On the choice of functionals obtained from the predictive distribution of future retweet counts

Abstract

The prediction of future retweet counts for tweets shared on Twitter has been a topic of immense interest recently. Numerous models have been proposed for such prediction, with their accuracy being assessed using certain choices of evaluation metrics. Admittedly, the majority of predictive models involved have overlooked the problem on the use of theoretically optimal functionals as point predictions and resort to employing options which are more accessible like the predictive mean. This motivates our discussion wherein the practicality of using theoretically consistent functionals with respect to the evaluation metrics considered is put forth. We discuss how the median of order (–1) and harmonic median are optimal in theory relative to the mean and median absolute percentage errors respectively, followed by highlighting in contrast how predictive models extant in the literature may suggest otherwise. Specifically, using a Poisson model supported by a large corpus of Twitter data, our numerical experiments indicate that predictions based on different functionals derived from the predictive distribution do not vary materially across the different metrics used, although predictions stemming from the predictive mean are slightly yet consistently more accurate than those based on the other functionals. We further outline how consistent functionals can be obtained accordingly under the settings of more complex predictive models.