### Abstract

Knowing the extent of influence an agent exerts over the other agents over online social networks such as Twitter and Facebook is important as it helps identify opinion leaders and predict how opinions are likely to evolve. However, this information regarding the extent of influence exerted by agents on each other is difficult to obtain as it is unobservable and the data available to estimate it is scarce, often incomplete, and noisy. Further, the number of unknown parameters that need to be estimated to infer the extent of influence between any given pair of agents is very large. A particle-learning-based algorithm is proposed to estimate the influence matrix that indicates the extent of influence any agent exerts on any other in a social network. Computational studies have been used to determine the efficiency, learning rates and asymptotic properties, and robustness (to missing information) of the proposed particle learning algorithms. The results indicate that the proposed algorithm shows fast convergence rates, yields efficient estimates of the influence matrix, is scalable, and is robust to incomplete information. Further, the network topology, and not just the network size, impacts the learning rate. The learning rate also slows down as the percentage of missing information increases.

Original language | English (US) |
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Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Computational Statistics and Data Analysis |

Volume | 126 |

DOIs | |

State | Published - Oct 2018 |

### Keywords

- Influence estimation
- Learning
- Opinion dynamics
- Particle filter
- Social networks

### ASJC Scopus subject areas

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics