# Contagion Effect Estimation Using Proximal Embeddings

arXiv: https://arxiv.org/abs/2306.02479 · HTML: https://mlsanity.com/paper/2306.02479/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 82 references that are in the map.
- First posted on arXiv 4 Jun 2023.

## Builds on (most cited first, 30 of 30)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Unsupervised Learning of 3D Structure from Images](https://mlsanity.com/paper/1607.00662/) (2016)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Learning Individual Causal Effects from Networked Observational Data](https://mlsanity.com/paper/1906.03485/) (2019)
- [Characterizing and Detecting Hateful Users on Twitter](https://mlsanity.com/paper/1803.08977/) (2018)
- [Counterfactual Representation Learning with Balancing Weights](https://mlsanity.com/paper/2010.12618/) (2020)
- [Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder](https://mlsanity.com/paper/2011.11878/) (2020)
- [Graph cluster randomization: network exposure to multiple universes](https://mlsanity.com/paper/1305.6979/) (2013)
- [Design and analysis of experiments in networks: Reducing bias from interference](https://mlsanity.com/paper/1404.7530/) (2014)
- [A confounding bridge approach for double negative control inference on causal effects](https://mlsanity.com/paper/1808.04945/) (2018)
- [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)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Fairness without the sensitive attribute via Causal Variational Autoencoder](https://mlsanity.com/paper/2109.04999/) (2021)
- [Causal Diagrams for Interference](https://mlsanity.com/paper/1403.1239/) (2014)
- [Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations](https://mlsanity.com/paper/1607.06565/) (2016)
- [Causal Effect Variational Autoencoder with Uniform Treatment](https://mlsanity.com/paper/2111.08656/) (2021)
- [Socio-Linguistic Characteristics of Coordinated Inauthentic Accounts](https://mlsanity.com/paper/2305.11867/) (2023)
- [Many Proxy Controls](https://mlsanity.com/paper/2110.03973/) (2021)
- [Identification and Estimation of Causal Peer Effects Using Double Negative Controls for Unmeasured Network Confounding](https://mlsanity.com/paper/2109.01933/) (2021)
- [Networks with Growth and Preferential Attachment: Modeling and Applications](https://mlsanity.com/paper/2007.01349/) (2020)
- [Understanding Stay-at-home Attitudes through Framing Analysis of Tweets](https://mlsanity.com/paper/2209.05729/) (2022)

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

- [Estimating Treatment Effects in Networks under Unknown Exposure Mappings](https://mlsanity.com/paper/2510.21457/) (2025)

## Abstract (arXiv)

Contagion effect refers to the causal effect of peers' behavior on the outcome of an individual in social networks. Contagion can be confounded due to latent homophily which makes contagion effect estimation very hard: nodes in a homophilic network tend to have ties to peers with similar attributes and can behave similarly without influencing one another. One way to account for latent homophily is by considering proxies for the unobserved confounders. However, as we demonstrate in this paper, existing proxy-based methods for contagion effect estimation have a very high variance when the proxies are high-dimensional. To address this issue, we introduce a novel framework, Proximal Embeddings (ProEmb), that integrates variational autoencoders with adversarial networks to create low-dimensional representations of high-dimensional proxies and help with identifying contagion effects. While VAEs have been used previously for representation learning in causal inference, a novel aspect of our approach is the additional component of adversarial networks to balance the representations of different treatment groups, which is essential in causal inference from observational data where these groups typically come from different distributions. We empirically show that our method significantly increases the accuracy and reduces the variance of contagion effect estimation in observational network data compared to state-of-the-art methods.