| Crédit : 6 ECTS |
| Langue du cours : anglais
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Volume horaire
- CM :
15 h
- Volume horaire global (hors stage) :
15 h
Compétences à acquérir
- Understand key principles of statistical learning and neural networks.
- Train feedforward networks using gradient-based methods and hyperparameter tuning.
- Generate data from stochastic differential equations for learning tasks.
- Estimate parameters and drift functions of stochastic processes with neural networks.
- Evaluate neural estimators and compare them to classical statistical methods.
Description du contenu de l'enseignement
Course Presentation Neural Networks for Stochastic Modeling explores how deep learning techniques can be used to analyze and estimate stochastic processes. The course introduces statistical learning fundamentals, then focuses on neural network architectures and training procedures. Finally, we apply these methods to estimate stochastic differential models through both theoretical analysis and hands-on implementation. Course Outline Chapter 1 — Statistical Learning Foundations & Neural Network Structure
- Supervised vs. unsupervised learning; regression vs. classification
- Pipeline of supervised learning and model evaluation
- Feedforward neural network architecture & activation functions
- Universal Approximation Theorem
Chapter 2 — Training Neural Networks
- Loss functions and optimization objectives
- Gradient-based optimization, backpropagation, SGD, Adam
- Hyperparameter selection and training heuristics
Chapter 3 — Parametric Estimation of Stochastic Processes
- Simulation and data generation for SDEs
- Neural estimation of unknown parameters from sample paths
Chapter 4 — Non-Parametric Estimation of Stochastic Processes
- Neural approximation of drift functions
- Performance evaluation against classical methods
- Optional outlook: diffusion models and generative approaches
Mode de contrôle des connaissances
Project (Report + code + oral defense)
Enseignant responsable
JULIEN CLAISSE