Introduction to Probabilistic Graphical Models and Deep Generative Models

Pierre Latouche - Pierre-Alexandre Mattei
UCA+Ecole Polytechnique, INRIA

Master recherche specialité "Mathématiques Appliquées",
Parcours M2 Mathématiques, Vision et Apprentissage (ENS Paris-Saclay), 1er semestre, 2023/2024

Lectures will be given on Wednedays (9-12am). This year, the students will be evaluated by a [report + poster presentation] on a research paper. 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)


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 one of the few historical courses at the core of the MVA program. Recent developments in deep latent variable models such as deep neural networks, variational autoencoders, generative adversarial networks are now part of the program of this course.


The course is based on the Pattern Recognition and Machine Learning book by C. Bishop . It is also based on the books Probabilistic Machine Learning: An Introduction and Probabilistic Machine Learning: Advanced Topics by K. Murphy.


List of research papers for the project.

Form to register a group and choose a research paper.

Internship offers

Internship: how to aggregate deep ensembles?
This internship will be supervised by Pierre-Alexandre Mattei (Research scientist at Inria, Maasai team), and will involve collaborations with Damien Garreau (Associate prof. at Université Côte d’Azur, also a member of Maasai). More details here.
Internship: learning why missing values are missing
To apply, please contact Pierre-Alexandre Mattei (pierre-alexandre.mattei\ and Aude Sportisse (aude.sportisse\ More details here.

Dates of classes

Date Lecturer Topics
October 4th

Pierre Latouche Introduction
Maximum likelihood
Linear regression
Logistic regression
October 11th

ENS Paris Saclay (salle 1Z18, bâtiment Nord 1er étage) + zoom
Pierre Latouche K-means
Gaussian mixtures
October 18th

Pierre Latouche Bayesian linear regression
Gaussian processes
EM revisited
Model selection
October 25th

ENS Paris Saclay (salle 0I10, bâtiment Ouest- RDC) + zoom
Pierre-Alexandre Mattei Directed graphical models: theory and examples
November 8th

Pierre-Alexandre Mattei Undirected graphical models
Sum-product algorithm
November 15th

Pierre Latouche Approximate inference I: variational techniques
Stochastic block models + VEM
Expectation propagation
November 22nd

Pierre-Alexandre Mattei Approximate inference II: Monte Carlo, MCMC
December 6th

ENS Paris Saclay (salle 0I10, bâtiment Ouest- RDC) + zoom
Pierre-Alexandre Mattei Approximate inference III: amortized variational inference
Deep latent variable models, variational auto-encoders
December 13th

Pierre-Alexandre Mattei Deep generative models beyond VAEs
GAN, autoregressive models, normalizing flows, ...
January 10th

ENS Paris Saclay (salle 0I10, bâtiment Ouest- RDC)

Poster session

Last updated: November 15th, 2023.