Jean–François Muzy

Ruihua Ruan, Emmanuel Bacry, Jean-François Muzy

Thanks to the access to the labeled orders on the CAC40 data from Euronext, we are able to analyze agents' behaviors in the market based on their placed orders. In this study, we construct a self-supervised learning model using triplet loss to effectively learn the representation of agent market orders. By acquiring this learned representation, various downstream tasks become feasible. In this work, we utilize the K-means clustering algorithm on the learned representation vectors of agent orders to identify distinct behavior types within each cluster.

Massil Achab, Emmanuel Bacry, Stéphane Gaïffas et al.

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 nodes 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 third-order integrated cumulants of the process. 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.

Emmanuel Bacry, Martin Bompaire, Stéphane Gaïffas et al.

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 $\ell_1$ 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 $\ell_1$ 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.