Prè-requis
Course on Probability
Objectif du cours
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.
Organisation des séances
- 9 lectures of 3 hours each
- All lectures and materials will be in English
- 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.
The course is open to external auditors, but without any grade, assessment or certificate.
Mode de validation
Références
Thèmes abordés
Maximum likelihood
Linear regression
Logistic regression
K-means
EM
Gaussian mixtures
PPCA
Bayesian linear regression
Gaussian processes
EM revisited
Model selection
Directed graphical models: theory and examples
Undirected graphical models
Energy-based models
Score-based diffusion models
Approximate inference: MCMC
Sum-product algorithm
HMM
Approximate inference: variational techniques
Stochastic block models + VEM
Expectation propagation
Approximate inference: amortized variational inference
Causal inference: potential outcomes, treatment effects and policy learning
Deep latent variable models, variational auto-encoders
Deep generative models beyond VAEs
GAN, autoregressive models, normalizing flows
Pierre LATOUCHE
(UCA)
Pierre-Alexandre MATTEI
(INRIA)
Mathieu EVEN
(INRIA)
