Hawkes Processes With Stochastic Exogenous Effects for Continuous-Time Interaction Modelling.

Area of Science:

• Data Science
• Network Analysis
• Statistical Modeling

Background:

• Continuous-time interaction data often arises in dynamic environments.
• Hawkes processes (HP) are standard for analyzing such data.
• Existing HP models typically assume a constant background interaction rate, limiting their ability to capture temporal evolution.

Purpose of the Study:

• To introduce a novel Hawkes process model capable of learning time variations in the exogenous rate.
• To address the limitations of current models in handling complex time-evolution in background rates.
• To develop a method that accurately describes dynamic interaction patterns.

Main Methods:

• Introduced the stochastic exogenous rate Hawkes process (SE-HP).
• Affiliated nodes with piecewise-constant membership distributions and unknown changepoint locations.
• Derived time-varying background rate functions from membership functions.
• Developed a stochastic gradient MCMC algorithm for scalable inference.

Main Results:

• The SE-HP model successfully learns time variations in the exogenous rate.
• The model's performance was evaluated on real-world, continuous-time interaction datasets.
• SE-HP demonstrated superior performance compared to state-of-the-art methods.

Conclusions:

• The proposed SE-HP model offers a significant advancement in analyzing time-evolving interaction data.
• The method accurately captures complex temporal dynamics in background interaction rates.
• SE-HP provides a more robust and accurate approach for network analysis in dynamic environments.