High-Dimensional Data Analysis and Optimization

linma2474  2025-2026  Louvain-la-Neuve

High-Dimensional Data Analysis and Optimization
5.00 credits
30.0 h + 30.0 h
Q2
> Schedule
Teacher(s)
Absil Pierre-Antoine; Jacques Laurent; Massart Estelle; Nunes Grapiglia Geovani;
Language
English
Prerequisites
Training in optimization (LINMA2471 level) and matrix calculation (LINMA2380 level).
Main themes
This course is dedicated to the analysis and optimization of high-dimensional data (“High-Dimensional Data Analysis and Optimization”). It addresses the following themes: solving regularized inverse problems, optimization on differential or derivative-free varieties, stochastic optimization methods for machine learning, and sketching and random projection methods.
Learning outcomes

At the end of this learning unit, the student is able to :

With regard to the AA standard, this course contributes to the development, acquisition and evaluation of the following learning outcomes:  
  • AA1.1, AA1.2, AA1.3 
  • AA2.1, AA2.2
  • AA5.5 
More precisely, at the end of the course, the student will be able to:
  • analyze in depth various methods and algorithms for the numerical computer resolution of scientific or technical problems, for the analysis and optimization of high-dimensional data.
Transversal learning outcomes:
  • Introduction to certain disciplines of applied mathematics (differential geometry, statistics, measurement concentration theory) and description of their use for the analysis and design of data processing algorithms (multidisciplinary approach).
  • Implementation of algorithms in the Python ecosystem.
 
Content
The following elements will be integrated into the course content, with variations from one year to the next depending on the teaching team:
  •  inverse problem solving, regularization by parsimonious and low-rank models, and applications
  •  analysis and processing of high-dimensional data or available in large quantities,
  •  sketching approaches, random projections, randomized principal component analysis
  •  the Nystrom method, and high-dimensional linear algebra
  • optimization without derivatives or on differential varieties
  • deep machine learning, stochastic gradient descent, and the Adam method.
Teaching methods
  • Audience lessons
  • Homework, exercises or practical work under the supervision of assistants
Evaluation methods
  • Work carried out during the term: homework, exercises, mini-project or practical work. These activities are therefore only organized (and evaluated) once per academic year.
  • Written or oral exam depending on the circumstances.
The final grade is (3/10) T + (7/10) E, where T is the grade for the work completed during the semester and E is the grade for the exam. Any violation of the instructions provided on Moodle, for any activity, may lead to a global grade T = 0.
More information is provided on Moodle.
Online resources
    https://moodle.uclouvain.be/course/view.php?id=893
Bibliography
Livres et articles de références disponibles gratuitement et référencés sur Moodle
Books and reference articles available free of charge and referenced on Moodle
Teaching materials
  • slides et notes de cours fournis sur Moodle
  • slides and course notes provided on Moodle
Faculty or entity
> MAP


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [120] in Electro-mechanical Engineering
ELME2M
5
Master [120] in Mathematical Engineering
MAP2M
5
Master [120] in Energy Engineering
NRGY2M
5