# Sublinear-Time Opinion Estimation in the Friedkin--Johnsen Model

arXiv: https://arxiv.org/abs/2404.16464 · HTML: https://mlsanity.com/paper/2404.16464/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2024.

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

- [Online Minimization of Polarization and Disagreement via Low-Rank Matrix Bandits](https://mlsanity.com/paper/2510.00803/) (2025)
- [Sublinear-Time Algorithms for Diagonally Dominant Systems and Applications to the Friedkin-Johnsen Model](https://mlsanity.com/paper/2509.13112/) (2025)

## Abstract (arXiv)

Online social networks are ubiquitous parts of modern societies and the discussions that take place in these networks impact people's opinions on diverse topics, such as politics or vaccination. One of the most popular models to formally describe this opinion formation process is the Friedkin--Johnsen (FJ) model, which allows to define measures, such as the polarization and the disagreement of a network. Recently, Xu, Bao and Zhang (WebConf'21) showed that all opinions and relevant measures in the FJ model can be approximated in near-linear time. However, their algorithm requires the entire network and the opinions of all nodes as input. Given the sheer size of online social networks and increasing data-access limitations, obtaining the entirety of this data might, however, be unrealistic in practice. In this paper, we show that node opinions and all relevant measures, like polarization and disagreement, can be efficiently approximated in time that is sublinear in the size of the network. Particularly, our algorithms only require query-access to the network and do not have to preprocess the graph. Furthermore, we use a connection between FJ opinion dynamics and personalized PageRank, and show that in d-regular graphs, we can deterministically approximate each node's opinion by only looking at a constant-size neighborhood, independently of the network size. We also experimentally validate that our estimation algorithms perform well in practice.