Hawkes Process with Flexible Triggering Kernels.

Area of Science:

• Computational Statistics
• Machine Learning
• Point Processes

Background:

• Transformer-inspired models for Hawkes processes offer improved prediction but suffer from high computational complexity.
• Existing models struggle to adequately capture the triggering function inherent in point processes.

Purpose of the Study:

• To develop an efficient and general method for encoding historical event sequences in Hawkes process modeling.
• To address the limitations of high computational cost and inadequate triggering function capture in current transformer-based models.

Main Methods:

• Replaced complex attention structures with triggering kernels derived from observed data.
• Incorporated a sigmoid gating mechanism into the triggering function estimator for local-in-time effects.
• Learned type-time kernel parameters using event type representations and temporal embeddings.

Main Results:

• The proposed model demonstrates superior performance compared to existing approaches on synthetic and real-world datasets.
• Achieved significant improvements in computational efficiency and reduced memory complexity.
• Provided interpretable results through the direct application of the novel triggering kernel.

Conclusions:

• The new Hawkes process model offers an efficient and effective alternative to transformer-based architectures.
• The use of triggering kernels with sigmoid gating enhances the modeling of temporal dependencies and event triggering.
• The model's interpretability and performance make it suitable for various applications, including epidemiological data analysis.