Model-Powered Conditional Independence Test
Model-Powered Conditional Independence Test
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发表时间：
2017-09
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通讯作者：
Rajat Sen;A. Suresh;Karthikeyan Shanmugam;A. Dimakis;S. Shakkottai
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作者：
Rajat Sen;A. Suresh;Karthikeyan Shanmugam;A. Dimakis;S. Shakkottai
研究连续随机变量的非参数条件独立检验问题。给定连续随机向量$ x,y $和$ z $的联合分布$f(x,y,z)$的i.i.d个样本，我们确定$ x \perp y | z $。我们通过将条件独立测试转换为分类问题来解决这个问题。这使我们能够利用非常强大的分类器，如梯度增强树和深度神经网络。这些模型可以处理复杂的概率分布，并允许我们在高维CI测试中比之前的技术状态表现得更好。分类问题的主要技术挑战是需要条件积分布$f^{CI}(x,y,z) = f(x|z)f(y|z)f(z)$的样本-联合分布当且仅当$ x \perp y|z $ -当给定只能访问来自真实联合分布$f(x,y,z)$的样本时。为了解决这个问题，我们提出了一种新的最近邻自举过程，并从理论上证明了我们生成的样本在总变分距离方面确实接近f^{CI}$。然后，我们开发了关于我们问题分类的泛化界限的理论结果，这些结果转化为CI测试的误差界限。我们提供了一种新的分析非i -i存在下的Rademacher型分类界。D近独立样本。我们在模拟和真实数据集上验证了我们的算法的性能，并显示了比以前的方法性能的提高。
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.