GFCM: A Tail-Sensitive Mixed-Type Conditional Independence Test for Causal Discovery
GFCM：面向因果发现的尾部敏感混合类型条件独立检验AI 解读 ↓
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GFCM：面向因果发现的尾部敏感混合类型条件独立检验
- 研究问题
- 因果发现算法依赖条件独立检验时，如何识别协方差之外的尺度和尾部依赖，同时处理混合类型数据并维持校准？
- 方法与思路
- 作者对条件均值为零的残差特征使用 GCM 框架，按块合并并采用 Cauchy 组合，同时以样条估计辅助函数。
- 材料陈述的贡献
- 摘要称给出尺度特征正交化、方向不对称修正和特征忠实性理论，并在模拟及半合成基准中报告尺度与尾部边识别优势。
- 阅读关注点
- 应核对加性辅助模型和特征忠实性条件、条件集增大时的校准，以及检验检测类与可恢复因果图之间的对应关系。
- 阅读边界
- 来源为 arXiv 预印本，同行评审与期刊接收未核实；有效性依赖加性辅助模型，尾部优势未在结构已知的完全真实数据中验证。
原文摘要
Constraint-based causal discovery like PC and FCI depends on its conditional independence test. Partial correlation and the Generalised Covariance Measure (GCM) detect only the conditional covariance of residuals, so they miss dependence in the mean's nonlinear part, the scale, and the tails. Tests that detect more are biased inside PC, not scalable, only continuous, or not aimed at the tails. Our Generalised Feature Covariance Measure (GFCM) is valid, sensitive beyond covariance, robust inside PC, and applicable to mixed-type data. It runs the GCM template on a configurable set of residual features with conditional mean zero (centered moments and conditional quantile indicators), pooled in blocks and combined by the Cauchy rule, with a growing-knot spline nuisance at regression cost. We contribute (i) a centering result making the scale feature Neyman orthogonal, where the uncentered version is biased; (ii) the orientation asymmetry the mean-quantile construction creates inside PC, and its fix; (iii) a Phi-faithfulness theory under which PC with GFCM recovers the CPDAG of the set's detection class; and (iv) a benchmark of CI tests sensitive beyond covariance on synthetic data, semi-synthetic tail injections, and PC discovery on random DAGs. Under size-corrected power, GFCM recovers the scale and tail edges the covariance family misses and alone keeps power at the deep conditioning sets PC issues. It stays calibrated as n grows, whereas FFCI, the boosted GCM, and the partial copula test do not, and it handles mixed-type data directly. Inside PC at scale it attains the lowest skeleton SHD among tests that stay calibrated, while the others inflate false edges. Validity rests on an additive nuisance, and the tail advantage is shown on simulated and semi-synthetic data, as no fully real benchmark with both heavy tails and known structure exists.