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, 2024/2025

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). The teaching assistant for this course is Rémi Khellaf.


Description

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.

References

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.

Projects

Description and list of research papers for the project.

Form to register a group and choose a research paper.

Examples from last year (report + poster).

Dates of classes

Date Lecturer Topics
October 2nd

ENS Paris Saclay, amphi Alain Aspect 1G58 - bât Sud au dessus de l'accueil + zoom
Pierre-Alexandre Mattei Introduction to directed graphical models
Maximum likelihood
Exemples (linear regression, logistic regression, neural networks)
October 9th

zoom
Pierre Latouche K-means
EM
Gaussian mixtures
PPCA
October 16th

ENS Paris Saclay, amphi Hodgkin 0I10 - bât Ouest RdC + zoom
Pierre Latouche Bayesian linear regression
Gaussian processes
EM revisited
Model selection
October 23rd

zoom
Pierre Latouche Directed graphical models: theory and examples
November 6th

ENS Paris Saclay, amphi d'Alembert 1Z18 - bât Nord + zoom
Pierre-Alexandre Mattei Undirected graphical models
Sum-product algorithm
HMM
November 13th

zoom
Pierre Latouche Approximate inference I: variational techniques
Stochastic block models + VEM
Expectation propagation
November 20th

ENS Paris Saclay, amphi Hodgkin 0I10 - bât Ouest RdC + zoom
Pierre-Alexandre Mattei Approximate inference II: amortized variational inference
Deep latent variable models, variational auto-encoders
November 26th

zoom
Pierre-Alexandre Mattei Approximate inference III: Monte Carlo, MCMC, energy based models, score based diffusion models
December 11th

zoom
Pierre-Alexandre Mattei Deep generative models beyond VAEs
GAN, autoregressive models, normalizing flows, diffusion models
December 18th

ENS Paris Saclay (atrium)

Poster session


Last updated: September 30th, 2024.