Séminaire MODAL'X : Charlotte Dion-Blanc (LPSM, Sorbonne Université)

Résumé :
We investigate the multiclass classification problem where the features are event sequences. More precisely, the data are assumed to be generated by a mixture of simple linear Hawkes processes. In this new setting, the classes are discriminated by various triggering kernels. A challenge is then to build an efficient supervised classification procedure. We derive the optimal Bayes rule and provide a two-step estimation procedure of the Bayes classifier. In the first step, the weights of the mixture are estimated; in the second step, an empirical risk minimization procedure is performed to estimate the parameters of the Hawkes processes. We establish the consistency of the resulting procedure and derive rates of convergence. Then, we tackle the case of multivariate Hawkes processes. The challenge here is the high-dimension of the classification problem which can be solved using a LASSO-type step in the procedure. We investigate this classification procedure and prove (based on the obtained consistency in support of the LASSO), the consistency of the classifier. 
Joint work with Christophe Denis, Romain Lacoste and Laure Sansonnet.