提出连续分布近似性检验新方法，用于有隐变量时的因果推断。
Sample Complexity of Nonparametric Closeness Testing for Continuous Distributions and Its Application to Causal Discovery with Hidden Confounding
- 基于冯·米塞斯展开估计KL散度，实现非参数下最优样本复杂度
- 在多维非线性非高斯模型中，首次给出有隐变量时因果推断的样本复杂度保证
- 适用于存在未观测混杂因素的高维连续变量因果结构识别
我们研究连续分布的近似性检验及其对因果发现的影响。具体而言，在非参数假设下，分析区分两个多维连续分布是否相同或在KL散度上至少相差ε所需的样本复杂度。为此，我们提出一种基于冯·米塞斯展开的KL散度估计器，该检验在光滑性假设下达到最优参数化率。利用该检验作为因果发现算法的核心组件，可识别两个多维随机变量间的因果结构，并建立该方法的样本复杂度保证。据我们所知，这是首个在存在未观测混杂因素的情况下，为多维非线性、非高斯连续变量模型提供因果关系区分样本复杂度保证的工作。
原文摘要 · Abstract (English)
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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