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.

翻译：从纯观测性二元数据推断因果方向具有脆弱性：许多方法即使在模糊或接近不可识别的机制下也会强行确定方向。我们提出拓扑残差不对称性（TRA），这是一种基于几何结构的加性噪声模型判据。TRA在基于秩的联结函数标准化后，比较两个交叉拟合的回归器-残差云形状：在正确方向上，残差近似独立，形成二维主体结构；而在反向方向上——尤其在低噪声条件下——残差云会聚集在近似一维管状结构附近。我们使用零维持续同调泛函量化这种主体-管状对比度，该泛函可通过欧几里得最小生成树边长度分布高效计算。我们证明了该方法在三角阵列小噪声机制下的相合性，通过分箱变体（TRA-s）将方法扩展至固定噪声场景，并引入TRA-C——一种基于高斯联结函数插件自助法校准的混杂感知弃权规则。大量涵盖具有挑战性的合成与真实数据场景的实验证明了该方法的优越性。