Equality Constraints in Linear Hawkes Processes

Søren Wengel Mogensen
Proceedings of the First Conference on Causal Learning and Reasoning, PMLR 177:576-593, 2022.

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 this Paper

BibTeX
@InProceedings{pmlr-v177-mogensen22a, title = {Equality Constraints in Linear Hawkes Processes}, author = {Mogensen, S{\o}ren Wengel}, booktitle = {Proceedings of the First Conference on Causal Learning and Reasoning}, pages = {576--593}, year = {2022}, editor = {Schölkopf, Bernhard and Uhler, Caroline and Zhang, Kun}, volume = {177}, series = {Proceedings of Machine Learning Research}, month = {11--13 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v177/mogensen22a/mogensen22a.pdf}, url = {https://proceedings.mlr.press/v177/mogensen22a.html}, 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.} }
Endnote
%0 Conference Paper %T Equality Constraints in Linear Hawkes Processes %A Søren Wengel Mogensen %B Proceedings of the First Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2022 %E Bernhard Schölkopf %E Caroline Uhler %E Kun Zhang %F pmlr-v177-mogensen22a %I PMLR %P 576--593 %U https://proceedings.mlr.press/v177/mogensen22a.html %V 177 %X 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.
APA
Mogensen, S.W.. (2022). Equality Constraints in Linear Hawkes Processes. Proceedings of the First Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 177:576-593 Available from https://proceedings.mlr.press/v177/mogensen22a.html.

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