  It is always a challenging problem to deliver a huge volume of videos over
the Internet. To meet the high bandwidth and stringent playback demand, one
feasible solution is to cache video contents on edge servers based on predicted
video popularity. Traditional caching algorithms (e.g., LRU, LFU) are too
simple to capture the dynamics of video popularity, especially long-tailed
videos. Recent learning-driven caching algorithms (e.g., DeepCache) show
promising performance, however, such black-box approaches are lack of
explainability and interpretability. Moreover, the parameter tuning requires a
large number of historical records, which are difficult to obtain for videos
with low popularity. In this paper, we optimize video caching at the edge using
a white-box approach, which is highly efficient and also completely
explainable. To accurately capture the evolution of video popularity, we
develop a mathematical model called \emph{HRS} model, which is the combination
of multiple point processes, including Hawkes' self-exciting, reactive and
self-correcting processes. The key advantage of the HRS model is its
explainability, and much less number of model parameters. In addition, all its
model parameters can be learned automatically through maximizing the
Log-likelihood function constructed by past video request events. Next, we
further design an online HRS-based video caching algorithm. To verify its
effectiveness, we conduct a series of experiments using real video traces
collected from Tencent Video, one of the largest online video providers in
China. Experiment results demonstrate that our proposed algorithm outperforms
the state-of-the-art algorithms, with 12.3\% improvement on average in terms of
cache hit rate under realistic settings.
