THPs: Topological Hawkes Processes for Learning Causal Structure on Event Sequences.

Area of Science:

• Data Science
• Network Science
• Causal Inference

Background:

• Learning causal structure from event sequences is challenging.
• Existing methods like Multivariate Hawkes Processes often overlook topological dependencies.
• Real-world event data frequently exhibits network structures influencing event occurrences.

Purpose of the Study:

• To propose a novel Topological Hawkes Process (THP) that integrates graph and temporal convolutions.
• To develop a robust causal structure learning method for THP within a likelihood framework.
• To address the limitations of independent sequence assumptions in existing event sequence models.

Main Methods:

• Developed the Topological Hawkes Process (THP) by connecting graph convolution and temporal convolution.
• Proposed a causal structure learning method based on the graph convolution-enhanced likelihood function of THP.
• Employed a sparse optimization scheme with Expectation-Maximization for likelihood optimization.

Main Results:

• Demonstrated the effectiveness of THP in capturing topological dependencies in event sequences.
• The proposed causal structure learning method showed superior performance on synthetic and real-world datasets.
• Successfully integrated graph convolution into the likelihood framework for improved causal inference.

Conclusions:

• The Topological Hawkes Process (THP) offers a powerful new approach for causal structure learning in networked event data.
• The method effectively models inter-sequence dependencies, overcoming limitations of traditional Hawkes process models.
• This work advances the field of causal inference for complex, interconnected event systems.