Topological Residual Asymmetry for Bivariate Causal Direction

• URL: http://arxiv.org/abs/2602.00427v1
• Date: Sat, 31 Jan 2026 00:38:53 GMT
• Title: Topological Residual Asymmetry for Bivariate Causal Direction
• Authors: Mouad El Bouchattaoui,
• Abstract summary: Topological Residual Asymmetry is a geometry-based criterion for additive-noise models.<n>We quantify a bulk-tube contrast using a 0D persistent-homology functional.<n>Experiments across many challenging synthetic and real-data scenarios demonstrate the method's superiority.
• Score: 1.2691047660244335
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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