Topological Causal Effects

Estimating causal effects becomes particularly challenging when outcomes possess complex, non-Euclidean structures, where conventional approaches often fail to capture meaningful structural variation. We introduce a novel framework for topological causal inference, defining treatment effects through changes in the underlying topological structure of outcomes. In our framework, intervention-driven topological shifts across homology are summarized via power-weighted silhouettes. We propose a doubly robust estimator, derive its asymptotic properties, and develop a formal test for the null hypothesis of no topological effect. Empirical studies demonstrate that our approach reliably quantifies treatment effects and remains robust across diverse, complex outcome spaces.