2023-2024 / MATH2021-1

High-dimensional statistics


30h Th, 15h Pr, 30h Proj.

Number of credits

 Master of Science (MSc) in Data Science5 crédits 
 Master of Science (MSc) in Data Science and Engineering5 crédits 


Gentiane Haesbroeck

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

The course is devoted to the following themes:

- Exploratory data analysis
- Dimension reduction techniques: Principal Component Analysis, Multidimensional Scaling, tSNE
- Multivariate estimation, with a particular emphasis on the estimation of the covariance matrix (classic technique under normality, penalized version and robust version)
- Multiple regression and generalized linear modeals (e.g. Poisson Model and Logistic model)
- Independent Component Analysis

Learning outcomes of the learning unit

The student will gain sufficient knowledge to be able to select the appropriate multivariate statistical technique to reduce the dimension of the problem or construct a linear/non linear model to explain a dependent variable by means of explanatory variables...

Prerequisite knowledge and skills

A strong background in univariate statistics is required. Moreover, even though the mathematical justifications are not developped in details, the students must be familiar with the basic notions of linear algebra (vector, matrix, determinant, eigen values and eigen vectors...).

Planned learning activities and teaching methods

The theory is exposed in an ex-cathedra way. During the practicals, the students work by themselves before an overall discussion on the results/approaches. It is the statistical software R which has to be used in this course.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course

Additional information:

The course is mainly scheduled in a face-to-face way but some lectures might, exceptionnally, be given via videos.

Additional information:

Recommended or required readings

There are no lecture notes. The slides will be available from eCampus. Moreover, for each theme, a reference book will be notified in order to suggest additionnal reading.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Written work / report

Additional information:

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

Written work / report

Additional information:

The final grade is a weighted mean computed on the grades obtained for

- two personal projects given during the semester: the dates for the release of the statements as well as the deadlines for the submission of the projets will be stated in Celcat. 

- the written exam consisting of some data analyses and detailed/explained applications of techniques taught in the lectures.

When both grades are superior or equal to 6/20, the weighted average is computed by means of equal weights (50%-50%). If at least one of the grades is inferior to 6/20, then the weights become 25%-75%, the largest weight being attributed to the lowest grade.

Work placement(s)

Organisational remarks and main changes to the course

The lectures are taught in English.

The lecture room does not provide a podcast equipment by default, the lectures given in a face-to-face way will not be available under another form.

Following some feedbacks written in the survey EVALENS about the duration of the exam, the professor wishes to emphasize that it is expected that all students have used at least once all the techniques taught during the semester (this is the goal of the practical sessions) before coming to the exam. On the day of the exam, all the commands (of the software R) must be readily available, in order to be slightly adapted to new data or to a new situation. 


Lecturer: Gentiane HAESBROECK, Institute of Mathematics (B37), g.haesbroeck@ulg.ac.be

Association of one or more MOOCs