Topological Causal Effects
Kwangho Kim, Hajin Lee
TL;DR
This paper introduces a novel topological causal inference framework that measures treatment effects via differences in the topological structure of potential outcomes, applicable to complex non-Euclidean spaces.
Contribution
It develops a nonparametric, doubly robust estimator for topological effects, along with theoretical guarantees and a formal hypothesis test.
Findings
Reliable quantification of topological treatment effects in complex data.
Effective estimator with functional weak convergence properties.
Empirical validation across diverse outcome types.
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.
Peer Reviews
Decision·ICLR 2026 Poster
The paper’s primary strength lies in its innovative problem formulation: reframing causal effects as treatment-induced topological changes (rather than scalar/vector shifts) and integrating topological data analysis tools to quantify these changes. This opens a new direction for causal inference on non-Euclidean data, with clear relevance to biomedicine, neuroscience, and other fields where structural outcomes matter. Experimental design uses well-characterized semi-synthetic datasets with known
W1: The paper suffers from inadequate theoretical rigor. It does not provide explicit bias and variance formulations for IPW and AIPW estimators. While claiming AIPW some kind of double robustness benefit? But it offers no verification, for instance, analyses of how misspecified propensity score or outcome prediction models, extreme predictions, or skewed propensity scores impact estimation performance are entirely absent. There is also no discussion of whether robustness holds under realistic c
**S1.** The work is novel and makes a foundational contribution that meaningfully extends causal inference to the topology of treatment units, addressing an important gap where structural changes encode scientifically relevant effects. **S2.** The authors propose a solid theoretical framework with comprehensive analysis. **S3.** The paper introduces a hypothesis test for no topological effect with consistency guarantees. **S4.** Experimental validation demonstrates effectiveness on semi-synth
**W1.** The authors do not discuss scalability and computational complexity in the main paper. This is mentioned briefly in the Discussion section as a limitation, but given the claim for practical relevance, I believe this needs to be discussed in the paper. **W2.** The silhouette is an aggregated representation of topological features, which could potentially obscure the change in each homological feature. Ideally this should also be discussed further in the paper. **W3.** The weighted sil
The connection between algebraic topology and causal inference is original and has a clear practical value, given that it allows addressing high-dimensional and/or structurally complex outcomes, for which few methods exist. The presentation is clear and provides example illustrations of the important concepts. There is a careful theoretical analysis with independently interesting results, such as the stability bounds for weighted silhouettes, and the experiments match the theoretical results an
The experimental evaluation would be stronger if a comparison to existing TE estimators were given if applicable, and the related work could be expanded with references to previous methods (esp. addressing a high-dimensional setting). Furthermore, while some comments on practical considerations are given (ln. 256-), the authors might consider including a section on implementation considerations and details in the main text or at least Appendix.
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Taxonomy
TopicsAdvanced Causal Inference Techniques · Topological and Geometric Data Analysis · Bayesian Modeling and Causal Inference