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PA - C8 - MAP670H : High-dimensional Matrix Estimation

Domaine > Mathématiques appliquées.


Syllabus :  Nowadays many data learning problems require to analyze the structure of a high-dimensional matrix with remarkable properties; In recommender systems, this could be a column sparse matrix or a low-rank matrix but more sophisticated structures could be considered by combining several notions of sparsity; In graph analysis, popular spectrum techniques to detect cliques are based on the analysis of the Laplacian matrix with specific sparse/low-rank structure. In this course, we will review several mathematical tools useful to develop statistical analysis methods and study their performances. Such tools include concentration inequalities, convex optimization, perturbation theory and minimax theory. 


Numerus Clausus : 30


Class Time: P2 Wednesday morning


Grading – 2.5 ECTS:

Written Exam



Topics covered:

  1. Principal Component Analysis
  2. Spectral clustering
  3. Matrix completion
  4. Robust Statistics
  5. Phase Retrieval
  6. Optimal Transport



  1. Vershynin. High-Dimensional Probability. Cambridge University.
  2. Gross, Recovering low-rank matrices from few coefficients in any basis, 2011, arXiv:0910.1879
  3. Guedon and R. Vershynin. Community detection in sparse networks viagrothendieck’s inequality.Probability Theory and Related Fields, 165(3-4):1025–1049,2016.
  4. Ma, R. Dudeja, J. Xu, A. Maleki, X. Wang. Spectral Method for Phase Retrieval: an Expectation Propagation Perspective. arXiv: 1903.02505
  5. M. Kouw, M. Loog. An introduction todomain adaptation and transfer learning, 2018. arXiv:1812.11806

effectifs minimal / maximal:


Diplôme(s) concerné(s)

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 Echanges PEI

    Le rattrapage est autorisé (Max entre les deux notes)
      L'UE est acquise si Note finale >= 10
      • Crédits ECTS acquis : 2.5 ECTS
      Veuillez patienter