The aim of this course is to present the statistical approaches for analysing multivariate data. The information age has resulted in masses of multivariate data in many different field: finance, marketing, economy, biology, environmental sciences,...The theoretical and practical aspects of multivariate data analysis are given equal importance. This balance is achieved through practicals involving actual data analysis using the R software.
1. Multiple linear regression. Least squares, Gaussian linear model, test of linear hypotheses, one-way analysis of variance.
2. Principal Components Analysis (PCA).
3. Classification, linear discriminant analysis, perceptron, Naive Bayes
4. Text mining, numeric representation of texts, connexion with graph clustering.
Elementary notions in probability theory (probability distribution, joint probability density function for random vectors, conditional distribution, expectation, variance, covariance, Gaussian distribution)
Elementary notions in mathematical statistics (estimator, confidence interval, statistical tests). As a bonus: simple linear regression.
Notions in linear algebra (matrix reductions).
As a bonus: elementary notions in Rstudio and the R software.
Practical exam with R (3 h) and reports on supervised practicals.
Authorized document and material: handwritten notes only. An electronic version of the booklet will be provided by the teacher.
The exam is given in english only
The course exists in the following branches:
Course ID : 4MMSADM
You can find this course among all other courses.
CM BISHOP (2006) Pattern recognition and machine Learning. Springer
C. CHATFIELD and AJ COLLINS (1980) Introduction to multivariate analysis. Science paperbacks
T HASTIE, R TIBSHIRANI, and J FRIEDMAN (2009). The Elements of Statistical Learning, 2d ed, Springer. http://www-stat.stanford.edu/~tibs/ElemStatLearn/
G. SAPORTA : Probabilités, statistique et analyse des données, Technip, 2006.
Date of update December 6, 2017