Hawkes processes for events in social media

This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and key concepts in point processes. We then introduce the Hawkes process and its event intensity function, as well as schemes for event simulation and parameter estimation. We also describe a practical example drawn from social media data---we show how to model retweet cascades using a Hawkes self-exciting process.We present a design of the memory kernel, and results on estimating parameters and predicting popularity. The code and sample event data are available in an online repository.