AI 中文总结
针对异构数据条件独立性检验难题，提出MixCIT方法，通过基于图的检验统计量及局部多项式去偏变体，建立渐近零分布，证明检测阈值，开发高效算法，为混合类型数据的条件独立性检验提供统一、高效且有统计保证的解决方案。
AI 中文摘要
条件独立性检验（CIT）是因果发现和变量选择等现代统计推断领域的基础。尽管边际独立性相对被理解得较好，但现有非参数CIT在异构数据上未能提供统一、高效且有统计保证的解决方案。我们引入一种基于图的检验统计量，在复合邻域内比较响应的核相似度，离散部分用精确匹配，连续部分用$k_n$近邻匹配。原始统计量在完全离散条件下足够，但至少有一个条件变量连续时，使用局部多项式去偏变体消除局部平滑偏差。我们严格建立其在所有数据类型组合下的渐近零分布，证明局部备择假设下的无维度$n^{-1/4}$检测阈值，开发了近二次复杂度的高效算法和基于图的解析校准。
英文摘要
Conditional independence testing (CIT) is fundamental to modern statistical inference in areas related to causal discovery and variable selection. While marginal independence is relatively well-understood, despite multiple advances, no existing non-parametric CIT provides a unified, efficient, and statistically guaranteed solution across heterogeneous data. We introduce a graph-based test statistic comparing kernel similarities of the response within composite neighborhoods that use exact matching on discrete components and $k_n$-nearest-neighbor matching on continuous ones. The raw statistic, related to prior constructions, suffices under fully discrete conditioning. However, when at least one conditioning variable is continuous, we instead use a local-polynomial debiased variant that cancels the local smoothing bias. We rigorously establish its asymptotic null distribution across all data-type combinations. We further prove a dimension-free $n^{-1/4}$ detection threshold under local alternatives, eliminating the phase transition that affects geometric estimators in high dimensions. Finally, we develop efficient algorithms with near-quadratic complexity and analytic graph-based calibration, bypassing the cubic bottlenecks of global kernel methods.
