mlsanityData to 7 Oct 2026

Topological Causal Effects

arXiv 2603.02289 ↗First posted 2 Mar 2026stat.ME cs.LG stat.MLcited by 3

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Abstract (arXiv)

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.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 16 of its 43 references that are in the map. First posted on arXiv 2 Mar 2026.

Builds on

16 of 43 references.

References · 16

  1. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  2. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  3. 2017An introduction to Topological Data Analysis: fundamental and practical aspects for data scientistscited by 171
  4. 2022Semiparametric doubly robust targeted double machine learning: a reviewcited by 129
  5. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
  6. 2013Stochastic Convergence of Persistence Landscapes and Silhouettescited by 43
  7. 2021Semiparametric counterfactual density estimationcited by 42
  8. 2017Nonparametric causal effects based on incremental propensity score interventionscited by 28
  9. 2018Sharp instruments for classifying compliers and generalizing causal effectscited by 22
  10. 2014Using persistent homology and dynamical distances to analyze protein bindingcited by 15
  11. 2018The importance of the whole: topological data analysis for the network neuroscientistcited by 11
  12. 2023Causal inference with a functional outcomecited by 8
4 more
  1. 2018A Short Survey of Topological Data Analysis in Time Series and Systems Analysiscited by 4
  2. 2025Doubly-Robust Functional Average Treatment Effect Estimationcited by 4
  3. 2019Fast and Fair Simultaneous Confidence Bands for Functional Parameterscited by 3
  4. 2021Classification of COVID-19 via Homology of CT-SCANcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Beyond Means: Topological Causal Effects under Persistent-Homology Ignorabilitycited by 1
  2. 2026A Mathematical Framework for Topological Causal Data Analysiscited by 1
  3. 2026Topological Ignorability for Structural Causal Effects Beyond Meanscited by 0