Mathematics for IA 1 (2023)

• Lecture Notes

Kernel and operator-theoretic methods in machine learning (2024)

• Lecture Notes (Work in progress, likely many typos and errors left!)
• List of papers to be presented by students:
  • Concentration Inequalities and Moment Bounds for Sample Covariance Operators. Vladimir Koltchinskii, Karim Lounici
    https://arxiv.org/abs/1405.2468
  • Kernel Methods are Competitive for Operator Learning. Pau Batlle, Matthieu Darcy, Bamdad Hosseini, Houman Owhadi
    https://arxiv.org/abs/2304.13202
  • Physics-informed machine learning as a kernel method. Nathan Doumèche, Francis Bach, Claire Boyer, Gérard Biau
    https://arxiv.org/abs/2304.13202
  • Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem. Mattes Mollenhauer, Nicole Mücke, T. J. Sullivan
    https://arxiv.org/abs/2211.08875
  • Nyström Kernel Mean Embeddings Antoine Chatalic, Nicolas Schreuder, Lorenzo Rosasco, Alessandro Rudi
    https://proceedings.mlr.press/v162/chatalic22a.html
    and
    Mean Nyström Embeddings for Adaptive Compressive Learning Antoine Chatalic, Luigi Carratino, Ernesto De Vito, Lorenzo Rosasco
    https://proceedings.mlr.press/v151/chatalic22a.html
  • A kernel-based analysis of Laplacian Eigenmaps Martin Wahl
    https://arxiv.org/abs/2402.16481