Apprentissage statistique

ECTS : 3

Volume horaire : 21

Description du contenu de l'enseignement :

1. Supervised Learning:  Bayes decision rule, Consistency and no free lunch theorem, Hypothesis class,Probably Approximately Correct (PAC) framework.  Empirical Risk Minimization (ERM), PA Cbounds with ERM 
2. Concentration Inequalities :  Chebyshev’s inequality,Hoeffding’s inequality,Sub-Gaussian random variables, Concentrations of functions of random variables,Bernstein’s deviation inequality,Deviation inequality for quadratic forms
3. Generalization Bounds via Uniform Convergence: Finite hypothesis class, Bounds for infinite hypothesis class via discretization, Rademacher complexity (RC), Empirical RC, 
4. Bounding the Rademacher complexity: Shattering numbers, VC theory, Covering number, entropy, Dudley’s chaining

Compétence à acquérir :

L'objectif du cours est d'acquérir des notions théoriques d'apprentissage statistique. 

Mode de contrôle des connaissances :

Examen final.