Statistical learning theory and stochastic optimization

This book is aimed at analyzing complex data with necessarily approximate models. It is intended for an audience with a graduate background in probability theory & statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, & PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare transitions are also included. They are meant to provide a better understanding of stochastic optimization algorithms of common use in computing estimators. The author focuses on non-asymptotic bounds of the statistical risk, allowing one to choose adaptively between rich and structured families of models & corresponding estimators.