Teaching · 2026–27
Courses
Teaching in applied mathematics and machine learning across the engineering and graduate programmes at École Polytechnique and Sorbonne Université. Materials are published as they become available.
Introduction to Machine Learning (ML1)
Master X-HEC · September–December 2026 · one tutorial group
Linear regression, k-nearest neighbours, decision trees, logistic regression, regularisation, cross-validation, metrics.
Monte Carlo Methods
Engineering Cycle, Year 3 · September–December 2026 · weekly practical sessions
Sampling, variance reduction, Markov chains, Metropolis–Hastings, Gibbs sampling, Monte Carlo for inference.
Statistics
Engineering Cycle, Year 2 · September–November 2026
Numerical explorations and problem sets.
Course notes and lecture material
Self-written notes for study and revision. When using them formally, refer to the official course material.
Measure theory
Riemann integrability, σ-algebras, measures and outer measures, measurable functions.
14 pages
From measurable sets to metric spaces
The pseudo-distance induced by a measure on measurable sets, and the Fréchet–Nikodym metric on equivalence classes.
10 pages
Monte Carlo methods: the essentials
Monte Carlo estimators, the law of large numbers and the central limit theorem, importance sampling.
6 pages
Logistic regression from scratch
Maximum likelihood and its gradient, gradient descent, Adam and mini-batch SGD, and a confusion-matrix check of the results.
21 pages
Modern topics in machine learning: GroupSort networks
Presentation of “Approximating Lipschitz continuous functions with GroupSort neural networks” (Tanielian, Sangnier, Biau): 1-Lipschitz networks, expressive power and approximation bounds, compared with ReLU networks. Sorbonne Université, M2A & M2 Stats.
Machine learning notebooks
Regularised logistic regression, dimensionality reduction (PCA, t-SNE), the Permuted MNIST benchmark, a CNN for breast-cancer imaging and data-challenge submissions. Notebooks are on GitHub.
Missing data in machine learning
Missingness mechanisms (MCAR, MAR, MNAR), imputation strategies, the risk of leakage before the train/test split, and reproducible examples. Produced in the context of a machine learning for health course at Sorbonne Université.