提出无需依赖特定回归模型的新型条件独立性检验方法。
The Generalised Kernel Covariance Measure
- 基于广义希尔伯特协方差框架，适配多种回归模型。
- 在多种数据生成过程下，显著提升检验效能与误差控制能力。
- 特别适合高维、非线性关系的条件独立性分析场景。
我们研究条件独立性（CI）检验问题，采用基于核的方法。现有方法依赖核岭回归，调参耗时且未调参时校准效果差，限制了实用性。本文提出广义核协方差度量（GKCM），一种不依赖具体回归模型的核基CI检验方法，可兼容多种回归估计器。基于Lundborg等（2022）的广义希尔伯特协方差框架，我们刻画了GKCM满足一致渐近水平保证的条件。模拟实验表明，当与树基回归模型结合时，GKCM在多种数据生成过程中频繁优于当前最优的CI检验方法，在类型I错误控制上表现更优，功效也具竞争力或更优。
原文摘要 · Abstract (English)
We consider the problem of conditional independence (CI) testing and adopt a kernel-based approach. Kernel-based CI tests embed variables in reproducing kernel Hilbert spaces, regress their embeddings on the conditioning variables, and test the resulting residuals for marginal independence. This approach yields tests that are sensitive to a broad range of conditional dependencies. Existing methods, however, rely heavily on kernel ridge regression, which is computationally expensive when properly tuned and yields poorly calibrated tests when left untuned, which limits their practical usefulness. We propose the Generalised Kernel Covariance Measure (GKCM), a regression-model-agnostic kernel-based CI test that accommodates a broad class of regression estimators. Building on the Generalised Hilbertian Covariance Measure framework (Lundborg et al., 2022), we characterise conditions under which GKCM satisfies uniform asymptotic level guarantees. In simulations, GKCM paired with tree-based regression models frequently outperforms state-of-the-art CI tests across a diverse range of data-generating processes, achieving better type I error control and competitive or superior power.
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