基于残差形状差异判断因果方向，有效避免误判。
Topological Residual Asymmetry for Bivariate Causal Direction
- 通过残差云的几何结构差异识别因果方向
- 在低噪声下正确方向残差呈二维分布，反向呈一维聚集
- 适用于复杂数据场景，对混杂因素有自适应回避能力
从纯观测的二元数据中推断因果方向具有挑战性：许多方法在模糊或近乎不可识别的情况下仍强行确定方向。本文提出拓扑残差不对称性（TRA），一种基于几何结构的加性噪声模型因果判定准则。TRA通过秩变换后的核密度标准化，比较两个交叉拟合回归残差云的形状：在正确方向上，残差近似独立，形成二维主体分布；而在反向，尤其在低噪声条件下，残差云集中在一条一维管状区域。利用0维持久同调函数量化这种体-管对比，通过欧几里得最小生成树边长分布高效计算。证明了在小噪声三角阵列设定下的收敛性，通过分箱变体TRA-s扩展至固定噪声情形，并引入TRA-C，一种基于高斯-柯普拉插值自助法校准的混杂感知拒答规则。大量合成与真实数据实验表明该方法显著优于现有技术。
原文摘要 · Abstract (English)
Inferring causal direction from purely observational bivariate data is fragile: many methods commit to a direction even in ambiguous or near non-identifiable regimes. We propose Topological Residual Asymmetry (TRA), a geometry-based criterion for additive-noise models. TRA compares the shapes of two cross-fitted regressor-residual clouds after rank-based copula standardization: in the correct direction, residuals are approximately independent, producing a two-dimensional bulk, while in the reverse direction -- especially under low noise -- the cloud concentrates near a one-dimensional tube. We quantify this bulk-tube contrast using a 0D persistent-homology functional, computed efficiently from Euclidean MST edge-length profiles. We prove consistency in a triangular-array small-noise regime, extend the method to fixed noise via a binned variant (TRA-s), and introduce TRA-C, a confounding-aware abstention rule calibrated by a Gaussian-copula plug-in bootstrap. Extensive experiments across many challenging synthetic and real-data scenarios demonstrate the method's superiority.
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