Counting Process Segmentation and Dynamic Models.

Summary In the first part of this thesis, we aim at estimating the intensity of a counting process by statistical learning techniques in high dimension. We introduce an estimation procedure based on the total variation penalty with weights. A first set of results aims at studying the intensity under an a priori hypothesis of sparse segmentation. In a second part, we study the binarization technique for continuous explanatory variables, for which we construct a regularization specific to this problem. This regularization is called ``binarsity'', it penalizes different values of a vector of parameters. In the third part, we focus on dynamic regression for Aalen and Cox models with high dimensional coefficients and covariates, and which can depend on time. For each of the proposed estimation procedures, we demonstrate non-asymptotic oracle inequalities in prediction. We finally use proximal algorithms to solve the underlying convex problems, and we illustrate our methods on simulated and real data.