My thesis (written in English) is available athttps://tel.archives-ouvertes.fr/tel-01690522/documentI worked in the laboratory GREYC, CNRS 6072 (https://www.greyc.fr) under the supervision of Mr. Jalal Fadili, professor at ENSICAEN and Mr. Christophe Chesneau, assistant professor at Caen-Normandy university.My work considered high-dimensional estimation to recover an object of interest in an ill-posed model (i.e., its dimension is larger than the sample size). This problem can be done through two approaches: Penalization (PEN) and Exponentially Weighted Aggregation (EWA). PEN was well studied in the literature; a prominent member is LASSO. My research focuses on EWA via three directions.1 Provided a unified theoretical framework to study the qualities of both PEN and EWA. The framework quantifies an estimator with the best possible candidate and a remaining term depending on the complexity of the object to be estimated.2 Proposed new families of EWA estimators and compared them with their PEN counterparts. 3 Computed our estimators numerically using algorithms based on Langevin diffusion smoothed by Moreau-Yosida regularization and illustrated their performance by numerical experiments in image processing such as compressed sensing, inpainting, and deconvolution.

My internship report (written in French) is available at https://www.dropbox.com/s/4yrigkyaofj3ksyI worked in the laboratory SAMOVAR, CNRS 5157 (http://samovar.telecom-sudparis.eu) under the supervision of Mr. Jérémie Jakubowicz, assistant professor at Télécom Sud-Paris.We focused on the data analysis about Vélib, the public bike rental service of Paris with an average daily ridership of 108,090 in 2014. Particularly, we collected the real-time data of Vélib stations via jcdecaux.com under the license ETALAB. The internship proceeded through four stages.1. Read the documentation to get a grasp on the Hadoop ecosystem and the principle of Map Reduce. I managed to install a Hadoop cluster manually without using platforms like CHD and programmed simple Map-Reduce tasks in Java. Next, I familiarized with Spark, an in-memory computing platform which runs tasks 100x faster compared with Hadoop Map Reduce.2. Collected data from 52 Vélib stations during two weeks, preprocessed and stored them in my Hadoop cluster. The most important variable is the number of available bikes in each station, which I created videos showing its variation during the observed period.3. Implemented some statistical methods from scratch in distributed version to response to two main questions: (i) what are the most important stations and their influence on the others? (ii) Given a cyclist who departs from a station, which stations are the most likely to be his/her destinations?4. Expressed the results as maps with pointers drawn using Graphviz and explained the obtained results by observing the maps.