Topological Residual Asymmetry for Bivariate Causal Direction

TL;DR

TRA is a geometry-based method for inferring causal direction in bivariate data, leveraging topological features of residuals to distinguish cause from effect with high accuracy.

Contribution

It introduces a novel topological criterion using persistent homology and copula standardization to improve causal inference in additive-noise models.

Findings

Outperforms existing methods on synthetic data.

Effective in low-noise and ambiguous regimes.

Provides a confounding-aware abstention mechanism.

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.