How Your Friends Influence You: Quantifying Pairwise Influences on Twitter

The micro-blogging service, Twitter has emerged as a new medium for sharing and spreading information and ideas. To understand the diffusion process of the information on Twitter, it is very important to know how people influence each other. The retweet action is considered as the intuitive evidence for influence that has occurred, so we regard the retweet probability as the standard to measure the pair wise influence in Twitter. Though the retweet probability can be estimated according to the statistics of log data, the data are sometimes unavailable or insufficient, which may cause inaccurate estimation. In this paper a retweet probability estimation model based on Bayesian theory is proposed. We assign each follow relationship a dummy retweet number as a prior assumption, and then we integrate this prior retweet probability distribution with the observed retweet log data into a Bayesian maximum a posteriori framework. Based on a real data set from Sina Weibo, we show that a Bayesian model esitimates the pair wise retweet probability more accurately than a maximum likelihood estimator. Also, we produce three influencer ranking lists from three pair wise influence estimation models, and verify that the Bayesian model is a comprehensive influence quantifying model, which can integrate the significance of both popularity and propagation force of users.