Uncovering Causality from Multivariate Hawkes Integrated Cumulants

Massil Achab, Emmanuel Bacry, Stéphane Gaı̈ffas, Iacopo Mastromatteo, Jean-François Muzy
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1-10, 2017.

Abstract

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows to prove that this new estimation technique is consistent. Moreover, we show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database and on financial order book data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-achab17a, title = {Uncovering Causality from Multivariate {H}awkes Integrated Cumulants}, author = {Massil Achab and Emmanuel Bacry and St{\'e}phane Ga\"{\i}ffas and Iacopo Mastromatteo and Jean-Fran{\c{c}}ois Muzy}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1--10}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/achab17a/achab17a.pdf}, url = {https://proceedings.mlr.press/v70/achab17a.html}, abstract = {We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows to prove that this new estimation technique is consistent. Moreover, we show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database and on financial order book data.} }
Endnote
%0 Conference Paper %T Uncovering Causality from Multivariate Hawkes Integrated Cumulants %A Massil Achab %A Emmanuel Bacry %A Stéphane Gaı̈ffas %A Iacopo Mastromatteo %A Jean-François Muzy %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-achab17a %I PMLR %P 1--10 %U https://proceedings.mlr.press/v70/achab17a.html %V 70 %X We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each node of the process, but also disentangles the causality relationships between them. Our approach is the first that leads to an estimation of this matrix without any parametric modeling and estimation of the kernels themselves. A consequence is that it can give an estimation of causality relationships between nodes (or users), based on their activity timestamps (on a social network for instance), without knowing or estimating the shape of the activities lifetime. For that purpose, we introduce a moment matching method that fits the second-order and the third-order integrated cumulants of the process. A theoretical analysis allows to prove that this new estimation technique is consistent. Moreover, we show on numerical experiments that our approach is indeed very robust to the shape of the kernels, and gives appealing results on the MemeTracker database and on financial order book data.
APA
Achab, M., Bacry, E., Gaı̈ffas, S., Mastromatteo, I. & Muzy, J.. (2017). Uncovering Causality from Multivariate Hawkes Integrated Cumulants. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1-10 Available from https://proceedings.mlr.press/v70/achab17a.html.

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