连续分布非参数接近性检验的样本复杂度及其在含隐藏混杂的因果发现中的应用
Sample Complexity of Nonparametric Closeness Testing for Continuous Distributions and Its Application to Causal Discovery with Hidden Confounding
AI总结：
本文研究连续分布接近性检验的样本复杂度，提出基于 von Mises 展开的 KL 散度估计器，并将其用于含隐藏混杂的多维非高斯非线性因果发现，首次给出因果方向判别的样本复杂度保证。
摘要：
我们研究连续分布的接近性检验问题及其对因果发现的意义。具体而言，在非参数假设下，我们分析区分两个多维连续分布是否相同或在 Kullback-Leibler（KL）散度意义上至少相差 $ε$ 的样本复杂度。为此，我们提出一个基于 von Mises 展开的 KL 散度估计器。在光滑性假设下，我们的接近性检验达到最优参数化速率。该检验作为我们因果发现算法的构建模块，用于识别两个多维随机变量之间的因果结构，我们为所提出的因果发现方法建立了样本复杂度保证。据我们所知，本工作是首个在存在未观测混杂的情况下，为多维非线性模型中非高斯连续变量的因果方向区分提供样本复杂度保证的工作。
英文摘要：
We study the problem of closeness testing for continuous distributions and its implications for causal discovery. Specifically, we analyze the sample complexity of distinguishing whether two multidimensional continuous distributions are identical or differ by at least $ε$ in terms of Kullback-Leibler (KL) divergence under non-parametric assumptions. To this end, we propose an estimator of KL divergence which is based on the von Mises expansion. Our closeness test attains optimal parametric rates under smoothness assumptions. Equipped with this test, which serves as a building block of our causal discovery algorithm to identify the causal structure between two multidimensional random variables, we establish sample complexity guarantees for our causal discovery method. To the best of our knowledge, this work is the first work that provides sample complexity guarantees for distinguishing cause and effect in multidimensional non-linear models with non-Gaussian continuous variables in the presence of unobserved confounding.
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