Ects : 3

Enseignant responsable :

• KATIA MULLER MEZIANI

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

Pré-requis recommandés :

Probabilités multidimensionnelles (lois et espérances conditionnelles).

Compétence à acquérir :

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

Mode de contrôle des connaissances :

Examen final.