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Article Dans Une Revue Journal of Machine Learning Research Année : 2020

Sparse and low-rank multivariate Hawkes processes

Résumé

We consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the least-squares loss associated with a multivariate Hawkes model, penalized by L1 and trace norm of the interaction tensor. We provide a first theoretical analysis for this problem, that includes sparsity and low-rank inducing penalizations. This result involves a new data-driven concentration inequality for matrix martingales in continuous time with observable variance, which is a result of independent interest and a broad range of possible applications since it extends to matrix martingales former results restricted to the scalar case. A consequence of our analysis is the construction of sharply tuned L1 and trace-norm penalizations, that leads to a data-driven scaling of the variability of information available for each users. Numerical experiments illustrate the significant improvements achieved by the use of such data-driven penalizations.
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Dates et versions

hal-02735273 , version 1 (02-06-2020)

Identifiants

  • HAL Id : hal-02735273 , version 1

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Emmanuel Bacry, Martin Bompaire, Stéphane Gaïffas, Jean-François Muzy. Sparse and low-rank multivariate Hawkes processes. Journal of Machine Learning Research, 2020, 21 (50), pp.1 - 32. ⟨hal-02735273⟩
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