Equality Constraints in Linear Hawkes Processes
Abstract
Conditional independence is often used as a testable implication of causal models of random variables. In addition, equality constraints have been proposed to distinguish between data-generating mechanisms. We show that one can also find equality constraints in linear Hawkes processes, extending this theory to a class of continuous-time stochastic processes. This is done by proving that Hawkes process models in a certain sense satisfy the equality constraints of linear structural equation models. These results allow more refined constraint-based structure learning in this class of processes. Arguing the existence of equality constraints leads us to new identification results for Hawkes processes. We also describe a causal interpretation of the linear Hawkes process which is closely related to its so-called cluster representation.
Cite
Text
Mogensen. "Equality Constraints in Linear Hawkes Processes." Proceedings of the First Conference on Causal Learning and Reasoning, 2022.Markdown
[Mogensen. "Equality Constraints in Linear Hawkes Processes." Proceedings of the First Conference on Causal Learning and Reasoning, 2022.](https://mlanthology.org/clear/2022/mogensen2022clear-equality/)BibTeX
@inproceedings{mogensen2022clear-equality,
title = {{Equality Constraints in Linear Hawkes Processes}},
author = {Mogensen, Søren Wengel},
booktitle = {Proceedings of the First Conference on Causal Learning and Reasoning},
year = {2022},
pages = {576-593},
volume = {177},
url = {https://mlanthology.org/clear/2022/mogensen2022clear-equality/}
}