Topological Causal Effects
This addresses the problem of causal inference in complex data structures for researchers in statistics and machine learning, representing a novel method for a known bottleneck.
The paper tackles the challenge of estimating causal effects for outcomes in complex, non-Euclidean spaces by developing a topological causal inference framework that defines effects through differences in topological structure, resulting in an efficient, doubly robust estimator with functional weak convergence and a formal test for no effect.
Estimating causal effects is particularly challenging when outcomes arise in complex, non-Euclidean spaces, where conventional methods often fail to capture meaningful structural variation. We develop a framework for topological causal inference that defines treatment effects through differences in the topological structure of potential outcomes, summarized by power-weighted silhouette functions of persistence diagrams. We develop an efficient, doubly robust estimator in a fully nonparametric model, establish functional weak convergence, and construct a formal test of the null hypothesis of no topological effect. Empirical studies illustrate that the proposed method reliably quantifies topological treatment effects across diverse complex outcome types.