We consider the problem of non-parametric Conditional Independence testing
(CI testing) for continuous random variables. Given i.i.d samples from the
joint distribution $f(x,y,z)$ of continuous random vectors $X,Y$ and $Z,$ we
determine whether $X \perp Y | Z$. We approach this by converting the
conditional independence test into a classification problem. This allows us to
harness very powerful classifiers like gradient-boosted trees and deep neural
networks. These models can handle complex probability distributions and allow
us to perform significantly better compared to the prior state of the art, for
high-dimensional CI testing. The main technical challenge in the classification
problem is the need for samples from the conditional product distribution
$f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$ -- the joint distribution if and only if $X
\perp Y | Z.$ -- when given access only to i.i.d. samples from the true joint
distribution $f(x,y,z)$. To tackle this problem we propose a novel nearest
neighbor bootstrap procedure and theoretically show that our generated samples
are indeed close to $f^{CI}$ in terms of total variational distance. We then
develop theoretical results regarding the generalization bounds for
classification for our problem, which translate into error bounds for CI
testing. We provide a novel analysis of Rademacher type classification bounds
in the presence of non-i.i.d near-independent samples. We empirically validate
the performance of our algorithm on simulated and real datasets and show
performance gains over previous methods.

针对连续随机变量，我们将条件独立性检验转化为分类问题并实现了非参数化的方案，通过最近邻引导采样策略生成训练样本，并提出一种大型数据集上性能更好的算法，从而实现有效测试。