Equality Constraints in Linear Hawkes Processes
(2022) 1st Conference on Causal Learning and Reasoning, CLeaR 2022 177. p.576-593- 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... (More)
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.
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- author
- Mogensen, Søren Wengel LU
- organization
- publishing date
- 2022
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- causal identification, equality constraints, linear Hawkes processes, structure learning
- host publication
- Proceedings of Machine Learning Research
- volume
- 177
- pages
- 18 pages
- publisher
- ML Research Press
- conference name
- 1st Conference on Causal Learning and Reasoning, CLeaR 2022
- conference location
- Eureka, United States
- conference dates
- 2022-04-11 - 2022-04-13
- external identifiers
-
- scopus:85162142026
- language
- English
- LU publication?
- yes
- id
- 72c20e90-74ea-4567-bb20-cf1ce2598fef
- date added to LUP
- 2023-10-20 14:48:16
- date last changed
- 2023-10-20 14:48:16
@inproceedings{72c20e90-74ea-4567-bb20-cf1ce2598fef,
abstract = {{<p>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.</p>}},
author = {{Mogensen, Søren Wengel}},
booktitle = {{Proceedings of Machine Learning Research}},
keywords = {{causal identification; equality constraints; linear Hawkes processes; structure learning}},
language = {{eng}},
pages = {{576--593}},
publisher = {{ML Research Press}},
title = {{Equality Constraints in Linear Hawkes Processes}},
volume = {{177}},
year = {{2022}},
}