distinguish the joint and
the CI distribution. Thus, as long as we have a good generative model and a
good classifier, we potentially have a sound CI Tester. With this modular
paradigm, CI Testing becomes amiable to be handled by state-of-the-art, both
generative and classification methods from the modern advances in Deep
Learning, which in general can handle issues related to curse of dimensionality
and operation in small sample regime. We show intensive numerical experiments
on synthetic and real datasets where new mimic methods such conditional GANs,
Regression with Neural Nets, outperform the current best CI Testing performance
in the literature. Our theoretical results provide analysis on the estimation
of null distribution as well as allow for general measures, i.e., when either
some of the random variables are discrete and some are continuous or when one
or more of them are discrete-continuous mixtures.
