# Inferring Individual Direct Causal Effects Under Heterogeneous Peer Influence

arXiv: https://arxiv.org/abs/2305.17479 · HTML: https://mlsanity.com/paper/2305.17479/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 65 references that are in the map.
- First posted on arXiv 27 May 2023.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (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)
- [Graph cluster randomization: network exposure to multiple universes](https://mlsanity.com/paper/1305.6979/) (2013)
- [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)
- [Causal Diagrams for Interference](https://mlsanity.com/paper/1403.1239/) (2014)
- [Causal Network Motifs: Identifying Heterogeneous Spillover Effects in A/B Tests](https://mlsanity.com/paper/2010.09911/) (2020)
- [Causal inference with misspecified exposure mappings: separating definitions and assumptions](https://mlsanity.com/paper/2103.06471/) (2021)
- [Causal Relational Learning](https://mlsanity.com/paper/2004.03644/) (2020)
- [A Sound and Complete Algorithm for Learning Causal Models from Relational Data](https://mlsanity.com/paper/1309.6843/) (2013)
- [Learning Individual Treatment Effects under Heterogeneous Interference in Networks](https://mlsanity.com/paper/2210.14080/) (2022)
- [Causal inference, social networks, and chain graphs](https://mlsanity.com/paper/1812.04990/) (2018)
- [Heterogeneous Treatment and Spillover Effects under Clustered Network Interference](https://mlsanity.com/paper/2008.00707/) (2020)
- [Using Embeddings for Causal Estimation of Peer Influence in Social Networks](https://mlsanity.com/paper/2205.08033/) (2022)
- [Towards Robust Relational Causal Discovery](https://mlsanity.com/paper/1912.02390/) (2019)
- [Causal Inference in the Presence of Interference in Sponsored Search Advertising](https://mlsanity.com/paper/2010.07458/) (2020)
- [Lifted Representation of Relational Causal Models Revisited: Implications for Reasoning and Structure Learning](https://mlsanity.com/paper/1508.02103/) (2015)
- [Heterogeneous Peer Effects in the Linear Threshold Model](https://mlsanity.com/paper/2201.11242/) (2022)
- [Modeling Interference Via Symmetric Treatment Decomposition](https://mlsanity.com/paper/1709.01050/) (2017)
- [Heterogeneous Treatment Effects in Social Networks](https://mlsanity.com/paper/2105.10591/) (2021)

## Built on by (most cited first, 5 of 5)

- [Learning Exposure Mapping Functions for Inferring Heterogeneous Peer Effects](https://mlsanity.com/paper/2503.01722/) (2025)
- [Estimating Treatment Effects in Networks under Unknown Exposure Mappings](https://mlsanity.com/paper/2510.21457/) (2025)
- [Causal Inference on Networks under Misspecified Exposure Mappings: A Partial Identification Framework](https://mlsanity.com/paper/2602.03459/) (2026)
- [Are Heterogeneous Graph Neural Networks Truly Effective for Node Classification? A Causal Perspective](https://mlsanity.com/paper/2510.05750/) (2025)
- [Treatment Effect Estimation with Differentiated Networked Effect on Graph Data](https://mlsanity.com/paper/2605.24358/) (2026)

## Abstract (arXiv)

Causal inference in networks should account for interference, which occurs when a unit's outcome is influenced by treatments or outcomes of peers. Heterogeneous peer influence (HPI) occurs when a unit's outcome is influenced differently by different peers based on their attributes and relationships, or when each unit has a different susceptibility to peer influence. Existing solutions to estimating direct causal effects under interference consider either homogeneous influence from peers or specific heterogeneous influence mechanisms (e.g., based on local neighborhood structure). This paper presents a methodology for estimating individual direct causal effects in the presence of HPI where the mechanism of influence is not known a priori. We propose a structural causal model for networks that can capture different possible assumptions about network structure, interference conditions, and causal dependence and enables reasoning about identifiability in the presence of HPI. We find potential heterogeneous contexts using the causal model and propose a novel graph neural network-based estimator to estimate individual direct causal effects. We show that state-of-the-art methods for individual direct effect estimation produce biased results in the presence of HPI, and that our proposed estimator is robust.