# Learning Exposure Mapping Functions for Inferring Heterogeneous Peer Effects

arXiv: https://arxiv.org/abs/2503.01722 · HTML: https://mlsanity.com/paper/2503.01722/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Can Graph Neural Networks Count Substructures?](https://mlsanity.com/paper/2002.04025/) (2020)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [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)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning](https://mlsanity.com/paper/2405.03342/) (2024)
- [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)
- [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)
- [Generalization bound for estimating causal effects from observational network data](https://mlsanity.com/paper/2308.04011/) (2023)
- [Causal Effect Variational Autoencoder with Uniform Treatment](https://mlsanity.com/paper/2111.08656/) (2021)
- [Estimating Treatment Effects Under Heterogeneous Interference](https://mlsanity.com/paper/2309.13884/) (2023)
- [Causal Inference in the Presence of Interference in Sponsored Search Advertising](https://mlsanity.com/paper/2010.07458/) (2020)
- [Heterogeneous Peer Effects in the Linear Threshold Model](https://mlsanity.com/paper/2201.11242/) (2022)
- [Inferring Individual Direct Causal Effects Under Heterogeneous Peer Influence](https://mlsanity.com/paper/2305.17479/) (2023)
- [Graph Machine Learning based Doubly Robust Estimator for Network Causal Effects](https://mlsanity.com/paper/2403.11332/) (2024)
- [Causal Inference from Observational Studies with Clustered Interference](https://mlsanity.com/paper/1711.04834/) (2017)
- [Exposure effects are not automatically useful for policymaking](https://mlsanity.com/paper/2401.06264/) (2024)

## Built on by (most cited first, 2 of 2)

- [Graph-Dependent Regret Bounds in Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2503.07555/) (2025)
- [Peer Effects in Signed Networks: Separating Influence Through Positive and Negative Ties](https://mlsanity.com/paper/2610.02872/) (2026)

## Abstract (arXiv)

In causal inference, interference refers to the phenomenon in which the actions of peers in a network can influence an individual's outcome. Peer effect refers to the difference in counterfactual outcomes of an individual for different levels of peer exposure, the extent to which an individual is exposed to the treatments, actions, or behaviors of peers. Estimating peer effects requires deciding how to represent peer exposure. Typically, researchers define an exposure mapping function that aggregates peer treatments and outputs peer exposure. Most existing approaches for defining exposure mapping functions assume peer exposure based on the number or fraction of treated peers. Recent studies have investigated more complex functions of peer exposure which capture that different peers can exert different degrees of influence. However, none of these works have explicitly considered the problem of automatically learning the exposure mapping function. In this work, we focus on learning this function for the purpose of estimating heterogeneous peer effects, where heterogeneity refers to the variation in counterfactual outcomes for the same peer exposure but different individual's contexts. We develop EgoNetGNN, a graph neural network (GNN)-based method, to automatically learn the appropriate exposure mapping function allowing for complex peer influence mechanisms that, in addition to peer treatments, can involve the local neighborhood structure and edge attributes. We show that GNN models that use peer exposure based on the number or fraction of treated peers or learn peer exposure naively face difficulty accounting for such influence mechanisms. Our comprehensive evaluation on synthetic and semi-synthetic network data shows that our method is more robust to different unknown underlying influence mechanisms when estimating heterogeneous peer effects when compared to state-of-the-art baselines.