# Heterogeneous Peer Effects in the Linear Threshold Model

arXiv: https://arxiv.org/abs/2201.11242 · HTML: https://mlsanity.com/paper/2201.11242/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 27 Jan 2022.

## Builds on (most cited first, 13 of 13)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [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)
- [Characterizing and Detecting Hateful Users on Twitter](https://mlsanity.com/paper/1803.08977/) (2018)
- [Empath: Understanding Topic Signals in Large-Scale Text](https://mlsanity.com/paper/1602.06979/) (2016)
- [Using Embeddings to Correct for Unobserved Confounding in Networks](https://mlsanity.com/paper/1902.04114/) (2019)
- [Causal Inference Under Interference And Network Uncertainty](https://mlsanity.com/paper/1907.00221/) (2019)
- [The Anatomy of a Scientific Rumor](https://mlsanity.com/paper/1301.2952/) (2013)
- [Causal Diagrams for Interference](https://mlsanity.com/paper/1403.1239/) (2014)
- [Minimizing Interference and Selection Bias in Network Experiment Design](https://mlsanity.com/paper/2004.07225/) (2020)
- [Learning Triggers for Heterogeneous Treatment Effects](https://mlsanity.com/paper/1902.00087/) (2019)
- [Detecting Social Influence in Event Cascades by Comparing Discriminative Rankers](https://mlsanity.com/paper/1802.06138/) (2018)
- [The Opacity Problem in Social Contagion](https://mlsanity.com/paper/1702.02700/) (2017)

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

- [Inferring Individual Direct Causal Effects Under Heterogeneous Peer Influence](https://mlsanity.com/paper/2305.17479/) (2023)
- [Optimizing Treatment Allocation in the Presence of Interference](https://mlsanity.com/paper/2410.00075/) (2024)
- [Learning Exposure Mapping Functions for Inferring Heterogeneous Peer Effects](https://mlsanity.com/paper/2503.01722/) (2025)
- [Data-Driven Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2301.06615/) (2023)
- [Treatment-Aware Hyperbolic Representation Learning for Causal Effect Estimation with Social Networks](https://mlsanity.com/paper/2401.06557/) (2024)

## Abstract (arXiv)

The Linear Threshold Model is a widely used model that describes how information diffuses through a social network. According to this model, an individual adopts an idea or product after the proportion of their neighbors who have adopted it reaches a certain threshold. Typical applications of the Linear Threshold Model assume that thresholds are either the same for all network nodes or randomly distributed, even though some people may be more susceptible to peer pressure than others. To address individual-level differences, we propose causal inference methods for estimating individual thresholds that can more accurately predict whether and when individuals will be affected by their peers. We introduce the concept of heterogeneous peer effects and develop a Structural Causal Model which corresponds to the Linear Threshold Model and supports heterogeneous peer effect identification and estimation. We develop two algorithms for individual threshold estimation, one based on causal trees and one based on causal meta-learners. Our experimental results on synthetic and real-world datasets show that our proposed models can better predict individual-level thresholds in the Linear Threshold Model and thus more precisely predict which nodes will get activated over time.