High-dimensional data analysis

Duration

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

Number of credits

Lecturer

Gentiane Haesbroeck

Language(s) of instruction

English language

Organisation and examination

Teaching in the first semester, review in January

Schedule

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 - Multivariate distributions (including the normal distribuion), point estimation (ML technique) and elements of inferential statistics - Estimation of the covariance matrix: classic technique, penalized version and robust version - Dimension reduction technique: Principal Component Analysis, Multidimensional Scaling, tSNE - Supervised classification: discriminant analysis and logistic regression - Multivariate ranks and quantiles

Learning outcomes of the learning unit

The student will gain sufficient knowledge to be able to select the appropriate multivariate technique to reduce the dimension of the problem or construct classification rules,...

Prerequisite knowledge and skills

A strong background in univariate statistics is required. Moreover, even though the mathematical justifications are not developped in details (in most chapters), 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 but the practicals require an active participation of the students. These practicals include data analyses and simulations in order to compare techniques, using the statistical package R. A description of the problem to tackle during the practical will be available on eCampus at the start of the practical and the students will then be invited to solve the problems, with the punctual help of an assistant who takes care of the sessions. At the end of the practical, a summary of the expected results will be presented.

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

The course is officially scheduled on Wednesday PM in the first semester. 
It is organised face-to-face. When possible (and when it works), a video recording of the theory presentation will be made and put on line on MyUliège several days after the lecture. No recording is made during the practicals as these consist of individual work.

Organisational adjustments related to the current health context

By default, the organisation of the course and exam is as explained in the corresponding sections. 
However, in the event that face-to-face sessions are no longer possible during the semester or during the exam period, here are the adaptations that will be provided:
- Presentation of the theory: the face-to-face lectures will be replaced either by videos which will be put on line on MyUliège before the scheduled lecture (with a short QR session on collaborate) or via a presentation of the material via Collaborate. 
- The statements of the practicals will be put on line just before the expected time slot of the practical and a virtual classroom on eCampus will be open during the practical in order to answer to questions. 
- The exams will be organised in a distance way: the questions will be put on line on eCampus and the R code as well as a report (either hand-written or typed) will have to be submitted at the end of the exam. A systematic check on the "individual" characteristic of the answers (plagiat,...) will be performed and in case of doubt, an oral and virtual examination with the professor will be scheduled. 

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.
 

Assessment methods and criteria

Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.

Any session :

- In-person

written exam ( open-ended questions )

- Remote

written exam ( open-ended questions )

- If evaluation in "hybrid"

preferred in-person


Additional information:

The final grade is a weighted mean computed on the grades obtained for
- the personal homeworks given during the semester
- the written exam consisting of a data analysis and simulations 

Work placement(s)

Organizational remarks

The lectures are taught in English.

Contacts

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