# Using Embeddings for Causal Estimation of Peer Influence in Social Networks

arXiv: https://arxiv.org/abs/2205.08033 · HTML: https://mlsanity.com/paper/2205.08033/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 17 May 2022.

## Builds on (most cited first, 20 of 20)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Deep Learning on Graphs: A Survey](https://mlsanity.com/paper/1812.04202/) (2018)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [A Review of Stochastic Block Models and Extensions for Graph Clustering](https://mlsanity.com/paper/1903.00114/) (2019)
- [Causal inference for social network data](https://mlsanity.com/paper/1705.08527/) (2017)
- [Using Embeddings to Correct for Unobserved Confounding in Networks](https://mlsanity.com/paper/1902.04114/) (2019)
- [Sparse graphs using exchangeable random measures](https://mlsanity.com/paper/1401.1137/) (2014)
- [Auto-G-Computation of Causal Effects on a Network](https://mlsanity.com/paper/1709.01577/) (2017)
- [Asymptotics of Network Embeddings Learned via Subsampling](https://mlsanity.com/paper/2107.02363/) (2021)
- [Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations](https://mlsanity.com/paper/1607.06565/) (2016)
- [Minimizing Interference and Selection Bias in Network Experiment Design](https://mlsanity.com/paper/2004.07225/) (2020)
- [Bias and high-dimensional adjustment in observational studies of peer effects](https://mlsanity.com/paper/1706.04692/) (2017)
- [Counterfactual Evaluation of Treatment Assignment Functions with Networked Observational Data](https://mlsanity.com/paper/1912.10536/) (2019)
- [Estimating Social Influence from Observational Data](https://mlsanity.com/paper/2204.01633/) (2022)
- [Properties of Latent Variable Network Models](https://mlsanity.com/paper/1506.07806/) (2015)
- [Empirical Risk Minimization and Stochastic Gradient Descent for Relational Data](https://mlsanity.com/paper/1806.10701/) (2018)
- [Edge-exchangeable graphs and sparsity (NIPS 2016)](https://mlsanity.com/paper/1612.05519/) (2016)
- [Identification and Estimation of Causal Peer Effects Using Double Negative Controls for Unmeasured Network Confounding](https://mlsanity.com/paper/2109.01933/) (2021)

## Built on by (most cited first, 9 of 9)

- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Learning Individual Treatment Effects under Heterogeneous Interference in Networks](https://mlsanity.com/paper/2210.14080/) (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)
- [Uplift Modeling Under Limited Supervision](https://mlsanity.com/paper/2403.19289/) (2024)
- [Estimating Heterogeneous Causal Effect on Networks via Orthogonal Learning](https://mlsanity.com/paper/2509.18484/) (2025)
- [SphUnc: Hyperspherical Uncertainty Decomposition and Causal Identification via Information Geometry](https://mlsanity.com/paper/2603.01168/) (2026)
- [Limits to Predicting Online Speech Using Large Language Models](https://mlsanity.com/paper/2407.12850/) (2024)
- [Population-Scale Network Embeddings Expose Educational Divides in Network Structure Related to Right-Wing Populist Voting](https://mlsanity.com/paper/2508.21236/) (2025)

## Abstract (arXiv)

We address the problem of using observational data to estimate peer contagion effects, the influence of treatments applied to individuals in a network on the outcomes of their neighbors. A main challenge to such estimation is that homophily - the tendency of connected units to share similar latent traits - acts as an unobserved confounder for contagion effects. Informally, it's hard to tell whether your friends have similar outcomes because they were influenced by your treatment, or whether it's due to some common trait that caused you to be friends in the first place. Because these common causes are not usually directly observed, they cannot be simply adjusted for. We describe an approach to perform the required adjustment using node embeddings learned from the network itself. The main aim is to perform this adjustment nonparametrically, without functional form assumptions on either the process that generated the network or the treatment assignment and outcome processes. The key contributions are to nonparametrically formalize the causal effect in a way that accounts for homophily, and to show how embedding methods can be used to identify and estimate this effect. Code is available at https://github.com/IrinaCristali/Peer-Contagion-on-Networks.