Topological Ignorability for Structural Causal Effects Beyond Means

Researchers introduce topological-geometrical causal metrics that capture structural changes in outcome distributions beyond mean-based estimates, proposing 'topological ignorability' as a weaker assumption than standard causal inference methods. The framework identifies cases where traditional average treatment effects miss important distributional shifts, validated through synthetic and real-world benchmarks.

This paper addresses a fundamental limitation in causal inference: the reliance on average treatment effects (ATE) obscures interventions that restructure outcome distributions without changing their means. Traditional causal estimands miss critical phenomena like population segmentation, multimodality creation, or topological reorganization. The authors develop a rigorous mathematical framework using persistent homology and Betti numbers—tools from topological data analysis—to quantify these structural effects. Topological ignorability emerges as a relaxed assumption compared to standard conditional ignorability, requiring only that a chosen structural feature remains invariant rather than the entire counterfactual distribution. This distinction matters practically: when an intervention creates disconnected regimes or reorganizes outcome clouds, conventional confounding adjustments fail silently while mean-based causal estimates appear unbiased. The validation framework is particularly compelling. In the Wisconsin breast-cancer benchmark, standard covariate balancing techniques achieve excellent standardized mean difference reduction yet leave ATE severely biased, while topological summaries (density-superlevel Betti contrasts, Euler signatures) remain stable across oracle, observational, and weighted specifications. This robustness suggests topological metrics capture genuine causal phenomena independent of confounding adjustment strategy. The work bridges causal inference and computational topology, introducing new estimands relevant wherever distributions matter more than averages—epidemiology, economics, and policy evaluation. However, practical adoption faces challenges: topological summaries require sufficient sample sizes for reliable estimation, interpretability demands expertise in algebraic topology, and researchers must justify feature selection theoretically rather than empirically.

• →Mean-based causal effects miss important structural changes in outcome distributions, including population splits, loops, and topological reorganization.
• →Topological ignorability provides weaker causal identification assumptions than standard conditional ignorability while targeting distributional features.
• →Persistent homology and Betti numbers quantify distributional differences beyond averages, enabling detection of causal effects invisible to conventional estimands.
• →Standard covariate balancing can appear successful by mean-difference metrics while leaving structural causal estimates severely biased.
• →Topological causal metrics demonstrate stability across confounding adjustment strategies in benchmarks where traditional ATE remains biased.