Sparse
Sparse models
Description: The course introduces principles behind data transformation and optimization methods at the heart of automatic learning and data science, from the perspective of sparsity and robustness, applied to digital data compression (mp3, jpg) and representations by predictive models, making extensive use of algorithmic experimentation, intuition and history of science.
Content: The course presents a travel through data analysis and learning, via different sparse tools and methods, aimed at explaining observations by a reduced number of parameters: data metrics, descriptors and transformations (norms, vector bases and frames, wavelets); implementation through data compression algorithms (audio, image, video, text); extension to prediction models (statistical moments, linear and polynomial regressions, parsimonious or robust models).
Learning outcomes: To understand practical and theoretical motivations of optimization algorithms used in automatic learning and data science. To implement related algorithms in an adapted manner by understanding their meaning in relation to the problem at hand. To link different methods and implement them in a data processing flow.
Teaching methods: On each theme, students are first confronted with a “toy” problem for which they must mobilize their knowledge, ask themselves questions and implement first algorithms (in pairs). In a second step, after an exchange on this first phase, theoretical aspects, mathematical proofs and algorithmic tools are presented. Finally, in a third part, students apply these skills to a more complex problem.
Means: Courses and practical work are given by Laurent Duval (ESIEE-Paris, Université Paris-Est Marne-la-Vallée and IFP Energies nouvelles). Courses and practical work are intertwined, using signals, images or experimental data ranging from simple simulations to real-world data.
Evaluation methods: The module will be evaluated by an oral examination in groups of two or three students, with a report provided in advance, on an integrative topic, designed to mobilize different skills and methods acquired during the course. If the number of students allows it, a project-type structure, allowing groups to collaborate, will be proposed.
Evaluated skills:
- Act, initiate, innovate in science and technology environment
- Demonstrate ethical, responsible, and honest engineering practice
- Lead a project, a team
Course supervisor: Laurent Duval
Geode ID: 3MD4020
