Duration
30h Th, 10h Pr, 20h Mon. WS
Number of credits
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
This course focuses on high-dimensional data analysis and multivariate models. The following thematics will be considered:
- General comments on high-dimension data (properties of variance matrices, curse of dimensionality)
- Estimation (including penalized estimation) : multivariate confidence regions
- Multivariate infenrential statistics (via the principles union/intersection or the ML principle).
- Dimension reduction via a linear technique (PCA) and a non-linear one (tSNE).
- Multiple linear regression.
Depending on the available time, an introduction to multivariate quantiles or to the ICA technique (independent component analysis) will be added.
Learning outcomes of the learning unit
After this course, the mathematician-student will have at his/her disposal several tools useful for analysing high-dimensional data.
Prerequisite knowledge and skills
This course is aimed for students with a strong mathematical background (bachelor in mathematics).
Planned learning activities and teaching methods
The learning activities consist in ex-cathedra sessions of theory and exercises. Some applications of the software R will also be considered either during practicals or at home.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
The practical organisation depends on the number of students.
If there are at least 3 students registered for the course, the lectures will be given in a face-to-face way.
If the number of students is smaller than 3, the lectures will be given by means of a guided reading assignment with some discussion organised face-to-face or in a virtual class.
Course materials and recommended or required readings
There are no lecture notes.
Slides and some reference books will be suggested during the course.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions ) AND oral exam
Additional information:
Exam with an oral part for the theory and a wrfitten part for the exercises and data analyses (with R).
Work placement(s)
Organisational remarks and main changes to the course
There is no assistant attached to this course. Therefore, an active implication of the students in the resolution of the exercises and data analyses is expected!
Moreover, the course is only given on "odd" academic years (25-26, 27-28...). Therefore, it will be taught this academic year 2025-2026 but will not be organized in 2026-2027.
Contacts
Gentiane Haesbroeck (G.Haesbroeck@uliege.be)