Linear regression and learning: contributions to regularization and aggregation methods.

Summary This thesis deals with the subject of linear regression in different frameworks, notably related to learning. The first two chapters present the context of the work, its contributions and the mathematical tools used. The third chapter is devoted to the construction of an optimal regularization function, allowing for example to improve on the theoretical level the regularization of the LASSO estimator. The fourth chapter presents, in the field of convex sequential optimization, accelerations of a recent and promising algorithm, MetaGrad, and a conversion from a so-called "deterministic sequential" framework to a so-called "stochastic batch" framework for this algorithm. The fifth chapter focuses on successive interval forecasts, based on the aggregation of predictors, without intermediate feedback or stochastic modeling. Finally, the sixth chapter applies several aggregation methods to a petroleum dataset, resulting in short-term point forecasts and long-term forecast intervals.