Local Independence Testing for Point Processes.

Area of Science:

• Statistics
• Machine Learning
• Causal Inference

Background:

• Constraint-based causal discovery for point processes relies on local independence tests.
• Existing methods often assume strong models like Hawkes processes and struggle with latent confounders.
• Latent confounders complicate causal structure learning as marginalized processes deviate from standard models.

Purpose of the Study:

• To develop a novel method for testing local independence in point processes.
• To address the limitations of existing tests, particularly concerning latent confounders.
• To provide a robust tool for causal structure learning in the presence of complex data generating processes.

Main Methods:

• Utilized an expansion analogous to Volterra expansions to represent marginalized intensity functions.
• Developed a new theoretical framework for approximating marginalized intensities.
• Proposed a novel test for local independence based on these expansions.

Main Results:

• Demonstrated that Volterra-like expansions can arbitrarily approximate true marginalized intensities.
• The proposed local independence test shows promise in both simulated and real-world data.
• The method effectively handles challenges posed by latent confounders in point process models.

Conclusions:

• The introduced expansion technique provides a powerful tool for analyzing marginalized point processes.
• The novel local independence test offers a more robust approach to causal discovery.
• This work advances the capability of constraint-based causal learning for complex temporal data.