# Topological Causal Effects

arXiv: https://arxiv.org/abs/2603.02289 · HTML: https://mlsanity.com/paper/2603.02289/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Builds on (most cited first, 16 of 16)

- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Semiparametric counterfactual density estimation](https://mlsanity.com/paper/2102.12034/) (2021)
- [Nonparametric causal effects based on incremental propensity score interventions](https://mlsanity.com/paper/1704.00211/) (2017)
- [Sharp instruments for classifying compliers and generalizing causal effects](https://mlsanity.com/paper/1801.03635/) (2018)
- [Using persistent homology and dynamical distances to analyze protein binding](https://mlsanity.com/paper/1412.1394/) (2014)
- [The importance of the whole: topological data analysis for the network neuroscientist](https://mlsanity.com/paper/1806.05167/) (2018)
- [Causal inference with a functional outcome](https://mlsanity.com/paper/2304.07113/) (2023)
- [A Short Survey of Topological Data Analysis in Time Series and Systems Analysis](https://mlsanity.com/paper/1809.10745/) (2018)
- [Doubly-Robust Functional Average Treatment Effect Estimation](https://mlsanity.com/paper/2501.06024/) (2025)
- [Fast and Fair Simultaneous Confidence Bands for Functional Parameters](https://mlsanity.com/paper/1910.00131/) (2019)
- [Classification of COVID-19 via Homology of CT-SCAN](https://mlsanity.com/paper/2102.10593/) (2021)

## Built on by (most cited first, 3 of 3)

- [Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability](https://mlsanity.com/paper/2603.14169/) (2026)
- [A Mathematical Framework for Topological Causal Data Analysis](https://mlsanity.com/paper/2607.28161/) (2026)
- [Topological Ignorability for Structural Causal Effects Beyond Means](https://mlsanity.com/paper/2606.01184/) (2026)

## 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.