Abstract
Constraint-based causal structure learning for point processes require empirical tests of local independence. Existing tests require strong model assumptions, e.g., that the true data generating model is a Hawkes process with no latent confounders. Even when restricting attention to Hawkes processes, latent confounders are a major technical difficulty because a marginalized process will generally not be a Hawkes process itself. We introduce an expansion similar to Volterra expansions as a tool to represent marginalized intensities. Our main theoretical result is that such expansions can approximate the true marginalized intensity arbitrarily well. Based on this, we propose a test of local independence and investigate its properties in real and simulated data.
Original language | English |
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Journal | IEEE Transactions on Neural Networks and Learning Systems |
Volume | 35 |
Issue number | 4 |
Pages (from-to) | 4902-4910 |
ISSN | 2162-237X |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
Publisher Copyright:IEEE
Keywords
- Causal discovery
- Data models
- Heuristic algorithms
- Kernel
- Learning systems
- local independence
- Mathematical models
- Neurons
- neuroscience
- point processes
- Testing