Lectures will be given on Thursdays (9h-12h, 4 lectures) or Fridays (14h-17h, 5 lectures). This year, the students will be evaluated by a project [poster + notebook] on a research paper and a written exam. All lectures will be on zoom and recorded. The lectures at ENS Paris Saclay will be used to answer questions in person, regarding the lectures and the project. All documents (slides / blackboard / lecture notes) are or will be put here. The teaching assistant for this course is Rémi Khellaf.
This course provides a unifying introduction to probabilistic modelling through the framework of graphical models, together with their associated learning and inference algorithms. It is an historical course at the core of the MVA program. Recent developments in mathematics are largely covered. In particular, this course cover deep latent variable models, variational autoencoders, energy based models, score-based diffusion models, amortised inference, and causal inference.
The course is based on the books Pattern Recognition and Machine Learning and Deep learning - Foundations and Concepts by C. Bishop. It is also based on the books Probabilistic Machine Learning: An Introduction and Probabilistic Machine Learning: Advanced Topics by K. Murphy. Finally, it relies on the book Causal Inference: A Statistical Learning Approach by Stefan Wager.
| Date | Lecturer | Topics |
| October 1st, Thursday, 9h-12h ENS Paris Saclay + zoom |
Pierre Latouche | Introduction to directed graphical models Maximum likelihood Exemples (linear regression, logistic regression, neural networks) |
| October 8th, Thursday, 9h-12h ENS Paris Saclay + zoom |
Pierre Latouche |
K-means EM Gaussian mixtures PPCA |
| October 15th, Thursday, 9h-12h zoom |
Pierre Latouche | Bayesian linear regression Gaussian processes EM revisited Model selection |
| October 22nd, Thursday, 9h-12h ENS Paris Saclay + zoom |
Pierre Latouche |
Approximate inference I: variational techniques Stochastic block models + VEM Expectation propagation |
| November 6th, Friday, 14h-17h ENS Paris Saclay + zoom |
Pierre-Alexandre Mattei | Directed graphical models: theory and examples |
| November 13th, Friday, 14h-17h zoom |
Pierre-Alexandre Mattei | Approximate Inference II: amortised variational inference
variational auto encoders |
| November 20th, Friday, 14h-17h ENS Paris Saclay + zoom |
Pierre-Alexandre Mattei | Undirected graphical models, energy-based models, score-based diffusion models, approximate inference III: MCMC |
| November 27th, Friday, 14h-17h ENS Paris Saclay + zoom |
Mathieu Even | Causal inference, potential outcomes, treatment effects and policy learning |
| December 4th, Friday, 14h-17h ENS Paris Saclay + zoom |
Pierre-Alexandre Mattei | Deep generative models beyond likelihood-based models: GANs, likelihood-free inference |
| December 17th, Thursday, 9h-12h ENS Paris Saclay |
Written exam |
Last updated: July 2nd, 2026.