# Estimating Heterogeneous Causal Effect on Networks via Orthogonal Learning

arXiv: https://arxiv.org/abs/2509.18484 · HTML: https://mlsanity.com/paper/2509.18484/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalization and Representational Limits of Graph Neural Networks](https://mlsanity.com/paper/2002.06157/) (2020)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Learning Individual Causal Effects from Networked Observational Data](https://mlsanity.com/paper/1906.03485/) (2019)
- [Identification and estimation of treatment and interference effects in observational studies on networks](https://mlsanity.com/paper/1609.06245/) (2016)
- [Towards Understanding the Generalization of Graph Neural Networks](https://mlsanity.com/paper/2305.08048/) (2023)
- [Causal Inference under Networked Interference and Intervention Policy Enhancement](https://mlsanity.com/paper/2002.08506/) (2020)
- [Causal inference for social network data](https://mlsanity.com/paper/1705.08527/) (2017)
- [Learning Causal Effects on Hypergraphs](https://mlsanity.com/paper/2207.04049/) (2022)
- [Validating Causal Inference Methods](https://mlsanity.com/paper/2202.04208/) (2022)
- [Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning](https://mlsanity.com/paper/2405.03342/) (2024)
- [Survey on Generalization Theory for Graph Neural Networks](https://mlsanity.com/paper/2503.15650/) (2025)
- [Learning Individual Treatment Effects under Heterogeneous Interference in Networks](https://mlsanity.com/paper/2210.14080/) (2022)
- [Heterogeneous Treatment and Spillover Effects under Clustered Network Interference](https://mlsanity.com/paper/2008.00707/) (2020)
- [Covering Numbers for Deep ReLU Networks with Applications to Function Approximation and Nonparametric Regression](https://mlsanity.com/paper/2410.06378/) (2024)
- [Using Embeddings for Causal Estimation of Peer Influence in Social Networks](https://mlsanity.com/paper/2205.08033/) (2022)
- [Adjusting for Unmeasured Spatial Confounding with Distance Adjusted Propensity Score Matching](https://mlsanity.com/paper/1610.07583/) (2016)
- [Estimating Treatment Effects Under Heterogeneous Interference](https://mlsanity.com/paper/2309.13884/) (2023)
- [Graph Machine Learning based Doubly Robust Estimator for Network Causal Effects](https://mlsanity.com/paper/2403.11332/) (2024)
- [Model-Based Regression Adjustment with Model-Free Covariates for Network Interference](https://mlsanity.com/paper/2302.04997/) (2023)

## Built on by (most cited first, 1 of 1)

- [Are Heterogeneous Graph Neural Networks Truly Effective for Node Classification? A Causal Perspective](https://mlsanity.com/paper/2510.05750/) (2025)

## Abstract (arXiv)

Estimating causal effects on networks is challenging because treatments may affect both treated units and their neighbors, while network homophily induces dependence and confounding. These challenges are amplified when causal effects are heterogeneous across units and edges. We propose a two-stage orthogonal learning framework for estimating heterogeneous direct and spillover effects on networks. The first stage uses graph neural networks to estimate nuisance components that capture complex dependence on covariates and network structure. The second stage residualizes these nuisance components and estimates causal effects through an interpretable attention-based interference model, yielding edge-level spillover estimates as well as node- and population-level summaries. Neyman orthogonalization and cross-fitting reduce sensitivity to first-stage estimation error, so nuisance errors enter only at higher order. We further develop a bootstrap-based uncertainty quantification procedure for the estimated spillover matrix, enabling pointwise and simultaneous inference for heterogeneous edge- and node-level effects. Experiments show that our method improves heterogeneous effect estimation while supporting interpretable downstream analyses such as influential-neighbor detection and spillover-sign recovery.