THAP: A Matlab Toolkit for Learning with Hawkes Processes (1708.09252v1)

Abstract: As a powerful tool of asynchronous event sequence analysis, point processes have been studied for a long time and achieved numerous successes in different fields. Among various point process models, Hawkes process and its variants attract many researchers in statistics and computer science these years because they capture the self- and mutually-triggering patterns between different events in complicated sequences explicitly and quantitatively and are broadly applicable to many practical problems. In this paper, we describe an open-source toolkit implementing many learning algorithms and analysis tools for Hawkes process model and its variants. Our toolkit systematically summarizes recent state-of-the-art algorithms as well as most classic algorithms of Hawkes processes, which is beneficial for both academical education and research. Source code can be downloaded from https://github.com/HongtengXu/Hawkes-Process-Toolkit.

• The paper introduces THAP as an open-source Matlab toolkit integrating classical and state-of-the-art algorithms for learning Hawkes processes.
• It supports robust data handling, simulation techniques, and both parametric and nonparametric modeling methods for event sequences.
• Additionally, THAP enables advanced analysis such as Granger causality and clustering, facilitating deeper insights in diverse research domains.

Overview of "THAP: A Matlab Toolkit for Learning with Hawkes Processes"

The paper, "THAP: A Matlab Toolkit for Learning with Hawkes Processes" by Hongteng Xu and Hongyuan Zha, addresses a significant gap in the available toolkit resources for Hawkes processes, specifically through their initiative to develop THAP, a Matlab-based open-source toolkit. Hawkes processes, as a subset of point processes, have gained attention for their ability to model self- and mutually-triggering patterns prevalent in complex asynchronous event sequences. These sequences are observed in various domains like financial markets, social networks, and bioinformatics, underscoring the applicability of Hawkes processes across multiple research fields.

Contributions and Implementation

The primary contribution of this paper is the development of THAP, which integrates both state-of-the-art and classical algorithms for learning with Hawkes processes. The toolkit is structured to provide a comprehensive framework encompassing data handling, simulation, modeling, analysis, and visualization.

1. Data Handling and Simulation: THAP supports importing and preprocessing of real-world datasets, with capabilities for conversion into formats suitable for Matlab operations. It also provides three methods for simulating synthetic data, including branch clustering and thinning methods tailored for Hawkes processes.
2. Modeling and Learning Algorithms: The toolkit accommodates both parametric and nonparametric Hawkes process models. Parametric approaches include models with predefined impact functions (e.g., exponential), whereas nonparametric models use arbitrary impact functions that may be represented using basis functions or discretized points. THAP applies learning methods such as maximum likelihood estimation (MLE) and its combination with ordinary differential equations (ODE) solvers for parameter estimation.
3. Advanced Analysis Tools: A noteworthy feature of THAP is its inclusion of Granger causality analysis to map triggering patterns in multi-dimensional Hawkes processes. Additionally, clustering analysis methods are integrated, allowing the classification of event sequences either through a mixture model approach or by employing distance metrics.
4. Visualization: The toolkit’s user interface supports the visualization of event sequences, learned impact functions, and analysis results, facilitating a better understanding and interpretation of the data.

Comparative Analysis

The paper provides a comparative review between THAP and existing toolkits in the field, such as R-hawkes, pyhawkes, PtPack, and tick. With comprehensive functionality covering a wide array of learning and simulation methods, THAP stands out due to its extensive feature set and capability to perform advanced analytical tasks previously unavailable in similar toolkits.

Implications and Future Prospects

The development of THAP significantly enhances the research and educational landscape for point processes by filling the existing void with a Matlab-based, extensible toolkit. It facilitates fair comparisons across different algorithms, supporting the improvement of existing models and aiding the development of new techniques. Looking forward, the paper suggests expanding THAP’s functionalities to incorporate novel Hawkes process models, thus promoting further exploration and innovation in this domain.

In summary, THAP serves as a vital tool for both academic research and practical applications, enabling a more profound understanding and utilization of Hawkes processes. The paper succeeds in detailing a solid foundation for researchers aiming to leverage the intricate capabilities of Hawkes processes in their respective fields, fostering developments that could lead to significant advancements in the analytical processing of event sequences.