Topological Causal Effects

Kwangho Kim; Hajin Lee

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arXiv · 2603.02289

Topological Causal Effects

Kwangho Kim·Hajin Lee

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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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Kwangho Kim, Hajin Lee. 2026-03-02. Topological Causal Effects. https://arxiv.org/abs/2603.02289

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