A Tutorial on Hawkes Processes for Events in Social Media (1708.06401v2)

Abstract: 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 the key concepts in point processes. We then introduce the Hawkes process, 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 presents a design of the memory kernel, and results on estimating parameters and predicting popularity. The code and sample event data are available as an online appendix

• The paper introduces Hawkes processes and demonstrates their use in modeling self-exciting event cascades on social media platforms.
• It details parameter estimation methods, including maximum likelihood and simulation via the thinning algorithm, to analyze real-world data.
• The work bridges theory and practice by offering practical insights into user interaction dynamics and predicting retweet cascades.

Review of "A Tutorial on Hawkes Processes for Events in Social Media"

In the chapter titled "A Tutorial on Hawkes Processes for Events in Social Media," the authors deliver a comprehensive introduction to Hawkes processes and their application in modeling discrete events, particularly in the field of social media. This work is structured to facilitate both theoretical understanding and practical implementation, addressing an audience of aspiring researchers, graduate students, and technically oriented readers with a vested interest in point processes and their practical applications.

Overview of Point Processes and Hawkes Processes

The chapter begins with an exploration of point processes, which are mathematical models for random events occurring over continuous time. The authors provide foundational knowledge of Poisson processes, including both homogeneous and non-homogeneous variants. This serves as the groundwork for introducing the more complex Hawkes processes, noted for their self-exciting properties. These processes are particularly effective for modeling scenarios where one event can increase the probability of subsequent events, a property that is critical for understanding dynamics such as earthquake aftershocks or, as emphasized in this paper, social media event cascades.

Hawkes Processes in Social Media Modeling

Focusing on social media contexts, the authors use Hawkes processes to model retweet cascades on platforms like Twitter. The goal is to understand and predict information diffusion patterns, encapsulating the influence of user interactions. A marked Hawkes process is employed, where event marks represent user influence, allowing for event intensity to be dependent on both time and social factors such as user popularity.

The formation of the Hawkes process for this application involves crafting the kernel function to reflect social dynamics accurately. The authors propose a power-law kernel with specific parameters tailored to capture the diffusion slowdown over time and the inherent virality of content. This choice reflects a realistic modeling of how information propagation diminishes as the novelty of content fades.

Parameter Estimation and Simulation

The authors provide detailed methodologies for simulating events and estimating parameters within the Hawkes framework. The chapter outlines the thinning algorithm and an efficient exponential kernel simulation method. Parameter estimation leveraging maximum likelihood is discussed, focusing on real-world social media data to fine-tune the model parameters. This section is crucial for researchers interested in applying these mathematical theories to real data sets.

Numerical Implications and Practical Applications

Numerically, the authors deal with computational challenges inherent in processing large social media data sets, such as optimizing the evaluation of the likelihood function and addressing potential edge effects and local maxima in parameter estimation. The practical example given, which involves predicting the eventual size of a Twitter retweet cascade, reinforces the real-world applicability of these methods.

Conclusion and Future Directions

The paper succeeds in bridging the gap between abstract mathematical models and practical applications in social media. It provides both the theoretical underpinnings necessary for understanding Hawkes processes and practical guidance on implementing these concepts with real-world data. The authors acknowledge areas for further research, such as exploring alternative inference techniques, multi-variate extensions, and doubly stochastic processes. These avenues suggest a rich field for future exploration, particularly as social media dynamics continue to evolve.

In sum, this work serves as both a tutorial and a springboard for broader investigations, equipping researchers with a robust toolkit for modeling and analyzing event-driven data in complex social systems.