Abstract Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test scales at least quadratically with sample size. We therefore devise two relaxations called the Randomized Conditional Independence Test (RCIT) and the Randomized conditional Correlation Test (RCoT) which both approximate KCIT by utilizing random Fourier features. In practice, both of the proposed tests scale linearly with sample size and return accurate p-values much faster than KCIT in the large sample size context. CCD algorithms run with RCIT or RCoT also return graphs at least as accurate as the same algorithms run with KCIT but with large reductions in run time.

中文翻译：

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用于快速非参数因果发现的近似基于内核的条件独立性测试

摘要 基于约束的因果发现 (CCD) 算法需要快速准确的条件独立 (CI) 测试。Kernel Conditional Independence Test (KCIT) 是目前非参数设置中最流行的 CI 测试之一，但许多研究人员不能将 KCIT 用于大型数据集，因为该测试至少与样本大小成二次方比例。因此，我们设计了两种称为随机条件独立性测试 (RCIT) 和随机条件相关性测试 (RCoT) 的松弛方法，它们都通过利用随机傅立叶特征来近似 KCIT。在实践中，两个提议的测试都与样本大小成线性比例，并且在大样本大小的上下文中比 KCIT 更快地返回准确的 p 值。