Technology Category
Machine Learning: Causal LearningReasoning under Uncertainty: CausalityKnowledge Representation and Reasoning: Action, Change, and Causality
Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability
🤖 AI Summary
Traditional causal effects, such as the average treatment effect (ATE) and conditional average treatment effect (CATE), capture only mean shifts and fail to reflect how treatments alter the topological structure of outcome distributions—such as multimodality. This work introduces persistent homology into causal inference for the first time, proposing topological causal effects (topological ATE/CATE). Under a persistent homology ignorability assumption, it establishes identifiability theory for these effects and clarifies the distinction between marginal and conditional topological effects. Experiments demonstrate that when the mean remains unchanged but the distribution’s topology undergoes significant transformation, the proposed method successfully identifies and recovers causal signals that conventional approaches miss.
Technology Category
Application Category
📝 Abstract
Average treatment effects (ATE) and conditional average treatment effects (CATE) are foundational causal estimands, but they target changes in expected outcomes and can miss treatment-induced changes in the shape of outcome distributions. A canonical failure mode occurs when control outcomes are unimodal, treated outcomes become bimodal, and both distributions have the same mean. In such cases mean-based causal estimands are zero even though the geometry and topology of the outcome law change substantially. This paper develops a topological causal framework based on persistent homology. We formalize a persistent-homology ignorability condition, define topological analogues of CATE and ATE, and prove that these estimands are identifiable up to an explicit error bound under approximate topological ignorability. We also clarify a subtle but important point: a marginal persistence-diagram effect is not identified from conditional topological ignorability alone because persistent homology does not in general commute with mixtures over covariates. To preserve the original intuition while ensuring scientific correctness, we retain the marginal effect as a motivating quantity, but place the mathematically sound conditional estimands at the center of the theory. A synthetic experiment with mean-preserving topology change shows that mean-based causal estimands remain near zero while the proposed topological effect increases sharply and remains recoverable after adjustment for confounding.
Problem
Research questions and friction points this paper is trying to address.
causal inference
persistent homology
topological data analysis
treatment effect
distributional shape
Innovation
Methods, ideas, or system contributions that make the work stand out.
persistent homology
topological causal inference
causal identifiability
treatment effect
distributional shape
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