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PA - C8 - DS-ENSAE-1 : Statistical Learning Theory


The main purpose of this course is to introduce the mathematical formalism of the learning theory and to showcase its relations with more classical statistical theory of nonparametric estimation. During the lectures, some exercises will be given and solved.

  • Presentation of 3 central problems: regression, binary classification, clustering or density estimation. Connection between these problems.


  • Universal consistency. Overfitting and underfitting. The Hoeffding inequality and empirical risk minimisation. Rademacher complexities.


  • Density estimation by histograms. Bias-variance decomposition and the rate of convergence over Holder classes.


  • Adaptive choice of the bandwidth by the method of estimated unbiased risk minimization. Local choice of the bandwidth by the Lepski method.


  • Nonparametric regression and sparsity. Thresholding Fourier coefficients.

 Evaluation : final exam, 2h.

effectifs minimal / maximal:


Diplôme(s) concerné(s)

Parcours de rattachement

Format des notes

Numérique sur 20

Littérale/grade réduit

Pour les étudiants du diplôme Data Sciences

Le rattrapage est autorisé (Max entre les deux notes)
    L'UE est acquise si Note finale >= 10
    • Crédits ECTS acquis : 3 ECTS

    Pour les étudiants du diplôme M1 - Applied Mathematics and statistics

    Le rattrapage est autorisé (Note de rattrapage conservée)
      L'UE est acquise si note finale transposée >= C
      • Crédits ECTS acquis : 3 ECTS
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