Topological Causal Effects

• URL: http://arxiv.org/abs/2603.02289v1
• Date: Mon, 02 Mar 2026 13:47:23 GMT
• Title: Topological Causal Effects
• Abstract summary: We develop a framework for topological causal inference that defines treatment effects through differences in the topological structure of potential outcomes.<n> Empirical studies illustrate that the proposed method reliably quantifies topological treatment effects across diverse complex outcome types.
• Score: 4.002004604568088
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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