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Nearly assumptionless screening for the mutually-exciting multivariate Hawkes process.

Shizhe Chen1, Daniela Witten2, Ali Shojaie2

  • 1Department of Statistics, Columbia University, New York, NY 10027.

Electronic Journal of Statistics
|August 29, 2017
PubMed
Summary

We introduce a new edge screening method for learning the structure of mutually-exciting multivariate Hawkes processes. This computationally inexpensive approach efficiently identifies potential graph edges in high-dimensional data.

Keywords:
62H12Hawkes processPrimary 60G55high-dimensionalityscreeningsecondary 62M10

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Area of Science:

  • Computational statistics
  • Network analysis
  • Time series analysis

Background:

  • Learning graph structures is crucial for understanding complex systems.
  • High-dimensional data presents challenges for traditional network inference methods.
  • Multivariate Hawkes processes model self- and mutually-exciting event data.

Purpose of the Study:

  • To develop an efficient method for learning graph structures in high-dimensional Hawkes processes.
  • To propose a computationally inexpensive edge screening approach.
  • To ensure the proposed method possesses a sure screening property.

Main Methods:

  • An edge screening technique is proposed for graph structure learning.
  • The method is applied to mutually-exciting multivariate Hawkes processes.
  • Theoretical properties, including the sure screening property, are analyzed.

Main Results:

  • The edge screening approach is computationally inexpensive.
  • It achieves the sure screening property with high probability, identifying a superset of true edges.
  • The screened edge set is demonstrated to be relatively small.

Conclusions:

  • The proposed edge screening method is effective for high-dimensional Hawkes process graph learning.
  • It offers a computationally efficient alternative to existing methods.
  • Simulation studies validate the performance of the edge screening approach.