Mathematical foundations of data sciences
G. PEYRE
Data ScienceLearning

Objectif du cours

This course reviews fundamental mathematical and numerical method for imaging sciences and machine learning. It starts by covering the basics of data representation and processing, including linear filtering and Wavelets. The core of the course is first order optimization methods (gradient descent, stochastic optimization and proximal splitting) with an emphasis on performance guarantees and their applications to inverse problems in imaging and supervised learning using linear models.
The last part of course covers more advanced problems related to the high dimensional setting, using in particular sparsity-inducing regularizers such as the Lasso and compressed sensing methods.
The course is complemented by Python numerical homeworks extracted from the web site www.numerical-tours.com.
The course is validated by a project (an article to read, some computer implementation, a short written report and an oral presentation).

Organisation des séances

6 courses of 2h30 + exam

Bibliography :

Gabriel Peyré, The Numerical Tours of Data Sciences, www.numerical-tours.com (for the homework and the projects)
Gabriel Peyré, The Mathematical Tours of Data Sciences, https://mathematical-tours.github.io/ (course notes)
Stéphane Mallat, A Wavelet Tour of Signal Processing (3rd ed.), 2010.
Jerome H. Friedman, Robert Tibshirani et Trevor Hastie, The Elements of Statistical Learning, 2009 N. Parikh and S. Boyd, Proximal algorithms, 2014
Les intervenants

Gabriel PEYRE

(CNRS et Ecole Normale Supérieure)

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