Data analysis : Unsupervised and supervised learning. Stochastic simulation.

In the first part of this course, we will look at various statistical learning techniques. More specifically, we will look at unsupervised learning with principal component analysis and partitioning methods, and supervised learning with regression and classification methods. These methods will be implemented in 3 practical sessions using the R programming language, followed by mini-projects. In the second part, we will present basic tools for the simulation of random variables, with applications to Monte-Carlo methods. We'll introduce Markov chains and see some applications of these models to stochastic optimization. Numerous examples will be presented and implemented using the Matlab language.

I- Introduction to data analysisII- Unsupervised learning 1. Determining principal components (PCA) 2. Partitioning data (clustering) III- Supervised learning 1. Simple linear regression 2. Multiple linear regression 3. What about non-linear? 4. ClassificationIV- Random variable simulation 1. Basic principles 2. Monte Carlo methods and applications
V- Introduction to Markov chains 1. Metropolis algorithm 2. Simulated annealing

Unsupervised learning: PCA, partitioning. Supervised learning: regression, classification, filtering, classification, estimators, learning.
Models and stochastic simulation: Monte-Carlo methods, stochastic algorithms
R language. Matlab