Predicting the popularity of tweets using internal and external knowledge: an empirical Bayes type approach

Abstract

The problem of tweet popularity prediction, or forecasting the total number of retweets stemming from an ancestral tweet, has attracted considerable interest recently. The prediction can be accomplished by fitting a point process model to the sequence of retweet times up to a certain censoring time and project the fitted model to a future time point. However, models employing such approach tend to have inferior prediction accuracy when the censoring time is too short before sufficient information can accumulate. To overcome this, we propose an empirical Bayes type approach of parameter estimation to combine internal knowledge on the times of historical retweets up to the censoring time and external knowledge on complete retweet sequences in the training data. We demonstrate the approach using several point process models with finite-dimensional parameters, where the prior distribution for the parameter of each model is constructed based on the external knowledge, and the likelihood is calculated based on the internal knowledge. The mode of the posterior distribution is used as the estimator of the finite-dimensional parameter, and the mean of the predictive distribution for the number of retweets implied by each of the estimated models is used to predict the tweet popularity. Using a large Twitter data set, we reveal that the proposed methodology not only enables prediction at time zero before the arrival of any retweet event, but also substantially improves the prediction performances of existing models, especially at earlier censoring times.

Appendix

See Fig. 5.

Fig. 5

A summary of the procedures involved to obtain the empirical Bayes estimates. The final criterion function combines the knowledge internal and external to a retweet sequence, depending, respectively, on the current log-likelihood function and the log-prior density function. When the censoring time is at zero, the maximizer of the prior density function is ${\tilde{\eta }}^0$, and $e^{{\tilde{\eta }}^0}$ will be taken as the estimator of the tweet-specific model parameters